Syllabus THE
of
SYLLABUS 2008 ------ Department of Mathematical Sciences
Introduction. Elementary integration. Definite and indefinite integrals. Techniques of integration: by parts, change of variable and partial fractions. Improper integrals. Applications to areas, average, root mean square, areas and volumes of revolution.
Introduction. Functions of more than one variable. Partial derivatives. Higher order derivatives, equality of mixed derivatives. Differentials, application to simple maximum error estimates. The chain rule, simple change of variable examples
Notation. Matrix algebra: addition, multiplication and transposition. Zero, identity and inverse matrices. Matrix equations. Determinants. Cramer's rule for solution of linear equations. Calculation of the inverse matrix. Gaussian elimination: application to solution of linear equations and determinants.
Scalars and vectors, Vector addition. Basis vectors and components. Scalar product. Vector product. Triple scalar product, co-planarity. Differentiation of vector- functions. Extension of product and chain rules.
Introduction. Initial and boundary conditions. First order equations, separation of variables and integrating factor. Second order linear equations. Second order linear equations with constant coefficients, complementary function and particular integrals.
Periodic waveforms, orthogonality, calculation of Fourier coefficients.
l ``Modern Engineering Mathematics", Glyn James, 3rd edition, Prentice Hall (2001) l ``Engineering Mathematics", Croft. Davison, Hargreaves, 2nd edition, Addison-Wesley (1996) l ``Engineering Mathematics", C. W. Evans, 2nd edition, Chapman & Hall. (1992)
(10% from worksheets, 10% from class test in March in week 7 - no other lectures in week 7).
Prof. Ke Chen |