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.
Continuous models of economy adopted to either define evolutions of economic
systems or investigate economic dynamics, amongst its other areas of applications, are
known to be related to differential equations. The considered model in this article takes
the form of a second order non-linear ordinary differential equation (ODE) which is
conventional solved by reducing to the system of first order. This approach is
computationally tasking, unlike block methods which bypasses reduction by directly
solving the model. A new approach is introduced named Modified Taylor Series
Approach (MTSA). Hence, the resultant MTSA-derived block method is implemented to
solve the second order non-linear model of economy under consideration.
Continuous models of economy adopted to either define evolutions of economic
systems or investigate economic dynamics, amongst its other areas of applications, are
known to be related to differential equations. The considered model in this article takes
the form of a second order non-linear ordinary differential equation (ODE) which is
conventional solved by reducing to the system of first order. This approach is
computationally tasking, unlike block methods which bypasses reduction by directly
solving the model. A new approach is introduced named Modified Taylor Series
Approach (MTSA). Hence, the resultant MTSA-derived block method is implemented to
solve the second order non-linear model of economy under consideration.
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 cálculo
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.
A Study of Some Systems of Linear and Nonlinear Partial Differential Equation...inventionjournals
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
Controller design of inverted pendulum using pole placement and lqreSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Controller design of inverted pendulum using pole placement and lqreSAT Journals
Abstract In this paper modeling of an inverted pendulum is done using Euler – Lagrange energy equation for stabilization of the pendulum. The controller gain is evaluated through state feedback and Linear Quadratic optimal regulator controller techniques and also the results for both the controller are compared. The SFB controller is designed by Pole-Placement technique. An advantage of Quadratic Control method over the pole-placement techniques is that the former provides a systematic way of computing the state feedback control gain matrix.LQR controller is designed by the selection on choosing. The proposed system extends classical inverted pendulum by incorporating two moving masses. The motion of two masses that slide along the horizontal plane is controllable .The results of computer simulation for the system with Linear Quardatic Regulator (LQR) & State Feedback Controllers are shown in section 6. Keyword-Inverted pendulum, Mathematical modeling Linear-quadratic regulator, Response, State Feedback controller, gain formulae.
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 cálculo
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.
A Study of Some Systems of Linear and Nonlinear Partial Differential Equation...inventionjournals
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
Controller design of inverted pendulum using pole placement and lqreSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Controller design of inverted pendulum using pole placement and lqreSAT Journals
Abstract In this paper modeling of an inverted pendulum is done using Euler – Lagrange energy equation for stabilization of the pendulum. The controller gain is evaluated through state feedback and Linear Quadratic optimal regulator controller techniques and also the results for both the controller are compared. The SFB controller is designed by Pole-Placement technique. An advantage of Quadratic Control method over the pole-placement techniques is that the former provides a systematic way of computing the state feedback control gain matrix.LQR controller is designed by the selection on choosing. The proposed system extends classical inverted pendulum by incorporating two moving masses. The motion of two masses that slide along the horizontal plane is controllable .The results of computer simulation for the system with Linear Quardatic Regulator (LQR) & State Feedback Controllers are shown in section 6. Keyword-Inverted pendulum, Mathematical modeling Linear-quadratic regulator, Response, State Feedback controller, gain formulae.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
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.
7. Real life applications of differential
calculus:
>> Calculation of profit or loss with respect to
buissness 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