1 Introduction
 1.1 Why mathematics for physics?
 1.2 Mathematics as the language for physics
2 Revision
 2.1 Powers, logs, exponentials
  2.1.1 Powers
  2.1.2 The product of two powers
  2.1.3 Exponential Function
  2.1.4 The Logarithmic Function
 2.2 Trigonometric functions
  2.2.1 Trigonometric identities
  2.2.2 Inverse Trig Functions
 2.3 Polar Coordinates
  2.3.1 Polar curves
3 Vectors in 2-space and 3-space
 3.1 solid geometry
 3.2 Vectors and vector arithmetic
  3.2.1 What is a vector?
  3.2.2 Graphical representation
  3.2.3 Equality and line of action
  3.2.4 Negative of a vector
  3.2.5 magnitude of a vector
  3.2.6 Multiplication by a scalar
  3.2.7 Unit vectors
 3.3 Vector Addition
  3.3.1 Triangle Law
  3.3.2 Parallelogram Law
  3.3.3 General Addition
  3.3.4 Associativity
  3.3.5 Closed sets of vectors: null vector
  3.3.6 Subtraction of vectors
  3.3.7 Zero or Null Vector
 3.4 Vectors: Component Form
  3.4.1 Components in 2 dimensions
  3.4.2 Vectors in 3 dimensions
  3.4.3 Sum and Difference of vectors in Component Form
  3.4.4 Unit vectors
  3.4.5 Scaling of Vector
  3.4.6 Physical example
 3.5 Vector products
 3.6 The scalar or dot product
  3.6.1 Component form of dot product
 3.7 Angle between two vectors
 3.8 Work
 3.9 The vector product
 3.10 *triple products*
  3.10.1 Component Form
  3.10.2 Some physical examples
 3.11 *Vector Triple Product*
 3.12 *The straight line*
  3.12.1 Standard form of L
4 Differentiation
 4.1 Assumed knowledge
  4.1.1 First principles definition
  4.1.2 Meaning as slope of a curve
  4.1.3 Differential of a sum
  4.1.4 Differential of product
  4.1.5 Differential of quotient
  4.1.6 Function of a function (chain rule)
  4.1.7 some simple physical examples
  4.1.8 Differential of inverse function
  4.1.9 Maxima and minima
  4.1.10 Higher Derivatives
 4.2 Other techniques
  4.2.1 Implicit Differentiation
  4.2.2 Logarithmic differentiation
  4.2.3 Differentiation of parametric equations
 4.3 Vector functions
  4.3.1 Polar curves
 4.4 Partial derivatives
  4.4.1 Multiple partial derivatives
 4.5 Differentiation and curve sketching
  4.5.1 Global vs. local maximum
  4.5.2 Curve sketching
 4.6 *Application of differentiation: Calculation of small errors*
5 Integration
 5.1 Basic integration
  5.1.1 standard integrals
 5.2 Rules for integration
  5.2.1 Sum rule
  5.2.2 Constant multiple
 5.3 Properties of definite integrals
 5.4 Improper integrals
  5.4.1 Divergent integrands
 5.5 Strategy
 5.6 Integration by Parts
 5.7 Integration by substitution
  5.7.1 Type 1
  5.7.2 Type 2
 5.8 Integrals of the inverse of a linear function
 5.9 Integrals of a linear function divided by a quadratic
  5.9.1 Completing the Square
  5.9.2 Method
 5.10 Integration of rational Functions
  5.10.1 Partial fractions
 5.11 Integrals with square roots in denominator
6 Applications of Integration
 6.1 Finding areas
  6.1.1 Area between two curves
  6.1.2 Basic Derivation of Area Formula
 6.2 Volumes of Revolution
 6.3 Centroids (First moment of area)
  6.3.1 First moment of the area about the y axis
  6.3.2 First Moment of the area about the x axis
  6.3.3 Centroid of a plane area
  6.3.4 Meaning of the centroid
 6.4 Second Moment of Area
7 Differential Equations
 7.1 introduction
 7.2 Some special types of DE
  7.2.1 Separable type
  7.2.2 linear type
  7.2.3 Homogeneous Type
 7.3 Bernoulli’s Equation