1 Special Functions. - 1 Functions. - 2 Polynomials and Step Functions. - 3 Trigonometrie Functions. - 4 Power and Exponential Functions. - 5 Inverse Functions. - 6 New Functions from Old. - 7 Numbers. - 2 Calculus: Differentiation. - 1 Introduction. - 2 Higher Derivatives. - 3 Maxima and Minima. - 4 Taylor Series and Approximations. - 5 Partial Derivatives. - 6 Higher Order Partial Derivatives. - 7 Optimisation. - 3 Integration. - 1 Introduction and Definition. - 2 The Relationship between Integration and Differentiation. - 3 Numerical Integration (Quadrature). - 4 Double Integration. - 5 Line Integrals. - 6 Differential Equations. - 4 Complex Numbers. - 1 Introduction. - 2 The Beginning. - 3 Functions of Complex Variables. - 4 Differentiation and Integration. - 5 Matrices. - 1 Introduction. - 2 Definitions and Elementary Properties. - 3 Matrices. - 4 Multiplication of Matrices. - 5 Special Types of Matrices. - 6 Matrices as Functions. - 7 Linear Equations. - 8 Eigenvalues and Quadratic Forms. - 6 Stochastic Processes Probability and Statistics. - 1 Introduction. - 2 Probability. - 3 Permutations and Combinations. - 4 Probability Distributions. - 5 Joint Distributions. - 6 Expected Values and Moments. - 7 Real Data Samples. - 8 Two Variables. - 9 Simulation and Monte Carlo Methods. - 10 Confidence Intervals. - 11 Stochastic Processes. - 7 Fourier Analysis. - 1 Introduction. - 2 Fourier Series. - 3 Some Examples of Fourier Analysis. - 4 The Phase Amplitude and Exponential Formulation. - 5 Fourier Transform. - 6 The z-Transform. - 7 The Discrete Fourier Transform. - 8 Fast Fourier Transform. - 9 Frequency Domain. - 8 Time Series. - 1 Stationary and Related Series. - 2 Aliasing and Sampling. - 3 Filters and Convolutions. - 9 Applications. - 1 Wavelets. - 2 Predictive Deconvolution. - Appendix 1 References To Applications. - Appendix 2Some Useful Formulae for Ready Reference. - Appendix 3 Programs. Language: English