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Differential Calculus (English) 1st Edition by Vinay Kumar

  • ISBN: 9781259003530
  • Authors: Vinay Kumar
Differential Calculus (English) 1st Edition by Vinay Kumar
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Differential Calculus (English) 1st Edition

Author: Vinay Kumar
Language: English
Length (Pages): 728 Pages
Publisher: Tata McGraw - Hill

Publication Year 2012
Edition:1stEdition
Exam:
ISBN: 9781259003530

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 Theorem
Target Problems
Things to Remember
Exercises
Answers

 

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