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This document provides an overview of differential calculus concepts including: 1) Differential calculus deals with finding exact derivatives directly from a function's formula without using graphs. It examines the rate of change of one quantity with respect to another. 2) Key concepts covered include derivative rules, the product rule, quotient rule, derivatives of trigonometric functions, and the squeeze/sandwich theorem. 3) Real-life applications of differential calculus include calculating profit/loss, rates of change like temperature, deriving physical equations, and calculating speed or distance over time.

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Aplicaciones de las derivadas

The document discusses applications of calculus, specifically derivatives, in the field of electronics and automation. It provides theoretical background on concepts like monotonicity, curvature, inflection points, maxima and minima. It then presents 3 problems involving optimization of electrical circuits and components using derivatives to find maximum power output or minimum resistance. The solutions demonstrate how derivatives can be applied in engineering contexts.

Taller 2

This document discusses applications of calculus in biotechnology and electronics/automation careers. It provides examples of how derivatives are used in areas like optimizing production costs, modeling chemical reaction rates, and analyzing resonant circuits. Three practice problems are developed applying derivatives to optimization problems in biotechnology involving tube volume, fertilizer production, and circuit voltage. The document concludes the derivative is important across fields for optimizing factors like money, materials, labor, and time.

Derivatives and it’s simple applications

The document provides an introduction to derivatives and their applications. It defines the derivative as the rate of change of a function near an input value and discusses how it relates geometrically to the slope of the tangent line. It then gives examples of finding the derivatives of common functions like constants, polynomials, and exponentials. The document also covers basic derivative rules like the constant multiple rule, sum and difference rules, product rule, and quotient rule. Finally, it discusses applications of derivatives in topics like physics, such as calculating velocity and acceleration from a position function.

derivatives math

This document is a presentation submitted by a group of 6 mechanical engineering students to their professor. It contains an introduction, definitions of derivatives, a brief history of derivatives attributed to Newton and Leibniz, and applications of derivatives in various fields such as automobiles, radar guns, business, physics, biology, chemistry, and mathematics. It also provides rules and examples of calculating derivatives using power, multiplication by constant, sum, difference, product, quotient and chain rules.

Lec5_Product & Quotient Rule.ppt

The document discusses differentiation rules for products and quotients of functions. It begins by introducing the product rule, which states that the derivative of a product of two functions f and g is equal to f times the derivative of g plus g times the derivative of f. Next, it derives the quotient rule through a similar process, concluding that the derivative of a quotient of two functions u and v is equal to the denominator v times the derivative of the numerator u minus the numerator u times the derivative of the denominator v, all over the square of the denominator v squared. Several examples are provided to demonstrate applying these rules to find derivatives.

Taller parcial 2 2021

This document discusses applications of calculus, specifically derivatives, in biotechnology engineering. It provides theoretical background on using derivatives to find maximums and minimums. It then presents three examples of applying derivatives to solve practical problems in biotechnology, such as determining when bacterial contamination in a lake reaches a minimum level or when a medication is most effective against bacteria. The document concludes that derivatives are an important tool in fields like physics, chemistry, and biology for measuring how quickly a situation changes.

Taller parcial 2 2021 (1)

This document discusses applications of calculus, specifically derivatives, in biology and biotechnology. It provides theoretical background on using derivatives to find maximum and minimum values of functions. It then presents three examples of using derivatives to solve practical problems in biotechnology, such as modeling bacterial growth over time or the effectiveness of antibiotics. The examples are worked through step-by-step. Overall, the document aims to demonstrate how calculus can be applied to quantitative problems in biotechnology.

Ijciet 10 02_085

The document presents a numerical method for solving a continuous model of the economy expressed as a second-order nonlinear ordinary differential equation (ODE). A new approach called the Modified Taylor Series Approach (MTSA) is used to derive a two-step block method for directly solving the model ODE without first reducing it to a system of first-order equations. The MTSA allows the derivation of the integration coefficients to obtain the block method schemes for solving the ODE at multiple grid points simultaneously. The resulting MTSA-derived two-step block method is then applied to solve the specific second-order nonlinear continuous model of the economy under consideration.

Aplicaciones de las derivadas

The document discusses applications of calculus, specifically derivatives, in the field of electronics and automation. It provides theoretical background on concepts like monotonicity, curvature, inflection points, maxima and minima. It then presents 3 problems involving optimization of electrical circuits and components using derivatives to find maximum power output or minimum resistance. The solutions demonstrate how derivatives can be applied in engineering contexts.

Taller 2

This document discusses applications of calculus in biotechnology and electronics/automation careers. It provides examples of how derivatives are used in areas like optimizing production costs, modeling chemical reaction rates, and analyzing resonant circuits. Three practice problems are developed applying derivatives to optimization problems in biotechnology involving tube volume, fertilizer production, and circuit voltage. The document concludes the derivative is important across fields for optimizing factors like money, materials, labor, and time.

Derivatives and it’s simple applications

The document provides an introduction to derivatives and their applications. It defines the derivative as the rate of change of a function near an input value and discusses how it relates geometrically to the slope of the tangent line. It then gives examples of finding the derivatives of common functions like constants, polynomials, and exponentials. The document also covers basic derivative rules like the constant multiple rule, sum and difference rules, product rule, and quotient rule. Finally, it discusses applications of derivatives in topics like physics, such as calculating velocity and acceleration from a position function.

derivatives math

This document is a presentation submitted by a group of 6 mechanical engineering students to their professor. It contains an introduction, definitions of derivatives, a brief history of derivatives attributed to Newton and Leibniz, and applications of derivatives in various fields such as automobiles, radar guns, business, physics, biology, chemistry, and mathematics. It also provides rules and examples of calculating derivatives using power, multiplication by constant, sum, difference, product, quotient and chain rules.

Lec5_Product & Quotient Rule.ppt

The document discusses differentiation rules for products and quotients of functions. It begins by introducing the product rule, which states that the derivative of a product of two functions f and g is equal to f times the derivative of g plus g times the derivative of f. Next, it derives the quotient rule through a similar process, concluding that the derivative of a quotient of two functions u and v is equal to the denominator v times the derivative of the numerator u minus the numerator u times the derivative of the denominator v, all over the square of the denominator v squared. Several examples are provided to demonstrate applying these rules to find derivatives.

Taller parcial 2 2021

This document discusses applications of calculus, specifically derivatives, in biotechnology engineering. It provides theoretical background on using derivatives to find maximums and minimums. It then presents three examples of applying derivatives to solve practical problems in biotechnology, such as determining when bacterial contamination in a lake reaches a minimum level or when a medication is most effective against bacteria. The document concludes that derivatives are an important tool in fields like physics, chemistry, and biology for measuring how quickly a situation changes.

Taller parcial 2 2021 (1)

This document discusses applications of calculus, specifically derivatives, in biology and biotechnology. It provides theoretical background on using derivatives to find maximum and minimum values of functions. It then presents three examples of using derivatives to solve practical problems in biotechnology, such as modeling bacterial growth over time or the effectiveness of antibiotics. The examples are worked through step-by-step. Overall, the document aims to demonstrate how calculus can be applied to quantitative problems in biotechnology.

Ijciet 10 02_085

The document presents a numerical method for solving a continuous model of the economy expressed as a second-order nonlinear ordinary differential equation (ODE). A new approach called the Modified Taylor Series Approach (MTSA) is used to derive a two-step block method for directly solving the model ODE without first reducing it to a system of first-order equations. The MTSA allows the derivation of the integration coefficients to obtain the block method schemes for solving the ODE at multiple grid points simultaneously. The resulting MTSA-derived two-step block method is then applied to solve the specific second-order nonlinear continuous model of the economy under consideration.

APLICACIONES DE LA DERIVADA EN LA CARRERA DE (Mecánica, Electrónica, Telecomu...

APLICACIONES DE LA DERIVADA EN LA CARRERA DE (Mecánica, Electrónica, Telecomu...WILIAMMAURICIOCAHUAT1

El cálculo diferencial proporciona información sobre el comportamiento de las funciones
matemáticas. Todos estos problemas están incluidos en el alcance de la optimización de funciones y pueden resolverse aplicando cálculoderivativesanditssimpleapplications-160828144729.pptx

The document discusses derivatives and their applications. It begins by introducing derivatives and defining them as the rate of change of a function near an input value. It then discusses rules for finding derivatives such as the constant multiple rule, sum and difference rules, product rule, and quotient rule. Examples are given to illustrate applying these rules. The document also covers composite functions, inverse functions, second derivatives, and applications of derivatives in physics for problems involving velocity and acceleration.

Taller parcial 2

This document discusses the application of calculus derivatives in the career of geospatial technologies. It begins with introducing the concept of the derivative and its calculation. It then discusses the criteria of the first and second derivatives, which can be used to find relative extremes of a function. Three practice exercises are included, relating to optimization problems that can be solved using derivatives. Graphs of the exercises are generated in Geogebra. The document emphasizes how derivatives can be useful for tasks like optimizing processes in geospatial technologies applications.

CALCULUS 2.pptx

This document provides information about Calculus 2, including lessons on indeterminate forms, Rolle's theorem, the mean value theorem, and differentiation of transcendental functions. It defines Rolle's theorem and the mean value theorem, provides examples of applying each, and discusses how Rolle's theorem can be used to find the value of c. It also defines inverse trigonometric functions and their derivatives. The document is for MATH 09 Calculus 2 and includes exercises for students to practice applying the theorems.

Aplicaciones de la derivadas en contabilidad

This document discusses the application of derivatives in accounting. It begins with introducing derivatives and their uses in economics and accounting. Specifically, derivatives represent a useful tool for calculating marginal costs, revenues, profits, and production. The document then presents two examples demonstrating how to use derivatives to find total cost, marginal cost, maximum and minimum prices, and average cost in accounting scenarios. It concludes that derivatives are a 100% useful tool that can simplify complex calculations and processes, with many applications in economics and accounting.

CHAPTER 7.pdfdjdjdjdjdjdjdjsjsjddhhdudsko

The document discusses various methods for developing empirical dynamic models from process input-output data, including linear regression and least squares estimation. Simple linear regression can be used to develop steady-state models relating an output variable y to an input variable u. The least squares approach is introduced to calculate the parameter estimates that minimize the error between measured and predicted output values. Graphical methods are also presented for estimating parameters of first-order and second-order dynamic models by fitting step response data. Finally, the development of discrete-time models from continuous-time models using finite difference approximations is covered.

Multivariate Regression Analysis

The work is done as part of graduate coursework at University of Florida. The author studied master's in environmental engineering sciences during the making of the presentation.

On the discretized algorithm for optimal proportional control problems constr...

This document presents a numerical algorithm for solving optimal control problems with delay differential equations. It discretizes the performance index and delay constraint terms to transform the problem into a large-scale nonlinear programming problem. Simpson's discretization method is used to generate sparse matrices representing the discretized performance index and constraint. The algorithm models the control as proportional to the state, with a constant feedback gain. It analyzes properties of the control operator to guarantee invertibility for use in a Quasi-Newton solver. A numerical example is presented and shown to converge linearly to the analytical solution.

poster2

The document compares several nonlinear and linear stabilization schemes (SUPG, dCG91, Entropy Viscosity) for solving advection-diffusion equations using finite element methods. It presents results of applying the different schemes to stationary and non-stationary test equations, comparing maximum overshoot and undershoot, smearing, and convergence orders. For both linear and quadratic elements, the nonlinear dCG91 and Entropy Viscosity schemes showed smaller overshoots and undershoots than linear schemes like SUPG and no stabilization.

Grupo#5 taller parcial 2

1) The document presents a theoretical analysis of the application of derivatives to problems that may arise in biotechnology and electronics careers.
2) It provides examples of using derivatives to find maximums and minimums, such as maximizing tree growth or signal coverage.
3) The analysis includes the geometric interpretation of derivatives, criteria for using the first and second derivatives to find critical points and determine if they are maximums or minimums.

Grupo#5 taller parcial 2

1) The document presents a theoretical analysis of the application of derivatives to problems that may arise in biotechnology and electronics careers.
2) It provides examples of using derivatives to find maximums and minimums, such as maximizing tree growth or signal coverage.
3) The analysis covers the geometric interpretation of derivatives, criteria for finding extremes using the first and second derivatives, and applies these concepts to sample problems involving quadratic functions.

_lecture_05 F_chain_rule.pdf

1. The document discusses the chain rule for functions of several variables. It provides examples of how to use a "tree diagram" to represent variable dependencies and derive the appropriate chain rule statement.
2. It also gives examples of applying the chain rule to find derivatives like df/dt for functions where variables like x, y, and z depend on t, or to find partial derivatives like ∂f/∂s and ∂f/∂t.
3. One example works through applying the chain rule to find df/dt for the function f(x,y) = x^2 + y^2, where x = t^2 and y = t^4, and verifies the

Calculus

This document discusses derivatives, including their definition, history, real-life applications, and use in various sciences. Derivatives are defined as the instantaneous rate of change of one variable with respect to another and geometrically as the slope of a curve at a point. Their modern conception is credited to Isaac Newton and Gottfried Leibniz in the 17th century. Derivatives have applications in business for estimating profits and losses, and in automobiles to calculate speed and distance traveled from odometer and speedometer readings. They are also used in physics to define velocity and acceleration and in mathematics to study extreme values, mean value theorems, and curve sketching.

The Fundamental theorem of calculus

The document discusses the Fundamental Theorem of Calculus, which has two parts. Part 1 establishes the relationship between differentiation and integration, showing that the derivative of an antiderivative is the integrand. Part 2 allows evaluation of a definite integral by evaluating the antiderivative at the bounds. Examples are given of using both parts to evaluate definite integrals. The theorem unified differentiation and integration and was fundamental to the development of calculus.

Lar calc10 ch02_sec4

The document discusses the chain rule, which is used to find the derivative of a composite function. It states that if y changes dy/du times as fast as u, and u changes du/dx times as fast as x, then y changes (dy/du)(du/dx) times as fast as x. It provides examples of applying the chain rule to find derivatives of composite functions, including functions with multiple compositions. It also discusses using the general power rule as a special case of the chain rule and simplifying derived functions using algebra. Finally, it outlines the chain rule versions of derivatives for trigonometric functions.

MATH PPT (MC-I)-2.pptx

This document presents reduction formulas for integrals involving trigonometric functions. It introduces reduction formulas and integration by parts, which is used to derive several common reduction formulas. Formulas are provided for integrals of sinx, cosx, tanx, cotx, secx, and cosecx raised to various powers. Examples are included to demonstrate applying the formulas to evaluate definite integrals.

Ydb ji n8 itc ko6esvj8 kgerx k8tc ko4sx k

This presentation introduces regression analysis. It discusses key contributors to the development of regression analysis. It also provides an overview of different types of regression models, including simple linear regression, multiple regression, and nonlinear regression. Examples are provided to demonstrate calculating regression equations using the method of least squares from raw data and data with means removed.

E E 481 Lab 1

1) The document describes a lab experiment using MATLAB and Simulink to model differential equations and a mechanical spring-mass damper system.
2) Two differential equations and one spring-mass system were modeled to analyze the transient and steady-state response.
3) The results showed that the solutions from MATLAB and Simulink matched the expected behaviors and verified the initial and final values as well as time constants of the systems.

K0737781

This document describes the design of a decoupler for an interacting two-tank system. The dynamic behavior of the system was studied using a mathematical model and experimentally by introducing step changes to the inlet flow rates. Relative gain array (RGA) analysis showed interaction between the liquid level controls and inlet flow rate manipulations. To reduce this interaction, decoupler blocks were designed with transfer functions that cancel the effect of one manipulated variable on the other controlled variable. Experimentally measured and theoretically calculated RGA values matched, validating the decoupler design approach. The decoupler was found to lessen interaction and allow independent control of liquid levels in each tank despite interactions in the physical process.

A Study of Some Systems of Linear and Nonlinear Partial Differential Equation...

In this paper, we introduce the solution of systems of linear and nonlinear partial differential equations subject to the initial conditions by using reduced differential transformation method. The proposed method was applied to three systems of linear and nonlinear partial differential equations, leading to series solutions with components easily computable. The results obtained are indicators of the simplicity and effectiveness of the method

Uniform and exponential distribution ppt

Engineering

Varsha.pptx

The decibel is a logarithmic unit used to express the ratio of two power levels or amplitudes. It is commonly used to measure sound levels or power in electronic systems. A decibel represents one tenth of a bel, with 0 dB representing a ratio of 1. Power gain in decibels is calculated as 10 times the log of the ratio between output and input power. A doubling of power equals a 3 dB gain. Total system gain is the sum of individual stage gains. Attenuation is expressed as a negative decibel value. Voltage and current gains can also be expressed in decibels by taking the log of the ratio of output to input levels.

APLICACIONES DE LA DERIVADA EN LA CARRERA DE (Mecánica, Electrónica, Telecomu...

APLICACIONES DE LA DERIVADA EN LA CARRERA DE (Mecánica, Electrónica, Telecomu...WILIAMMAURICIOCAHUAT1

El cálculo diferencial proporciona información sobre el comportamiento de las funciones
matemáticas. Todos estos problemas están incluidos en el alcance de la optimización de funciones y pueden resolverse aplicando cálculoderivativesanditssimpleapplications-160828144729.pptx

The document discusses derivatives and their applications. It begins by introducing derivatives and defining them as the rate of change of a function near an input value. It then discusses rules for finding derivatives such as the constant multiple rule, sum and difference rules, product rule, and quotient rule. Examples are given to illustrate applying these rules. The document also covers composite functions, inverse functions, second derivatives, and applications of derivatives in physics for problems involving velocity and acceleration.

Taller parcial 2

This document discusses the application of calculus derivatives in the career of geospatial technologies. It begins with introducing the concept of the derivative and its calculation. It then discusses the criteria of the first and second derivatives, which can be used to find relative extremes of a function. Three practice exercises are included, relating to optimization problems that can be solved using derivatives. Graphs of the exercises are generated in Geogebra. The document emphasizes how derivatives can be useful for tasks like optimizing processes in geospatial technologies applications.

CALCULUS 2.pptx

This document provides information about Calculus 2, including lessons on indeterminate forms, Rolle's theorem, the mean value theorem, and differentiation of transcendental functions. It defines Rolle's theorem and the mean value theorem, provides examples of applying each, and discusses how Rolle's theorem can be used to find the value of c. It also defines inverse trigonometric functions and their derivatives. The document is for MATH 09 Calculus 2 and includes exercises for students to practice applying the theorems.

Aplicaciones de la derivadas en contabilidad

This document discusses the application of derivatives in accounting. It begins with introducing derivatives and their uses in economics and accounting. Specifically, derivatives represent a useful tool for calculating marginal costs, revenues, profits, and production. The document then presents two examples demonstrating how to use derivatives to find total cost, marginal cost, maximum and minimum prices, and average cost in accounting scenarios. It concludes that derivatives are a 100% useful tool that can simplify complex calculations and processes, with many applications in economics and accounting.

CHAPTER 7.pdfdjdjdjdjdjdjdjsjsjddhhdudsko

The document discusses various methods for developing empirical dynamic models from process input-output data, including linear regression and least squares estimation. Simple linear regression can be used to develop steady-state models relating an output variable y to an input variable u. The least squares approach is introduced to calculate the parameter estimates that minimize the error between measured and predicted output values. Graphical methods are also presented for estimating parameters of first-order and second-order dynamic models by fitting step response data. Finally, the development of discrete-time models from continuous-time models using finite difference approximations is covered.

Multivariate Regression Analysis

The work is done as part of graduate coursework at University of Florida. The author studied master's in environmental engineering sciences during the making of the presentation.

On the discretized algorithm for optimal proportional control problems constr...

This document presents a numerical algorithm for solving optimal control problems with delay differential equations. It discretizes the performance index and delay constraint terms to transform the problem into a large-scale nonlinear programming problem. Simpson's discretization method is used to generate sparse matrices representing the discretized performance index and constraint. The algorithm models the control as proportional to the state, with a constant feedback gain. It analyzes properties of the control operator to guarantee invertibility for use in a Quasi-Newton solver. A numerical example is presented and shown to converge linearly to the analytical solution.

poster2

The document compares several nonlinear and linear stabilization schemes (SUPG, dCG91, Entropy Viscosity) for solving advection-diffusion equations using finite element methods. It presents results of applying the different schemes to stationary and non-stationary test equations, comparing maximum overshoot and undershoot, smearing, and convergence orders. For both linear and quadratic elements, the nonlinear dCG91 and Entropy Viscosity schemes showed smaller overshoots and undershoots than linear schemes like SUPG and no stabilization.

Grupo#5 taller parcial 2

1) The document presents a theoretical analysis of the application of derivatives to problems that may arise in biotechnology and electronics careers.
2) It provides examples of using derivatives to find maximums and minimums, such as maximizing tree growth or signal coverage.
3) The analysis includes the geometric interpretation of derivatives, criteria for using the first and second derivatives to find critical points and determine if they are maximums or minimums.

Grupo#5 taller parcial 2

1) The document presents a theoretical analysis of the application of derivatives to problems that may arise in biotechnology and electronics careers.
2) It provides examples of using derivatives to find maximums and minimums, such as maximizing tree growth or signal coverage.
3) The analysis covers the geometric interpretation of derivatives, criteria for finding extremes using the first and second derivatives, and applies these concepts to sample problems involving quadratic functions.

_lecture_05 F_chain_rule.pdf

1. The document discusses the chain rule for functions of several variables. It provides examples of how to use a "tree diagram" to represent variable dependencies and derive the appropriate chain rule statement.
2. It also gives examples of applying the chain rule to find derivatives like df/dt for functions where variables like x, y, and z depend on t, or to find partial derivatives like ∂f/∂s and ∂f/∂t.
3. One example works through applying the chain rule to find df/dt for the function f(x,y) = x^2 + y^2, where x = t^2 and y = t^4, and verifies the

Calculus

This document discusses derivatives, including their definition, history, real-life applications, and use in various sciences. Derivatives are defined as the instantaneous rate of change of one variable with respect to another and geometrically as the slope of a curve at a point. Their modern conception is credited to Isaac Newton and Gottfried Leibniz in the 17th century. Derivatives have applications in business for estimating profits and losses, and in automobiles to calculate speed and distance traveled from odometer and speedometer readings. They are also used in physics to define velocity and acceleration and in mathematics to study extreme values, mean value theorems, and curve sketching.

The Fundamental theorem of calculus

The document discusses the Fundamental Theorem of Calculus, which has two parts. Part 1 establishes the relationship between differentiation and integration, showing that the derivative of an antiderivative is the integrand. Part 2 allows evaluation of a definite integral by evaluating the antiderivative at the bounds. Examples are given of using both parts to evaluate definite integrals. The theorem unified differentiation and integration and was fundamental to the development of calculus.

Lar calc10 ch02_sec4

The document discusses the chain rule, which is used to find the derivative of a composite function. It states that if y changes dy/du times as fast as u, and u changes du/dx times as fast as x, then y changes (dy/du)(du/dx) times as fast as x. It provides examples of applying the chain rule to find derivatives of composite functions, including functions with multiple compositions. It also discusses using the general power rule as a special case of the chain rule and simplifying derived functions using algebra. Finally, it outlines the chain rule versions of derivatives for trigonometric functions.

MATH PPT (MC-I)-2.pptx

This document presents reduction formulas for integrals involving trigonometric functions. It introduces reduction formulas and integration by parts, which is used to derive several common reduction formulas. Formulas are provided for integrals of sinx, cosx, tanx, cotx, secx, and cosecx raised to various powers. Examples are included to demonstrate applying the formulas to evaluate definite integrals.

Ydb ji n8 itc ko6esvj8 kgerx k8tc ko4sx k

This presentation introduces regression analysis. It discusses key contributors to the development of regression analysis. It also provides an overview of different types of regression models, including simple linear regression, multiple regression, and nonlinear regression. Examples are provided to demonstrate calculating regression equations using the method of least squares from raw data and data with means removed.

E E 481 Lab 1

1) The document describes a lab experiment using MATLAB and Simulink to model differential equations and a mechanical spring-mass damper system.
2) Two differential equations and one spring-mass system were modeled to analyze the transient and steady-state response.
3) The results showed that the solutions from MATLAB and Simulink matched the expected behaviors and verified the initial and final values as well as time constants of the systems.

K0737781

This document describes the design of a decoupler for an interacting two-tank system. The dynamic behavior of the system was studied using a mathematical model and experimentally by introducing step changes to the inlet flow rates. Relative gain array (RGA) analysis showed interaction between the liquid level controls and inlet flow rate manipulations. To reduce this interaction, decoupler blocks were designed with transfer functions that cancel the effect of one manipulated variable on the other controlled variable. Experimentally measured and theoretically calculated RGA values matched, validating the decoupler design approach. The decoupler was found to lessen interaction and allow independent control of liquid levels in each tank despite interactions in the physical process.

A Study of Some Systems of Linear and Nonlinear Partial Differential Equation...

In this paper, we introduce the solution of systems of linear and nonlinear partial differential equations subject to the initial conditions by using reduced differential transformation method. The proposed method was applied to three systems of linear and nonlinear partial differential equations, leading to series solutions with components easily computable. The results obtained are indicators of the simplicity and effectiveness of the method

APLICACIONES DE LA DERIVADA EN LA CARRERA DE (Mecánica, Electrónica, Telecomu...

APLICACIONES DE LA DERIVADA EN LA CARRERA DE (Mecánica, Electrónica, Telecomu...

derivativesanditssimpleapplications-160828144729.pptx

derivativesanditssimpleapplications-160828144729.pptx

Taller parcial 2

Taller parcial 2

CALCULUS 2.pptx

CALCULUS 2.pptx

Aplicaciones de la derivadas en contabilidad

Aplicaciones de la derivadas en contabilidad

CHAPTER 7.pdfdjdjdjdjdjdjdjsjsjddhhdudsko

CHAPTER 7.pdfdjdjdjdjdjdjdjsjsjddhhdudsko

Multivariate Regression Analysis

Multivariate Regression Analysis

On the discretized algorithm for optimal proportional control problems constr...

On the discretized algorithm for optimal proportional control problems constr...

poster2

poster2

Grupo#5 taller parcial 2

Grupo#5 taller parcial 2

Grupo#5 taller parcial 2

Grupo#5 taller parcial 2

_lecture_05 F_chain_rule.pdf

_lecture_05 F_chain_rule.pdf

Calculus

Calculus

The Fundamental theorem of calculus

The Fundamental theorem of calculus

Lar calc10 ch02_sec4

Lar calc10 ch02_sec4

MATH PPT (MC-I)-2.pptx

MATH PPT (MC-I)-2.pptx

Ydb ji n8 itc ko6esvj8 kgerx k8tc ko4sx k

Ydb ji n8 itc ko6esvj8 kgerx k8tc ko4sx k

E E 481 Lab 1

E E 481 Lab 1

K0737781

K0737781

A Study of Some Systems of Linear and Nonlinear Partial Differential Equation...

A Study of Some Systems of Linear and Nonlinear Partial Differential Equation...

Uniform and exponential distribution ppt

Engineering

Varsha.pptx

The decibel is a logarithmic unit used to express the ratio of two power levels or amplitudes. It is commonly used to measure sound levels or power in electronic systems. A decibel represents one tenth of a bel, with 0 dB representing a ratio of 1. Power gain in decibels is calculated as 10 times the log of the ratio between output and input power. A doubling of power equals a 3 dB gain. Total system gain is the sum of individual stage gains. Attenuation is expressed as a negative decibel value. Voltage and current gains can also be expressed in decibels by taking the log of the ratio of output to input levels.

mas-150813232504-lva1-app6892.pdf

This document discusses various topics in engineering including electrical engineering, electronics, mechanical/civil engineering, sports and exercise engineering, energy systems engineering, and engineering applications. It provides examples of using different engineering disciplines like modeling traffic volumes, designing airplane landing gear, and developing sun-tracking mirrors for solar power plants.

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This document discusses threats to biodiversity such as habitat loss from deforestation, wetland destruction, and fragmentation for agriculture, development, and raw materials. Poaching of wildlife for traditional use, commercial trade, and illegal wildlife products also reduces biodiversity. Man-wildlife conflicts have increased due to competition over limited resources from agricultural expansion, urbanization, and infrastructure development. Solutions proposed include strengthening biodiversity laws, adjusting cropping patterns and compensation schemes, and providing food and water for wildlife.

chemistry ppt modified-1.pptx

The document is a presentation by team 6 on types of batteries. It introduces the team members and provides an agenda that covers an introduction to batteries, types of batteries, advantages of batteries, and usage of batteries. The main types discussed are primary batteries, which are single-use, and secondary batteries, which are rechargeable. Examples of primary batteries include zinc carbon and manganese dioxide cells, while common secondary batteries are nickel-cadmium, lead acid, and lithium-ion. The presentation notes that lithium batteries currently provide the highest energy density and are widely used in electronics like smartphones, tablets, and laptops.

maths diff.calculus ppt (1).pptx

This document provides an overview of differential calculus concepts including:
1. It defines differential calculus as dealing with finding exact derivatives directly from a function's formula without using graphical methods, and as a method that deals with the rate of change of one quantity with respect to another.
2. It introduces key concepts like the derivative, which represents the slope of a function at every point, and covers derivative rules for logarithmic, trigonometric, and other common functions.
3. It explains derivative techniques like the product rule, quotient rule, and squeeze/sandwich theorem, and provides examples of applying these rules to find derivatives of various functions.

E-Textiles.doc

The document discusses electronic textiles (e-textiles) and their applications for military use. E-textiles are fabrics that can function electrically like electronics while behaving physically like textiles, enabling computing and digital components to be embedded. The document outlines a brief history of e-textiles development from the 1990s to present. It then lists several potential military applications of e-textiles such as sensing tank movements, monitoring homes for chemicals, and helping firefighters navigate smoky buildings.

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The document discusses using Python for game development, including popular game engines like Pygame and Panda3D that can be used to create 2D and 3D games in Python. It provides guidelines for designing a game, such as brainstorming ideas, writing pseudocode, adding assets, and testing. The document also includes code for a sample quiz game in Python to demonstrate how games can be created using the language.

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- 1. DIFFERENTIAL CALCULUS BATCH-6: 1. VANATHI.S 2. VARSHINIE.A.L 3. SRIRAM.R 4.THIRUNAVUKARASU.S 5. VISHAL.S 6. SURANJANA.N.S >>> ENGINEERING MATHEMATICS
- 2. TABLE OF CONTENTS 1. INTRODUCTION 2. BAKING ANALOGY 3. DIFFERENTIAL CALCULUS 4. DERIVATIVE RULES 5. PRODUCT RULE 6. QUOTIENT RULE 7. DERIVATIVE OF TRIGNOMETRIC FUCTIONS 8. THE SANDWICH/SQUEEZE THEOREM 9. CONCLUSIONS
- 3. INTRODUCTION >> Differential calculus is a procedure for finding the exact derivative directly from the formula of the function without having to use graphical methods. >> It is a method that deals with the rate of change of one quantity with respect to another.
- 4. BAKING ANALOGY >> In this we will focus on the formulas and rules for both differentiation, the method by which we calculate the derivative of a function. >> Before we dive into formulas and rules for differentiation , let’s look at some notations for differentiation. >> we can write f(X) as d/dx f(x),f’(x),df(x) and Df(x) We read these as d by dx of f of x, f’ prime of f of x, df of x and cap Df of x.
- 5. DIFFERENTIAL CALCULUS >> Differential calculus is the area of calculus dealing with cutting something into smaller pieces in order to analyze how it changes. >> The primary operation of differential calculus is the derivative. The derivative of a function given the infinitesimal change of the function with respect to one of it’s variable. >> The derivative represents the slope of function at every point it is defined.
- 6. DERIVATIVE RULES LOGARITHMIC FUNCTIONS (d/dx): 1. e^x = e^x 2. a^x = a^x ln(a) 3. Ln(x) = 1/x 4. Log a ^x = 1/xln(a) TRIGONOMETRIC FUNCTIONS (d/dx): 1. Sin(x)= cos(x) 2. Cos(x)= -sin(x) 3. Tan(x)= sec^2(x) 4. Cosec(x)= - cosec(x) cot(x) 5. Sec(x)= sec(x) tan(x) 6. Cot(x)= -cosec^2(x)
- 7. Real life applications of differential calculus: >> Calculation of profit or loss with respect to business using graphs. >> Calculation of rate of change of temperature. >> To derive many physical equations. >> Calculation of speed or distance covered such as miles per hour , km/hour.
- 8. PRODUCT RULE >> The derivative of the product of two differentiable functions is equal to the addition of the first multiplied by the derivative of the second and the second function multiplied by the derivative of the first function. APPLICATION: 1. The product rule is used in calculus, when you are asked to take derivative of the function. 2. It makes calculation clean and easier to solve. 3. It is used to differentiate product of two or more functions.
- 9. DERIVATIVE PRODUCT RULE If u and v are differentiable at x, then so is their product uv and d/dx(u.v) = u (dv/dx) +v (du/dx) Example: Q) Find the derivative of y=(x^2 +1)(x^3+3) Answer: d/dx(x^2+1)(x^3+3)=(x^2+1)(3x^2)+ (2x)(x^3+3) =3x^4+3x^2+2x^4+6x =5x^4+3x^2+6x The particular product can be differentiated as well by multiplying out the original expression for y and differentiating the resulting polynomial. Y=(x^2+1)(x^3+3)=x^5+x^3+3x^2+3 dy/dx=5x^4+3x^2+6x This is in agreement with our first calculation.
- 10. QUOTIENT RULE >> A quotient rule is similar to product rule. A quotient rule is stated as the ratio of the quantity of the denominator times the derivative of the numerator function minus the numerator times the derivative of the denominator function to the square of the denominator function. APPLICATION: 1. It is used for finding the derivative of a quotient of functions. 2. It is used for extend the power rule to functions with negative exponents. 3. To combine differentiation rule to find the derivative of a polynomial or rational function.
- 11. DERIVATIVE QUOTIENT RULE If u and v are differentiable at x and if v(x) is not equal to 0 then the quotient u/v is differentiable at x and d/dx(u/v)= v (du/dx) – u (dv/dx)/ v^2 Example: Q)Find the derivative of y=(t^2-1)/(t^3+1) Answer: u=t^2-1 v=t^3+1 dy/dt=(t^3+1).2t- (t^2-1).3t^2/(t^3+1)^2 =2t^4+2t-3t^4+3t^2/(t^3+1)^2 =-t^4+3t^2+2t/(t^3+1)^2
- 12. SQUEEZE THEOREM >> In calculus the squeeze theorem is a theorem regarding the limit of a function that is trapped between two other function. >> The squeeze theorem is used in calculus and mathematical analysis typically to confirm the limit of a function via comparison with other function whose limits are known. >> If the right hand limits and left hand limits do not equal eachother we cannot utilize squeeze theorem. If f(x)<g(x)<h(x) when x is near a If limxa f(x)=limxa h(x)=L then limxa g(x)=L.
- 13. WHY IS IT CALLED SANDWICH THEOREM? >> The squeeze theorem is also called as sandwich or pinching theorem. It is a way to find the limit of one function if we know the limits of two functions it is “sandwiched” between. APPLICATION: It is used for calculating the limit of a given trigonometric funtions.
- 14. EXAMPLE OF SANDWICH THEOREM Q) Using sandwich theorem show that: limx0 x^2 sin (1/x)=0 ANSWER: Let -1<sin(1/x)<1 Multiply by x^2 -x^2<x^2 sin 1/x <x^2 Lim x0 (–x^2)<lim x0 x^2 sin (1/x)< lim x0 x^2 Lim x->0 (-x^2)=-0=0 Lim x x^2=0=0 Lim x0 (-x^2)= lim x (x^2) Lim x0 x^2 sin (1/x)=0
- 15. THANK YOU!