MAT112- DIFFERENTIAL CALCULUS

Introduction

Limits

Limits at Infinity

Special Limits

The Gradient of a Curve

Further Differentiation

Higher Derivatives

Differentiation of a Sum: Sum Rule

Standard Derivatives

Functions ofa Function

Differentiation of a Product:Product Rule

Differentiation of a Quotient: Quotient Rule

Implicit Differentiation

Derivative of Trigonometric Functions

Derivative of Logarithmic Functions

Derivative of Exponential Functions

Tangents and Normals to Curves

Maxima and Minima

Maxima and Minima Value Problems

Rate of Change

Rectilinear Motion

Calculus of Integration

The Constant of Integration

Some Standard Integrals

Methods of Integration

Method of Substitution

Algebraic Substitution

Trigonometric Substitution

Fractional Integrands whose Numerators are Equal to the Derivatives of Denominators

Fractional Integrands whose Denominators are Linear

Fractional Integrands whose Denominators DO NOT Resolve into Rational Factors I

Fractional Integrands whose Denominators DO NOT Resolve into Rational Factors II

Area under the Curve

Area between two Curves

Volume of Soids of Revolution