Krishna Tb Advance Calculus Edition 1c Pages 332 Code 843 Mathematics 13

This book is designed for students who are studying advanced calculus. It covers a wide range of topics, including limits, derivatives, integrals, and differential equations. The book is written in a clear and concise style, and it includes numerous examples and exercises to help students learn the material.

Krishna's TB Advance Calculus|Edition-1C|Pages-332|Code-843 (Mathematics Book 13)

by A.R Vasishtha

4.1 out of 5

Language	:	English
File size	:	12747 KB
Screen Reader	:	Supported
Print length	:	54 pages
Lending	:	Enabled

FREE

Table of Contents

• Limits
• Derivatives
• Integrals
• Differential Equations

Limits

A limit is a value that a function approaches as the input approaches some value. Limits are used to define derivatives and integrals, and they are also used to solve many other problems in calculus.

There are many different ways to find limits. One common method is to use the epsilon-delta definition of a limit. This definition states that a function f(x) has a limit L as x approaches a if for every epsilon > 0, there exists a delta > 0 such that whenever 0

Another common method for finding limits is to use L'Hopital's rule. This rule states that if the limit of f(x)/g(x) as x approaches a is 0/0 or infinity/infinity, then the limit of f(x)/g(x) as x approaches a is equal to the limit of f'(x)/g'(x) as x approaches a.

Derivatives

A derivative is a measure of the rate of change of a function. Derivatives are used to find the slope of a curve, to find the velocity of an object, and to solve many other problems in calculus.

There are many different ways to find derivatives. One common method is to use the power rule. The power rule states that if f(x) = x^n, then f'(x) = nx^(n-1).

Another common method for finding derivatives is to use the chain rule. The chain rule states that if f(x) = g(h(x)),then f'(x) = g'(h(x)) * h'(x).

Integrals

An integral is a measure of the area under a curve. Integrals are used to find the area of a region, to find the volume of a solid, and to solve many other problems in calculus.

There are many different ways to find integrals. One common method is to use the fundamental theorem of calculus. The fundamental theorem of calculus states that if f(x) is a continuous function on the interval [a, b], then the integral of f(x) from a to b is equal to the net area between the curve y = f(x) and the x-axis from a to b.

Another common method for finding integrals is to use integration by parts. Integration by parts states that if u and v are two differentiable functions, then the integral of uv is equal to uv - integral u'v dx.

Differential Equations

A differential equation is an equation that contains derivatives of a function. Differential equations are used to model many different phenomena, such as the motion of a projectile, the growth of a population, and the flow of heat.

There are many different ways to solve differential equations. One common method is to use separation of variables. Separation of variables involves rewriting the differential equation in a form where the variables can be separated and integrated.

Another common method for solving differential equations is to use Laplace transforms. Laplace transforms involve converting the differential equation into a algebraic equation that can be solved using algebra.

This book is a comprehensive to advanced calculus. It covers a wide range of topics, including limits, derivatives, integrals, and differential equations. The book is written in a clear and concise style, and it includes numerous examples and exercises to help students learn the material.

Krishna's TB Advance Calculus|Edition-1C|Pages-332|Code-843 (Mathematics Book 13)

by A.R Vasishtha

4.1 out of 5

Language	:	English
File size	:	12747 KB
Screen Reader	:	Supported
Print length	:	54 pages
Lending	:	Enabled

FREE