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Differential Equation is a very important topic of Mathematics. We tried our best to describes applications of differential equation in this presentation.

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Applications of differential equations(by Anil.S.Nayak)

the simplest description of applications of differential equations presented in the minimal number of slides as possible!!.....hope this helps!!!!

Applications of differential equations

The document discusses applications of differential equations. It begins by providing a brief history of differential equations, noting they were independently invented by Newton and Leibniz. It then defines ordinary and partial differential equations. Examples of applications are given for modeling phenomena like cooling, oscillations, and game development. Specific differential equations like Laplace's, heat, and wave equations are discussed along with physical applications in fields like physics, engineering, and biology. Newton's law of cooling is provided as a motivating example and its applications are outlined.

application of differential equations

This document provides an introduction to differential equations and their applications. It discusses the history of differential equations, types of differential equations including ordinary differential equations (ODEs) and partial differential equations (PDEs). Examples of first order ODE applications given include Newton's Law of Cooling, electrical circuits, and population growth modeling. Mechanical oscillation modeling is also discussed. The document concludes that differential equations have wide applications in fields like rocket science, economics, and gaming.

Applications of differential equation in Physics and Biology

This document discusses several applications of differential equations in physics. It provides examples of how differential equations are used to model radioactive decay, linear and projectile motion, harmonic oscillations, and more. Solving these differential equations provides insights into the physical processes being modeled and has allowed technological progress across many scientific disciplines. Differential equations are necessary to describe most physical phenomena accurately because real-world relationships are typically non-linear rather than linear.

APPLICATIONS OF DIFFERENTIAL EQUATIONS-ZBJ

This document discusses applications of differential equations. It begins by covering the invention of differential equations by Newton and Leibniz. It then defines differential equations and covers types like ordinary differential equations (ODEs) and partial differential equations (PDEs). Examples of commonly used differential equations are provided, such as the Laplace equation, heat equation, and wave equation. Applications of differential equations are discussed, including modeling mechanical oscillations, electrical circuits, and Newton's law of cooling.

Application of differential equation in ETE

This document provides a summary of a presentation on applications of differential equations in electronics and telecommunications engineering. It begins with introducing the presenters and their department at Daffodil International University in Bangladesh. It then defines what a differential equation is and describes common types like ordinary and partial differential equations. Specifically, it discusses the wave equation and electromagnetic wave equation, which are important second-order linear partial differential equations used in fields like acoustics, electromagnetics, and fluid dynamics to model wave propagation. The document provides examples of these differential equations and notes their derivation from Maxwell's equations.

Applications of differential equation

1. The document discusses differential equations and their applications. It defines differential equations and describes their use in fields like physics, engineering, biology and economics to model complex systems.
2. Examples of first order differential equations are given to model exponential growth, exponential decay, and an RL circuit. Higher order differential equations are used to model falling objects and Newton's law of cooling.
3. The key applications covered are population growth, radioactive decay, free falling objects, heat transfer, and electric circuits. Solving the differential equations gives mathematical models relating variables like position, temperature, and current over time.

First order linear differential equation

1. A differential equation relates an unknown function and its derivatives, and can be ordinary (involving one variable) or partial (involving partial derivatives).
2. Linear differential equations have dependent variables and derivatives that are of degree one, and coefficients that do not depend on the dependent variable.
3. Common methods for solving first-order linear differential equations include separation of variables, homogeneous equations, and exact equations.

Applications of differential equations(by Anil.S.Nayak)

the simplest description of applications of differential equations presented in the minimal number of slides as possible!!.....hope this helps!!!!

Applications of differential equations

The document discusses applications of differential equations. It begins by providing a brief history of differential equations, noting they were independently invented by Newton and Leibniz. It then defines ordinary and partial differential equations. Examples of applications are given for modeling phenomena like cooling, oscillations, and game development. Specific differential equations like Laplace's, heat, and wave equations are discussed along with physical applications in fields like physics, engineering, and biology. Newton's law of cooling is provided as a motivating example and its applications are outlined.

application of differential equations

This document provides an introduction to differential equations and their applications. It discusses the history of differential equations, types of differential equations including ordinary differential equations (ODEs) and partial differential equations (PDEs). Examples of first order ODE applications given include Newton's Law of Cooling, electrical circuits, and population growth modeling. Mechanical oscillation modeling is also discussed. The document concludes that differential equations have wide applications in fields like rocket science, economics, and gaming.

Applications of differential equation in Physics and Biology

This document discusses several applications of differential equations in physics. It provides examples of how differential equations are used to model radioactive decay, linear and projectile motion, harmonic oscillations, and more. Solving these differential equations provides insights into the physical processes being modeled and has allowed technological progress across many scientific disciplines. Differential equations are necessary to describe most physical phenomena accurately because real-world relationships are typically non-linear rather than linear.

APPLICATIONS OF DIFFERENTIAL EQUATIONS-ZBJ

This document discusses applications of differential equations. It begins by covering the invention of differential equations by Newton and Leibniz. It then defines differential equations and covers types like ordinary differential equations (ODEs) and partial differential equations (PDEs). Examples of commonly used differential equations are provided, such as the Laplace equation, heat equation, and wave equation. Applications of differential equations are discussed, including modeling mechanical oscillations, electrical circuits, and Newton's law of cooling.

Application of differential equation in ETE

This document provides a summary of a presentation on applications of differential equations in electronics and telecommunications engineering. It begins with introducing the presenters and their department at Daffodil International University in Bangladesh. It then defines what a differential equation is and describes common types like ordinary and partial differential equations. Specifically, it discusses the wave equation and electromagnetic wave equation, which are important second-order linear partial differential equations used in fields like acoustics, electromagnetics, and fluid dynamics to model wave propagation. The document provides examples of these differential equations and notes their derivation from Maxwell's equations.

Applications of differential equation

1. The document discusses differential equations and their applications. It defines differential equations and describes their use in fields like physics, engineering, biology and economics to model complex systems.
2. Examples of first order differential equations are given to model exponential growth, exponential decay, and an RL circuit. Higher order differential equations are used to model falling objects and Newton's law of cooling.
3. The key applications covered are population growth, radioactive decay, free falling objects, heat transfer, and electric circuits. Solving the differential equations gives mathematical models relating variables like position, temperature, and current over time.

First order linear differential equation

1. A differential equation relates an unknown function and its derivatives, and can be ordinary (involving one variable) or partial (involving partial derivatives).
2. Linear differential equations have dependent variables and derivatives that are of degree one, and coefficients that do not depend on the dependent variable.
3. Common methods for solving first-order linear differential equations include separation of variables, homogeneous equations, and exact equations.

Application of-differential-equation-in-real-life

The document is a slide presentation on differential equations consisting of 5 slides. It includes definitions of ordinary and partial differential equations, classifications based on the number of independent variables, and examples of applications in fields like physics, engineering, and computer science. Real-life applications are discussed along with the use of software packages to study differential equations. The conclusion and references sections are also outlined. The presentation is attributed to a lecture by MD. Ashraful Islam from the Department of CSE at Dhaka International University.

Differential equations

This document contains information about a group project on differential equations. It lists the group members and covers topics like the invention of differential equations, types of ordinary and partial differential equations, applications, and examples. The group will discuss differential equations including the history, basic concepts of ODEs and PDEs, types like first and second order ODEs, linear and non-linear PDEs, and applications in fields like mechanics, physics, and engineering.

Applications of Differential Equations of First order and First Degree

The document describes how to calculate the time it takes for a population growing at 5% annually to double in size using a differential equation model. It is also solved to be 20loge2 years, or approximately 14 years. A second problem involves calculating the final temperature of liquid in an insulated cylindrical tank over 5 days using a heat transfer model. A third problem uses kinematics equations to find how far a drag racer will travel in 8 seconds if its speed increases by 40 feet per second each second.

introduction to differential equations

This document discusses differential equations and includes the following key points:
1. It defines differential equations and provides examples of ordinary and partial differential equations of varying orders.
2. It classifies differential equations as ordinary or partial, linear or non-linear, and of first or higher order. Examples are given of each type.
3. Applications of differential equations are listed, including modeling projectile motion, electric circuits, heat transfer, vibrations, population growth, and chemical reactions.
4. Methods of solving differential equations including finding general and particular solutions are explained. Initial value and boundary value problems are also defined.

application of differential equation and multiple integral

This document discusses differential equations and their applications. It begins by defining differential equations as mathematical equations that relate an unknown function to its derivatives. There are two types: ordinary differential equations involving one variable, and partial differential equations involving two or more variables. Applications are given for modeling physical systems involving mass, springs, dampers, fluid dynamics, heat transfer, and rigid body dynamics. The document also discusses surface and volume integrals involving vectors, with examples of calculating fluid flow rates and mass of water in a reservoir. Differential equations and multiple integrals find diverse applications in engineering fields.

Ordinary differential equation

1. The document defines ordinary and partial differential equations and discusses the order and degree of differential equations.
2. Examples of common second order linear differential equations with constant coefficients are given, including equations for free fall, spring displacement, and RLC circuits.
3. The document also discusses homogeneous linear equations and Newton's law of cooling as examples of differential equations.

Partial differential equation & its application.

Partial differential equations (PDEs) involve partial derivatives of dependent variables with respect to more than one independent variable. PDEs can be linear if the dependent variable and all its partial derivatives occur linearly, or non-linear. PDEs are used to model systems in fields like physics, engineering, and quantum mechanics, with examples being the Laplace, heat, and wave equations used in fluid dynamics, heat transfer, and quantum mechanics respectively. The heat equation specifically describes the distribution of heat over time in a given region.

Partial differential equations

Partial Differential Equation plays an important role in our daily life.In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a computer model. A special case is ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.
PDEs can be used to describe a wide variety of phenomena such as sound, heat, diffusion, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.

Ordinary differential equations

The document is an introduction to ordinary differential equations prepared by Ahmed Haider Ahmed. It defines key terms like differential equation, ordinary differential equation, partial differential equation, order, degree, and particular and general solutions. It then provides methods for solving various types of first order differential equations, including separable, homogeneous, exact, linear, and Bernoulli equations. Specific examples are given to illustrate each method.

Differential equations of first order

This document discusses first order differential equations. It defines differential equations and classifies them as ordinary or partial based on whether they involve derivatives with respect to a single or multiple variables. First order differential equations are classified into four types: variable separable, homogeneous, linear, and exact. The document provides examples of each type and explains their general forms and solution methods like separating variables, making substitutions, and integrating.

ORDINARY DIFFERENTIAL EQUATION

1) The document presents information on ordinary differential equations including definitions, types, order, degree, and solution methods.
2) Differential equations can be written in derivative, differential, and differential operator forms. Common solution methods covered are variable separable, homogeneous, linear, and exact differential equations.
3) Applications of differential equations include physics, astronomy, meteorology, chemistry, biology, ecology, and economics for modeling various real-world systems.

Partial differential equations

The document discusses partial differential equations (PDEs). It defines PDEs and gives their general form involving independent variables, dependent variables, and partial derivatives. It describes methods for obtaining the complete integral, particular solution, singular solution, and general solution of a PDE. It provides examples of types of PDEs and how to solve them by assuming certain forms for the dependent and independent variables and their partial derivatives.

APPLICATION OF PARTIAL DIFFERENTIATION

The document discusses concepts related to partial differentiation and its applications. It covers topics like tangent planes, linear approximations, differentials, Taylor expansions, maxima and minima problems, and the Lagrange method. Specifically, it defines the tangent plane to a surface at a point using partial derivatives, describes how to find the linear approximation of functions, and explains how to find maximum and minimum values of functions using critical points and the second derivative test.

Ordinary differential equation

This document provides an introduction to ordinary differential equations (ODEs). It defines ODEs as differential equations containing functions of one independent variable and its derivatives. The document discusses some key concepts related to ODEs including order, degree, and different types of ODEs such as variable separable, homogeneous, exact, linear, and Bernoulli's equations. Examples of each type of ODE are provided along with the general methods for solving each type.

Homogeneous Linear Differential Equations

The document defines a homogeneous linear differential equation as an equation of the form:
a0(dx/dy)n + a1(dx/dy)n-1 + ... + an-1(dx/dy) + any = X, where a0, a1, ..., an are constants and X is a function of x.
It provides the method of solving such equations by first reducing it to a linear equation with constant coefficients, then taking a trial solution of the form y = emz, and finally solving the resulting auxiliary equation.
It proves identities relating derivatives of y with respect to x and z, then uses these identities to solve two sample homogeneous linear differential equations of orders 2 and

A presentation on differencial calculus

This presentation provides an introduction to differential calculus. It defines calculus and differentiation, and classifies calculus into differential calculus and integral calculus. Differential calculus deals with finding rates of change of functions with respect to variables using derivatives, while integral calculus involves determining lengths, areas, volumes, and solving differential equations using integrals. The presentation explains key calculus concepts like derivatives, differentiation, and differential curves. It concludes by presenting some common formulas for differentiation.

Ode powerpoint presentation1

The document presents information about differential equations including:
- A definition of a differential equation as an equation containing the derivative of one or more variables.
- Classification of differential equations by type (ordinary vs. partial), order, and linearity.
- Methods for solving different types of differential equations such as variable separable form, homogeneous equations, exact equations, and linear equations.
- An example problem demonstrating how to use the cooling rate formula to calculate the time of death based on measured body temperatures.

Application of Differential Equation in Real Life

This presentation discusses applications of differential equations in real life, including Newton's Law of Cooling, exponential population growth, radioactive decay, and falling objects. It will be presented by Md. Sumon Sarder and explores differential equation models for how temperature changes over time according to Newton's Law, how a population grows exponentially assuming positive population and growth rate, how radioactive material decreases exponentially over time, and the differential equation that describes falling objects. The presentation concludes with an opportunity for any questions.

Differential equations of first order

1) A differential equation contains an independent variable (x), a dependent variable (y), and the derivative of the dependent variable with respect to the independent variable (dy/dx).
2) The order of a differential equation refers to the highest order derivative present. For example, an equation containing dy/dx would be first order, while one containing d2y/dx2 would be second order.
3) The degree of a differential equation refers to the highest power of the highest order derivative. For example, an equation containing (d2y/dx) would be degree 1, while one containing (d2y/dx)2 would be degree 2.
4) There are several methods for solving first

Differential equations

- A differential equation relates an independent variable, dependent variable, and derivatives of the dependent variable with respect to the independent variable.
- The order of a differential equation is the order of the highest derivative, and the degree is the degree of the highest derivative.
- Differential equations can be classified based on their order (first order vs higher order) and linearity (linear vs nonlinear).
- The general solution of a differential equation contains arbitrary constants, while a particular solution gives specific values for those constants.

Lecture 2-Introduction-Civil Eng [Repaired].pptx

This document provides an introduction to biology and discusses the relationships between biology, medicine, and engineering. It explains that biology and medicine study living organisms and biological functions, some of which can be modeled and analyzed using engineering principles. This led to the emergence of fields like biomedical engineering that apply engineering concepts to medical problems. Examples are given of how engineering tools have been used to address issues like the COVID-19 pandemic. Biological engineering is defined as applying biological principles and engineering tools to create useful products. The roles and examples of work done in bioengineering research are outlined.

Application of differentiation

This document discusses differential equations and their application. It begins by defining what a differential equation is and provides examples of first order differential equations. It then discusses Newton's Law of Cooling, providing the derivation and formulation of the law. Several applications of Newton's Law of Cooling are presented, including using it to estimate time of death from temperature readings and determining cooling system specifications for computer processors. Other topics covered include the Mean Value Theorem, precalculus concepts, and examples of how calculus is applied in various fields such as credit cards, biology, engineering, architecture, and more.

Application of-differential-equation-in-real-life

The document is a slide presentation on differential equations consisting of 5 slides. It includes definitions of ordinary and partial differential equations, classifications based on the number of independent variables, and examples of applications in fields like physics, engineering, and computer science. Real-life applications are discussed along with the use of software packages to study differential equations. The conclusion and references sections are also outlined. The presentation is attributed to a lecture by MD. Ashraful Islam from the Department of CSE at Dhaka International University.

Differential equations

This document contains information about a group project on differential equations. It lists the group members and covers topics like the invention of differential equations, types of ordinary and partial differential equations, applications, and examples. The group will discuss differential equations including the history, basic concepts of ODEs and PDEs, types like first and second order ODEs, linear and non-linear PDEs, and applications in fields like mechanics, physics, and engineering.

Applications of Differential Equations of First order and First Degree

The document describes how to calculate the time it takes for a population growing at 5% annually to double in size using a differential equation model. It is also solved to be 20loge2 years, or approximately 14 years. A second problem involves calculating the final temperature of liquid in an insulated cylindrical tank over 5 days using a heat transfer model. A third problem uses kinematics equations to find how far a drag racer will travel in 8 seconds if its speed increases by 40 feet per second each second.

introduction to differential equations

This document discusses differential equations and includes the following key points:
1. It defines differential equations and provides examples of ordinary and partial differential equations of varying orders.
2. It classifies differential equations as ordinary or partial, linear or non-linear, and of first or higher order. Examples are given of each type.
3. Applications of differential equations are listed, including modeling projectile motion, electric circuits, heat transfer, vibrations, population growth, and chemical reactions.
4. Methods of solving differential equations including finding general and particular solutions are explained. Initial value and boundary value problems are also defined.

application of differential equation and multiple integral

This document discusses differential equations and their applications. It begins by defining differential equations as mathematical equations that relate an unknown function to its derivatives. There are two types: ordinary differential equations involving one variable, and partial differential equations involving two or more variables. Applications are given for modeling physical systems involving mass, springs, dampers, fluid dynamics, heat transfer, and rigid body dynamics. The document also discusses surface and volume integrals involving vectors, with examples of calculating fluid flow rates and mass of water in a reservoir. Differential equations and multiple integrals find diverse applications in engineering fields.

Ordinary differential equation

1. The document defines ordinary and partial differential equations and discusses the order and degree of differential equations.
2. Examples of common second order linear differential equations with constant coefficients are given, including equations for free fall, spring displacement, and RLC circuits.
3. The document also discusses homogeneous linear equations and Newton's law of cooling as examples of differential equations.

Partial differential equation & its application.

Partial differential equations (PDEs) involve partial derivatives of dependent variables with respect to more than one independent variable. PDEs can be linear if the dependent variable and all its partial derivatives occur linearly, or non-linear. PDEs are used to model systems in fields like physics, engineering, and quantum mechanics, with examples being the Laplace, heat, and wave equations used in fluid dynamics, heat transfer, and quantum mechanics respectively. The heat equation specifically describes the distribution of heat over time in a given region.

Partial differential equations

Partial Differential Equation plays an important role in our daily life.In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a computer model. A special case is ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.
PDEs can be used to describe a wide variety of phenomena such as sound, heat, diffusion, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.

Ordinary differential equations

The document is an introduction to ordinary differential equations prepared by Ahmed Haider Ahmed. It defines key terms like differential equation, ordinary differential equation, partial differential equation, order, degree, and particular and general solutions. It then provides methods for solving various types of first order differential equations, including separable, homogeneous, exact, linear, and Bernoulli equations. Specific examples are given to illustrate each method.

Differential equations of first order

This document discusses first order differential equations. It defines differential equations and classifies them as ordinary or partial based on whether they involve derivatives with respect to a single or multiple variables. First order differential equations are classified into four types: variable separable, homogeneous, linear, and exact. The document provides examples of each type and explains their general forms and solution methods like separating variables, making substitutions, and integrating.

ORDINARY DIFFERENTIAL EQUATION

1) The document presents information on ordinary differential equations including definitions, types, order, degree, and solution methods.
2) Differential equations can be written in derivative, differential, and differential operator forms. Common solution methods covered are variable separable, homogeneous, linear, and exact differential equations.
3) Applications of differential equations include physics, astronomy, meteorology, chemistry, biology, ecology, and economics for modeling various real-world systems.

Partial differential equations

The document discusses partial differential equations (PDEs). It defines PDEs and gives their general form involving independent variables, dependent variables, and partial derivatives. It describes methods for obtaining the complete integral, particular solution, singular solution, and general solution of a PDE. It provides examples of types of PDEs and how to solve them by assuming certain forms for the dependent and independent variables and their partial derivatives.

APPLICATION OF PARTIAL DIFFERENTIATION

The document discusses concepts related to partial differentiation and its applications. It covers topics like tangent planes, linear approximations, differentials, Taylor expansions, maxima and minima problems, and the Lagrange method. Specifically, it defines the tangent plane to a surface at a point using partial derivatives, describes how to find the linear approximation of functions, and explains how to find maximum and minimum values of functions using critical points and the second derivative test.

Ordinary differential equation

This document provides an introduction to ordinary differential equations (ODEs). It defines ODEs as differential equations containing functions of one independent variable and its derivatives. The document discusses some key concepts related to ODEs including order, degree, and different types of ODEs such as variable separable, homogeneous, exact, linear, and Bernoulli's equations. Examples of each type of ODE are provided along with the general methods for solving each type.

Homogeneous Linear Differential Equations

The document defines a homogeneous linear differential equation as an equation of the form:
a0(dx/dy)n + a1(dx/dy)n-1 + ... + an-1(dx/dy) + any = X, where a0, a1, ..., an are constants and X is a function of x.
It provides the method of solving such equations by first reducing it to a linear equation with constant coefficients, then taking a trial solution of the form y = emz, and finally solving the resulting auxiliary equation.
It proves identities relating derivatives of y with respect to x and z, then uses these identities to solve two sample homogeneous linear differential equations of orders 2 and

A presentation on differencial calculus

This presentation provides an introduction to differential calculus. It defines calculus and differentiation, and classifies calculus into differential calculus and integral calculus. Differential calculus deals with finding rates of change of functions with respect to variables using derivatives, while integral calculus involves determining lengths, areas, volumes, and solving differential equations using integrals. The presentation explains key calculus concepts like derivatives, differentiation, and differential curves. It concludes by presenting some common formulas for differentiation.

Ode powerpoint presentation1

The document presents information about differential equations including:
- A definition of a differential equation as an equation containing the derivative of one or more variables.
- Classification of differential equations by type (ordinary vs. partial), order, and linearity.
- Methods for solving different types of differential equations such as variable separable form, homogeneous equations, exact equations, and linear equations.
- An example problem demonstrating how to use the cooling rate formula to calculate the time of death based on measured body temperatures.

Application of Differential Equation in Real Life

This presentation discusses applications of differential equations in real life, including Newton's Law of Cooling, exponential population growth, radioactive decay, and falling objects. It will be presented by Md. Sumon Sarder and explores differential equation models for how temperature changes over time according to Newton's Law, how a population grows exponentially assuming positive population and growth rate, how radioactive material decreases exponentially over time, and the differential equation that describes falling objects. The presentation concludes with an opportunity for any questions.

Differential equations of first order

1) A differential equation contains an independent variable (x), a dependent variable (y), and the derivative of the dependent variable with respect to the independent variable (dy/dx).
2) The order of a differential equation refers to the highest order derivative present. For example, an equation containing dy/dx would be first order, while one containing d2y/dx2 would be second order.
3) The degree of a differential equation refers to the highest power of the highest order derivative. For example, an equation containing (d2y/dx) would be degree 1, while one containing (d2y/dx)2 would be degree 2.
4) There are several methods for solving first

Differential equations

- A differential equation relates an independent variable, dependent variable, and derivatives of the dependent variable with respect to the independent variable.
- The order of a differential equation is the order of the highest derivative, and the degree is the degree of the highest derivative.
- Differential equations can be classified based on their order (first order vs higher order) and linearity (linear vs nonlinear).
- The general solution of a differential equation contains arbitrary constants, while a particular solution gives specific values for those constants.

Application of-differential-equation-in-real-life

Application of-differential-equation-in-real-life

Differential equations

Differential equations

Applications of Differential Equations of First order and First Degree

Applications of Differential Equations of First order and First Degree

introduction to differential equations

introduction to differential equations

application of differential equation and multiple integral

application of differential equation and multiple integral

Ordinary differential equation

Ordinary differential equation

Partial differential equation & its application.

Partial differential equation & its application.

Partial differential equations

Partial differential equations

Ordinary differential equations

Ordinary differential equations

Differential equations of first order

Differential equations of first order

ORDINARY DIFFERENTIAL EQUATION

ORDINARY DIFFERENTIAL EQUATION

Partial differential equations

Partial differential equations

APPLICATION OF PARTIAL DIFFERENTIATION

APPLICATION OF PARTIAL DIFFERENTIATION

Ordinary differential equation

Ordinary differential equation

Homogeneous Linear Differential Equations

Homogeneous Linear Differential Equations

A presentation on differencial calculus

A presentation on differencial calculus

Ode powerpoint presentation1

Ode powerpoint presentation1

Application of Differential Equation in Real Life

Application of Differential Equation in Real Life

Differential equations of first order

Differential equations of first order

Differential equations

Differential equations

Lecture 2-Introduction-Civil Eng [Repaired].pptx

This document provides an introduction to biology and discusses the relationships between biology, medicine, and engineering. It explains that biology and medicine study living organisms and biological functions, some of which can be modeled and analyzed using engineering principles. This led to the emergence of fields like biomedical engineering that apply engineering concepts to medical problems. Examples are given of how engineering tools have been used to address issues like the COVID-19 pandemic. Biological engineering is defined as applying biological principles and engineering tools to create useful products. The roles and examples of work done in bioengineering research are outlined.

Application of differentiation

This document discusses differential equations and their application. It begins by defining what a differential equation is and provides examples of first order differential equations. It then discusses Newton's Law of Cooling, providing the derivation and formulation of the law. Several applications of Newton's Law of Cooling are presented, including using it to estimate time of death from temperature readings and determining cooling system specifications for computer processors. Other topics covered include the Mean Value Theorem, precalculus concepts, and examples of how calculus is applied in various fields such as credit cards, biology, engineering, architecture, and more.

FOTS Lecture 1.pptx

This document provides an overview of the course MCT-114: Fundamentals of Thermal Sciences. The objectives of the course are to provide a solid grounding in engineering thermodynamics and its fundamental concepts. Topics covered include the basic concepts, laws of energy, ideal gas model, entropy, and power/refrigeration cycles. The course also introduces heat transfer concepts. The document outlines the suggested textbooks, course learning objectives, and provides an introduction to thermal-fluid sciences, thermodynamics, heat transfer, and fluid mechanics.

Theoretical ecology

This document discusses theoretical ecology, which uses theoretical methods such as mathematical models, computational simulations, and data analysis to study ecological systems. It provides examples of different types of mathematical models used to model population dynamics and species interactions, including exponential growth models, logistic growth models, structured population models using matrices, predator-prey models, host-pathogen models, and competition/mutualism models. It also discusses how theoretical ecology aims to explain a variety of ecological phenomena and how computational modeling has benefited from increased computing power.

The Cell Method

Discover what is the Cell Method and how to apply it to physical problems. This presentation will guide you through some interesting computational implementations.
Youtube video: https://youtu.be/ZyyRovtibjo

Biological thermodynamics

Thermodynamic laws describe the flows and interchanges of heat, energy and matter.
Almost all chemical and biochemical processes are as a result of transformation of energy.
Laws can provide important insights into metabolism and bioenergetics.
The energy exchanges between the system and the surroundings balance each other.
There is a hierarchy of energetics among organisms

Temperature scale

Thermodynamics is the study of energy and its transformation. It deals with the relationship between heat, work, and the physical properties of substances. Thermodynamics can be studied through both a microscopic approach considering molecular behavior, and a macroscopic approach considering average properties without molecular details. A thermodynamic system is defined as a quantity of matter bounded by a surface, and can be classified as closed, open, or isolated depending on its interactions with the surroundings. Key thermodynamic properties describe the state of a system.

Pdf thermo

This document discusses applying thermodynamic concepts and methods to ecology. The author proposes the "entropy pump hypothesis" - that climatic and environmental conditions organize ecosystems in a way that only a natural ecosystem specific to those conditions can achieve dynamic equilibrium. The author then calculates the entropy production for an ecosystem under anthropogenic stress over a one-year period, showing that the entropy produced must be "pumped out" by solar energy to maintain steady-state conditions. The document examines how thermodynamic concepts like entropy, exergy, and information theory can provide a physical approach and criteria to analyze ecosystems.

Statmech

This document provides an introduction to an intermediate-level course on thermodynamics and statistical mechanics. It discusses how thermodynamics applies to many-body systems and can explain many everyday phenomena. It notes that while the atomic motions can be described by known physics equations, directly solving these equations for macroscopic systems is impossible due to their enormous complexity and number of particles. Therefore, thermodynamics takes a statistical approach, focusing on average properties rather than individual particle motions.

Thermodynamics (chapter-1 introduction)

Thermodynamics is the study of energy, its transformations, and interactions with matter. It focuses on heat, work, and their conversion. The document defines key thermodynamic concepts like system, surroundings, boundary, state, process, cycle, and properties. It also covers the first law of thermodynamics, gas laws, and the ideal gas equation. Reversible and irreversible processes are distinguished, with examples of each provided.

Chemical reactions and thermodynamics

1. Chemical reactions can be either exergonic or endergonic, with exergonic reactions releasing energy and endergonic reactions requiring energy.
2. The laws of thermodynamics state that energy is conserved but tends to dissipate such that entropy increases over time, making energy less usable.
3. The second law of thermodynamics explains that living organisms require a constant input of energy to maintain life functions against the natural increase in entropy.

Basic concepts and laws of thermodynamics

The document provides an overview of basic thermodynamics concepts including:
- Thermodynamics deals with heat, work, temperature and their relation to energy and matter.
- Key terms like system, surroundings, state functions, extensive/intensive properties, and processes are defined.
- The three laws of thermodynamics are summarized: 1) energy is conserved, 2) entropy always increases, and 3) entropy approaches zero as temperature approaches absolute zero.
- Equations for several thermodynamic properties and processes like enthalpy, entropy, and adiabatic, isochoric and isothermal processes are also presented.

Differentiation

The document discusses differentiation and its applications. It provides a brief history of differentiation and introduces concepts such as the derivative and reverse process of integration. Some key applications of differentiation discussed include using it to determine maximum/minimum values, in subjects like physics, chemistry, and economics, and in devices like odometers, speedometers, and radar guns. Two surveys were conducted on the awareness and uses of differentiation. In conclusion, differentiation can help improve devices and make tomorrow better by finding how one variable changes with respect to another.

Thermodynamics.pptx

Thermodynamics is the study of heat, work, temperature, and energy. The laws of thermodynamics describe how energy changes in a system and whether it can do work. The first law states that energy cannot be created or destroyed, only changed from one form to another. The second law states that entropy increases in irreversible processes and remains constant in reversible ones. Free energy determines if a process is spontaneous. Biological systems require constant energy to maintain order and live, demonstrating the laws of thermodynamics.

Precise definition of basic concepts forms a sound foundation for the.pdf

Precise definition of basic concepts forms a sound foundation for the development of a science
and prevents possible misunderstandings. True/False? What is the definition of
Thermodynamics? What is the definition of Energy? State the First law of Thermodynamics.
State the Second Law of Thermodynamics. What is the definition of a \"System\" in
Thermodynamics? What is the definition of \"Closed\" system? In a closed system; can energy
such as Heat, Work, etc. cross the boundary? Yes/No What is an \"Isolated System\",
Definition? What is an \"Open System\", Definition? What is the definition of \"Intensive\"
properties of a system? What is the definition of \"Extensive\" properties of a system? Write a
statement (two-three lines) about \"Continuum\".
Solution
2) Thermodynamics:
Thermodynamics is the branch of physics that deals with the relationships between heat and
other forms of energy. In particular, it describes how thermal energy is converted to and from
other forms of energy and how it affects matter.
3) Energy :
Measure of the ability of a body or system to do work or produce a change, expressed usually in
joules or kilowatt hours (kWh). No activity is possible without energy and its total amount in the
universe is fixed. In other words, it cannot be created or destroyed but can only be changed from
one type to another.
4) First law of thermodynamics:
The First Law of Thermodynamics states that heat is a form of energy, and thermodynamic
processes are therefore subject to the principle of conservation of energy. This means that heat
energy cannot be created or destroyed. It can, however, be transferred from one location to
another and converted to and from other forms of energy.
5) Second law of Thermodynamics :
The second law of thermodynamics states that the total entropy of an isolated system always
increases over time, or remains constant in ideal cases where the system is in a steady state or
undergoing a reversible process. The increase in entropy accounts for the irreversibility of
natural processes, and the asymmetry between future and past.
6) System :
A thermodynamic system is a quantity of matter of fixed identity, around which we can draw a
boundary.
7)Closed system :
Closed systems exchange energy but not matter with an outside system.
8) Yes, In closed system energy may cross the boundary.
9) Isolated system:
In Isolated system there is no transfer of heat and mass with surroundings.
10) Open systems:
In Open systems there is transfer of both heat and mass with the surroundings.
11) Intesive property:
An intensive property, is a physical property of a system that does not depend on the system size
or the amount of material in the system.
eg: density, pressure and temperature
12) Extensive Property:
An extensive property of a system does depend on the system size or the amount of material in
the system.
eg : volume, internal energy
13 ) continuum :
Anything that goes through a gradual transition from one condition, to a diff.

Entropy

The document discusses the concept of entropy. It begins by defining entropy as a measure of disorder in a system and relating it to the number of microscopic states available to a system. It then discusses different types of disorder, provides an example, and gives mathematical expressions to define and calculate entropy. The document notes the importance of entropy in geochemical thermodynamics and applications like thermobarometric models. It concludes by restating that entropy increases with heat transfer at low temperatures and decreases with heat removal, and is a key concept in understanding the direction of natural processes.

34-Sofazzal Hosen.pptx

Differential equations are used to model physical phenomena like light rays, describe exponential growth and decay, and model complex systems in biology and economics. They are essential for describing the natural world, which is governed by differential equations. Differential equations and their numerical solutions are commonly used in scientific computing to model problems that cannot be solved analytically or are difficult to solve. Applications of differential equations can be found in many fields including physics, chemistry, engineering, mathematics, biology, and economics.

entropy-170828073801.pdf

The document discusses the concept of entropy. It begins by defining entropy as a measure of disorder in a system and relating it to the number of microscopic states available to a system. It then discusses different types of disorder, provides an example, and gives mathematical expressions to define and calculate entropy. The document notes the importance of entropy in geochemical thermodynamics and applications like thermobarometric models. It concludes by restating that entropy increases with heat transfer at low temperatures and decreases with heat removal, and is a key concept in understanding the direction of natural processes.

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Rethinking Embedded System Design

Embedded engineering is designed using objects of nature and it also interacts with nature. Therefore it is forced to obey the laws of nature. Nature does not make any assumptions. But all our mathematical and scientific theories do. Therefore these theories cannot be valid for embedded engineering applications. In this paper we present four new laws of nature that all embedded systems follow. These laws are (1) Boundedness (2) Finite time (3) Simultaneity and (4) Complexity. During the last fifty years embedded analog and digital engineering have evolved and changed significantly. However our mathematical and scientific theories remained in the original state. We select several theories commonly used in embedded engineering and show that none of them satisfy these laws. As a result, when we implement these theories in our embedded software, we are forced to add so many patches and kludges to make the engineering work, that our systems become very unreliable.

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Precise definition of basic concepts forms a sound foundation for the.pdf

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Rethinking Embedded System Design

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Famous Quotes of Famous People

The document contains quotes from six individuals about creativity and thinking outside the box. Albert Einstein states that imagination is more important than knowledge. George S. Patton says that if everyone is thinking alike, then somebody isn't thinking. John Burroughs expresses that believing you can do something enables you to do it. Dan Stevens describes how staying out of one's comfort zone is important for creativity. Matshona Dhliwayo argues that thinking outside the box allows one to achieve more. Edward De Bono defines creativity as breaking patterns to see things in new ways.

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The variance is a measure of variability. It is calculated by taking the average of squared deviations from the mean. Variance tells you the degree of spread in your data set. The more spread the data the larger the variance is

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Digital image processing is the use of a digital computer to process digital images through an algorithm. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing.

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RAM or Random Access Memory is a Volatile memory which performs very fast. Ram Processes all task of Computer. In this Presentation we tried to discuss about RAM and their Types.

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Relational Schema in Database is a very important topic. This Presentation presents them very easily to understand.

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Intellectual Property is a Part of Social and Professional Issues in Computing. Intellectual Property relates to intangible creative work that is protected for the creator's use under the law as a patent, copyright, trademark, or trade secret. There are four types of protection in intellectual property Copyright, Patent, Trademark and Trade Secret.

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إضغ بين إيديكم من أقوى الملازم التي صممتها
ملزمة تشريح الجهاز الهيكلي (نظري 3)
💀💀💀💀💀💀💀💀💀💀
تتميز هذهِ الملزمة بعِدة مُميزات :
1- مُترجمة ترجمة تُناسب جميع المستويات
2- تحتوي على 78 رسم توضيحي لكل كلمة موجودة بالملزمة (لكل كلمة !!!!)
#فهم_ماكو_درخ
3- دقة الكتابة والصور عالية جداً جداً جداً
4- هُنالك بعض المعلومات تم توضيحها بشكل تفصيلي جداً (تُعتبر لدى الطالب أو الطالبة بإنها معلومات مُبهمة ومع ذلك تم توضيح هذهِ المعلومات المُبهمة بشكل تفصيلي جداً
5- الملزمة تشرح نفسها ب نفسها بس تكلك تعال اقراني
6- تحتوي الملزمة في اول سلايد على خارطة تتضمن جميع تفرُعات معلومات الجهاز الهيكلي المذكورة في هذهِ الملزمة
واخيراً هذهِ الملزمة حلالٌ عليكم وإتمنى منكم إن تدعولي بالخير والصحة والعافية فقط
كل التوفيق زملائي وزميلاتي ، زميلكم محمد الذهبي 💊💊
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Agenda
● What is event processing in MuleSoft?
● Types of event processing models in Mule 4
● Distinction between the reactive, parallel, blocking & non-blocking processing
For Upcoming Meetups Join Mysore Meetup Group - https://meetups.mulesoft.com/mysore/YouTube:- youtube.com/@mulesoftmysore
Mysore WhatsApp group:- https://chat.whatsapp.com/EhqtHtCC75vCAX7gaO842N
Speaker:-
Shivani Yasaswi - https://www.linkedin.com/in/shivaniyasaswi/
Organizers:-
Shubham Chaurasia - https://www.linkedin.com/in/shubhamchaurasia1/
Giridhar Meka - https://www.linkedin.com/in/giridharmeka
Priya Shaw - https://www.linkedin.com/in/priya-shaw

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- 1. Application of Differential Equation Presenting by Group Abacus
- 3. Group Members: Yeasin Hossain Emran ID: 162-15-1037 Mohammad Salim Hosen ID: 162-15-1044 MD. Rifat Rahman ID: 162-15-1049 MD.Hashibur Rahman Anik ID: 162-15-1032
- 4. About Differential Equation An equation containing the derivatives of one or more dependent variables, with respect to one or more independent variables, is said to be a differential equation (DE). There are two types of differential equation. Ordinary Differential Equation. Partial Differential Equation. A differential equation is written in the form: 𝑑𝑦 𝑑𝑥 = … …….
- 5. Applications of Differential Equations Differential equations have a remarkable ability to predict the world around us. They are used in a wide variety of disciplines, from biology, economics, physics, chemistry and engineering. Some Applications of Differential Equations in real life are, In Population Models In Newtons law of cooling In radioactive decay law In molecular biology In Computer Science
- 6. Application 1 : Exponential Growth - Population One of the most basic examples of differential equations is the Malthusian Law of population growth 𝑑𝑝 𝑑𝑡 = 𝑟𝑝 shows how the population (p) changes with respect to time. The constant r will change depending on the species. More complicated differential equations can be used to model the relationship between predators and prey. For example, as predators increase then prey decrease as more get eaten. But then the predators will have less to eat and start to die out, which allows more prey to survive. The interactions between the two populations are connected by differential equations.
- 7. Graph of Growth Population First Graph shows when the predator is both very aggressive it will attack the prey and rapidly eat the prey population, growing rapidly – before it runs out of prey to eat and then there will be no other food, thus dying off again. Then predators will be less aggressive and it will lead to both populations in a stable position (Graph two).
- 8. Application 2 : Newton's Law of Cooling It is a model that describes, mathematically, the change in temperature of an object in a given environment. The law states that the rate of change (in time) of the temperature is proportional to the difference between the temperature T of the object and the temperature Te of the environment surrounding the object. Equation is: 𝑑𝑇 𝑑𝑡 = −𝑘(𝑇 = −𝑇𝑒) If the above equation is solved we get, T(t) = Te + (To - Te)e - k t express how the temperature T of the object changes with time.
- 9. Example of Newtons cooling law Forensics experts use Newton's Law of Cooling to find out when victims of crimes died. They take the temperature of the body when they find it, and by knowing that the average temperature of the human body is 98.6 degrees initially and measuring the room temperature, they can find k and then find t.
- 10. Application 3 : Exponential Decay - Radioactive Material We can find radioactive material half life by solving differential equation. Let M be the amount of a product that decreases with time t and the rate of decrease is proportional to the amount M as follows, dM / d t = - kM where k > 0 and t is the time. Solving the above first order differential equation we obtain M = A e- k t where A is non zero constant.
- 11. Application 4 : In molecular biology Differential equations are of basic importance in molecular biology because many biological laws and relations appear mathematically in the form of a differential equation. The vast majority of quantitative models in cell and molecular biology are formulated in terms of ordinary differential equations. Mathematical cell biology is a very active and fast growing interdisciplinary area in which mathematical concepts, techniques, and models are applied to a variety of problems in developmental medicine and bioengineering.
- 12. Application 5 : In Computer Science Computer applications are involved in several aspects such as modeling underlying logic or complex fluid flow, machine learning or financial analysis. Differential equation are greatly used in game development For example, In a simple video game involving a jumping motion, a differential equation is used to model the velocity of a character after the command is given to return them to the ground in a simulated gravitational field.
- 13. Some Other Applications of Differential Equations Some Other Applications of Differential Equations are, 1) In medicine for modelling cancer growth or the spread of disease 2) In engineering for describing the movement of electricity 3) In chemistry for modelling chemical reactions 4) In economics to find optimum investment strategies 5) In physics to describe the motion of waves, pendulums or chaotic systems.
- 14. THANK YOU