Contents

• Introduction
• Contents
• Algebra
  • Factorizations
  • Rules of Indices
  • Quadratic Equations
  • Binomial Theorem
  • Logarithms
  • Complex Numbers
  • De Moivre's Theorem
• Trigonometry
  • Basic Trigonometric Formulas
  • Symmetries
  • Inverse Trigonometric Functions
• Coordinate Geometry
  • Straight Line
  • Areas & Volumes
  • Plane Polar Coordinates
• Matrices
  • Matrix Definitions
  • Formulas for Matrix Inversion
  • Properties of Determinants
• Calculus
  • Standard Derivatives
  • Standard Taylor Series
  • Standard Integrals
  • Summary of Integration Formulas
• Vectors
  • Products of 3-dimensional vectors
• Exp and Log
  • Exponential Function
  • Natural Logarithm
  • Hyperbolic Functions
• Numerical Methods
  • Newton-Raphson
  • Numerical Integration
• Eigenvalues and Eigenvectors
  • Eigenvalues
  • Diagonalisation
• Several Variable Calculus
  • Chain Rule for Several Variables
  • Vector Calculus Definitions
  • Vector Calculus Formulas
  • Divergence Theorem
  • Stokes' Theorem
• Fourier Series
  • Fourier Series Definitions
• Transforms
  • Fourier Transform Definitions
  • Fourier Transform Properties
  • Laplace Transform
  • z-Transform
• Data Handling
  • Polynomial Fitting
  • Cubic Spines
  • Central Difference Table & Bessel's Interpolation Formula
  • Numerical Solution of Ordinary Differential Equations
  • Euler's Method--Linear Approximation
  • Improved Euler Method--Predictor-Corrector
  • Runge-Kutta Method (fourth order)
  • Systems of Ordinary Differential Equations
• Appendix
  • Cumulative Normal Distribution (by NAG)
• Index
• About this document ...