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MATHEMATICS FOR ENGINEERS AND SCIENTISTS 1

Logarithmic and Exponential Functions: Introduction to the log function; Log function to different bases; log versus ln. Functions, Fractions and Logarithms: Exponential functions and their relationships with logarithms. Hyperbolic functions sinh x and cosh x; Derivation of tanh x. Application of Linear and Log Functions: Revision of the equation of a straight line. Methods for linearisation of non-linear functions. Log plots. Interpolation and extrapolation. Differentiation: Gradients. Tangents. Derivatives from first principles. Derivatives of common functions. Higher Order derivatives. Chain Rule. Product and Quotient Rule. Implicit differentiation. Parametric differentiation. Curve Sketching. Introduction to Integration: Basic ideas and definitions. Indefinite integrals. Tables of Standard Integrals. Definite integrals. Infinite integrals; “improper” integrals. Statistics and Probability: Mean, median - measures of location. Variance, standard deviation - measures of spread. Frequency tables. Probability theory. Combined probabilities. Independent events. Tree diagrams. Probability distributions. Normal distribution. Standard Normal distribution. Binomial distribution. Vectors: Basic operation of vectors. Components of vectors. Components of vectors in 3D. Addition of vectors. Unit vectors. Scalar product. Vector product. Scalar triple product. Equation of line in 3D. Equation of plane.