Dr. Sean Stewart and Dr. Geluk's courses.
- A first course in linear algebra covering the basic concepts and
algebra of matrices, special and inverse matrices, linear systems of
equations, determinants and their properties; vector spaces,
subspaces, row, column, and nullspaces, linear independence, basis,
dimension, and rank of a matrix; matrix and properties of linear
transformations, change of base; eigenvalues and eigenvectors,
diagonalisation of matrices; inner products, orthogonality,
orthonormal bases and the Gram-Schmidt process. Applications of the
mathematics to a number of situations important to both engineering
and science will be made. - Write a concise and interesting paragraph here that explains what this course is about
A second course in mathematics covering some techniques of integration, parametric equations and polar coordinates; sequences and series including infinite series, alternating series, tests for convergence, and Taylor and Maclaurin series; matrices with eigenvalues and eigenvectors, determinants; vectors in both two and three dimensions, planes and surfaces, curves and arc length, and vector-valued functions with their derivatives and integrals. Applications of the material to a number of physical situations relevant to both science and engineering will be made.
A third course in calculus covering sequences and series including infinite series such as Taylor and Maclaurin series. Methods of solution to first-order differential equations. Vector calculus including vector fields, line and surface integrals, Green's, Stokes' and the divergence theorem. Applications of the mathematics to a number of physical situations important to both science and engineering will be made.
A first course in calculus covering the concepts of a limit, continuity and differentiable. Rules for differentiation and applications to rates of change problems. Rolle's theorem, intermediate value theorem and the mean theorem. Calculus of the fundamental transcendental functions such as the trigonometric and inverse trigonometric functions, logarithmic and exponential functions, the hyperbolic and inverse hyperbolic functions. Maxima and minima problems, optimisation problems. The definite and indefinite integral, the fundamental theorem of calculus. Techniques of integration, numerical integration, application of integration to arc lengths, areas and volumes (by slices and shells). Applications of the mathematics to a number of physical situations important to both science and engineering will be made.
A first course in ordinary differential equations covering methods of solution to first-order equations. Methods of solution of second-order linear equations. Series solutions to differential equations including the method of Fröbenius. Some special functions including the gamma, error, and Bessel functions. Laplace transforms and the convolution theorem. Linear systems of differential equations. Applications of the mathematics to a number of physical situations important to both science and engineering will be made.
An advanced course in mathematics covering topics pertaining to engineering. Topics covered include complex numbers and functions, modulus-argument form and the Argand diagram; some special functions including the gamma and beta functions, the incomplete gamma functions, error and complementary error functions, and the Lambert W function; Fourier series, Fourier sine and cosine series, complex Fourier series, Fourier sine and cosine ransforms and the complex Fourier transform, Parseval and convolution theorems; partial differential equations, analytical methods of solution including separation of variables, Fourier series and Fourier transform methods with applications to the wave and heat equations.
