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The module is designed to introduce you to the principles, techniques and applications of calculus. The fundamentals of differentiation and integration are extended to include differential equations and multivariable calculus.
On this module you will learn:
Differentiation: derivative as slope and rate of change, standard derivatives; product, quotient, function of a function rules; implicit, parametric and logarithmic differentiation; maxima / minima, curve sketching; Maclaurin's and Taylor's series.
Integration: standard integrals, definite integrals, area under a curve; using substitution, partial fractions and by parts; applications (eg volumes, r.m.s. values).
Ordinary differential equations: Solution by direct integration. Solution of first order equations by separation of variables and use of an integrating factor. Solution of homogeneous and non-homogeneous second order equations with constant coefficients.
Functions of several variables: partial differentiation, Taylor's series in two variables, total first order change, analysis of errors, total rate of change, change of variables; stationary points, maxima / minima / saddle points of functions of two variables.
Method of Lagrange Multipliers: constrained maxima / minima, classification of stationary points.
Multiple integrals: double and triple integrals, change of order of integration, use of polar coordinates, simple applications.