PinkMonkey.com Calculus Study Guide

Introduction

Chapter 1 Function
1.1 Functions And Mapping
1.2 Functions, Their Graphs & Classification
1.3 Rules For Drawing The Graph Of A Curve
1.4 Classification Of Functions
1.5 Standard Forms For The Equation Of A Straight Line
1.6 Circular Function And Trigonometry

Chapter 2 Limits
2.1 Modulus
2.2 Inequalities
2.3 Limits Of Functions
2.4 Left Hand And Right Hand Limits
2.5 Theorems On The Algebra Of Limits
2.6 Evaluating Limits
2.7 Limits Of Trigonometric Functions
2.8 The Exponential Limits

Chapter 3 Continuity
3.1 Continuity At A Point
3.2 Continuity In An Interval
3.3 Some Very-often-encountered Continuous Functions
3.4 Algebra Of Continuous Functions
3.5 Discontinuity And Its Classification
3.6 Properties of Functions Continues on an Interval

Chapter 4 Derivatives
4.1 Derivability At A Point
4.2 Derivability In An Interval
4.3 Derivability And Continuity Of A Function At A Point
4.4 Some Counter Examples
4.5 Interpretation Of Derivatives
4.6 Theorems On Derivatives (differentiation Rules)
4.7 Derivatives Of Standard Functions
4.8 Derivative Of A Composite Function
4.9 Differentiation Of Implicit Functions
4.10 Derivative Of An Inverse Function
4.11 Derivatives Of Inverse Trigonometric Functions
4.12 Derivatives Of Exponential & Logarithmic Functions
4.13 Logarithmic Differentiation
4.14 Derivatives Of Functions In Parametric Form
4.15 Higher order Derivatives

Chapter 5 Application Of The Derivative
5.1 Tangent And Normal Lines
5.2 Angle Between Two Curves
5.3 Interpretation Of The Sign Of The Derivative
5.4 Locality Increasing Or Decreasing Functions
5.5 Critical Points
5.6 Turning Points
5.7 Extreme Value Theorem
5.8 The Mean-value Theorem
5.9 First Derivative Test For Local Extrema
5.10 Second Derivative Test For Local Extrema
5.11 Stationary Points
5.12 Concavity And Points Of Inflection
5.13 Rate Measure (distance, Velocity And Acceleration)
5.14 Related Rates
5.15 Differentials : Errors And Approximation

Chapter 6 Integration
6.1 Anti-derivatives (indefinite Integral)
6.2 Integration Of Some Trigonometric Functions
6.3 Methods Of Integration
6.4 Substitution And Change Of Variables
6.5 Some Standard Substitutions
6.6 Integration By Parts
6.7 Integration By Partial Fractions

Chapter 7 Definite Integral
7.1 Definition
7.2 Definite Integral As An Area Under Curve
7.3 Working Rule For Evaluation Of A Definite Integral As A Limit Of A Sum
7.4 Fundamental Theorem Of Integrated Calculus
7.5 Properties Of Definite Integrals
7.6 Evaluation Of Definite Integral
7.7 Reduction Formulas

Chapter 8 Applications Of The Definite Integrals
8.1 Area
8.2 Volumes
8.3 Mean Value
8.4 Arc Length (Rectification)