Contents
Introduction
1 Introduction
 1.1 Why mathematics for physics?
 1.2 Mathematics as the language for physics
2 Revision
 2.1 Powers, logs, exponentials
 2.2 Trigonometric functions
 2.3 Polar Coordinates
3 Vectors in 2-space and 3-space
 3.1 solid geometry
 3.2 Vectors and vector arithmetic
 3.3 Vector Addition
 3.4 Vectors: Component Form
 3.5 Vector products
 3.6 The scalar or dot product
 3.7 Angle between two vectors
 3.8 Work
 3.9 The vector product
 3.10 *triple products*
 3.11 *Vector Triple Product*
 3.12 *The straight line*
4 Differentiation
 4.1 Assumed knowledge
 4.2 Other techniques
 4.3 Vector functions
 4.4 Partial derivatives
 4.5 Differentiation and curve sketching
 4.6 *Application of differentiation: Calculation of small errors*
5 Integration
 5.1 Basic integration
 5.2 Rules for integration
 5.3 Properties of definite integrals
 5.4 Improper integrals
 5.5 Strategy
 5.6 Integration by Parts
 5.7 Integration by substitution
 5.8 Integrals of the inverse of a linear function
 5.9 Integrals of a linear function divided by a quadratic
 5.10 Integration of rational Functions
 5.11 Integrals with square roots in denominator
6 Applications of Integration
 6.1 Finding areas
 6.2 Volumes of Revolution
 6.3 Centroids (First moment of area)
 6.4 Second Moment of Area
7 Differential Equations
 7.1 introduction
 7.2 Some special types of DE
 7.3 Bernoulli’s Equation