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	Differential Calculus by Vinay Kumar
	Price : Rs 350.00
	Your Price : Rs 315.00

Differential Calculus is a comprehensive theory cum practice book that aims to acquaint aspirants with all aspects of the topic. It helps sharpen the problem solving skills in Calculus through solved and unsolved problems. The solutions to the problems are supported by time saving strategies and tips to avoid mistakes while applying the laws of Calculus.

Table of Contents
1. Limit

Introduction
Concept of Infinity
Theorems on Limits
One-sided limits
determinate and Indeterminate Forms
Factorisation and Cancellation of Common Factors
Rationalization
Limit Using Exapnasion Series of Functions
Standard of Limits
Algebra of limits
Limits when (Some function)
Asymptotes
Limits of a Sequence
Limits of Forms
Sandwich Theorem / Squeeze Play Theorem
L`Hospital`s Rule
Geometerical Limits
Miscellaneous Limits
Target Problems
Things to Remember
Exercises
Answers

2. Continuity of Functions

Definition of Continuity
Continuity in an Interval
Classification of Discontinuity
Algebra of Continous Functions
Properties of Functions Continous on a Closed Interval
Intermediate Value Theorem
Target Problems
Things to Remember
Exercises
Answers

3. Differentiability

Introduction
Differentiability
Reasons of Non-differentiability
Relation between Continuity and Differentiability
Derivability at Endpoints
Differentiability over an interval
Alternative limit form of the Derivative
Derivatives of Higher Order
Algebra of Differentiable Functions
Functional Equations
Target Problems
Things to Remember
Exercises
Answers

4. Methods of Differentiation

Introduction
Derivative using First principle (ab initio) Method
Derivative of Standard Functions
Rules of Differentiation
The Chain Rule
Logarithmic Differentiation
Derivative of Inverse Functions
Parametric Differentiation
Differentiation of Implicit Functions
Differentiation by Trigonometric Substitution
Derivatives of Higher Order
Successive Differentiation
Derivative of a Determinant
Properties of Derivative
L`Hospital Rule
Target Problems
Things to Remember
Exercises
Answers

5. Tangent and Normal

Introduction
Rate Measurement
Approximation
Error
Tangent and Normal
Angle of Intersection
Common Tangents
Length of Tangent
Target Problems
Things to Remember
Exercises
Answers

6. Monotonicity

Definitions
Monotonicity over an interval
Critical Point
Intervals of Monotonicity
Monotonicity in Parametric Functions
Algebra of Monotonous Functions
Proving Inequalities
Concavity and Point of Inflection
Target Problems
Things to Remember
Exercises
Answers

7. Maxima and Minima

Introduction
Concept of Local Maxima and Local Minima
Fermat Theorem
The First Derivative Test
The First Derivative Procedure for Sketching the Graph of a Continous Function
Second Derivative Test
Higher Order Derivative Test
Extrema of Parametric Functions
Operations on Functions having points of Extrema
Global Maximum and Minimum
Boundedness
Algebra of Global Extrema
Miscellaneous Methods
Optimisation Problems
Asymptotes
Points of Inflection
Curve Sketching
Isolation of Roots
Rolle`s Theorem
Deductions of Rolle`s Theorem
Lagrange`s mean Value Theorem
Corollaries of LMVT
Related Inequalities
Cauchy`s Mean Value Th isbn
9781259003530

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