SyllabusTHE UNIVERSITY of LIVERPOOL MATH192 :  Mathematics II for Electrical Engineering SYLLABUS  2008 ------ Department of Mathematical Sciences   1. Methods and applications of integration: 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. 2. Partial differentiation: 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 3. Matrices and determinants: 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. 4. Vector applications: 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. 5. Ordinary differential equations (O.D.E.s): 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. 6. Fourier series: Periodic waveforms, orthogonality, calculation of Fourier coefficients.   Reference Books: 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) Assessment: 80% 'Exam 20% Continuous assessment  (10% from worksheets, 10% from class test in March in week 7 - no other lectures in week 7). Total of 36 lectures - 12 tutorials Prof. Ke Chen