Mathematics for Chemical Engineering
taught at Imperial College 2003/04

Examination information

Distribution of topics between the two Part I papers in the First Year Engineering Maths Examinations:
Paper 1 covers calculus of ONE variable (differentiation, integration, limits, curve sketching, Taylor series, etc). Also complex numbers and hyperbolic functions.
Paper 2 covers all other topics.

Formulae sheet (issued in the exam)

Current problem sheets

Sheet 7 (1st order ODE's)
Sheet 8 (mainly 2nd order ODE's)
Sheet 9 (mainly power series)

Solutions to problem sheets

(courtesy Dr David Herbert)
Sheet 1
Sheet 2
Sheet 3
Sheet 4
Sheet 5
Sheet 6
Sheet 7
Sheet 8
Sheet 9
Sheet 10

Current lecture notes

Part 5 (Second order linear ODE's)

Aims

To ensure that students acquire the mathematical knowledge and skills required for their first year chemical engineering courses. Also, to provide a basis for the more advanced techniques to be introduced in the 2nd year mathematics course, and which are required later.

Syllabus

VECTOR ALGEBRA AND GEOMETRY (approximately 6 lectures): Basic rules, Cartesian coordinates, scalar and vector products. Applications to geometry, equations of lines and planes, triple products, linear dependence.
MATRIX ALGEBRA (approximately 12 lectures): Double suffix notation, basic rules, transpose, symmetric, diagonal, identity, triangular, inverse and orthogonal matrices. Determinants: basic properties, Cramer's rule. Elementary row operations, linear dependence, Gauss-Jordan method, Gaussian elimination, LU factorization. Eigenvalues and eigenvectors, reduction of matrices to diagonal form.
ORDINARY DIFFERENTIAL EQUATIONS (approximately 12 lectures): First order equations, separable, homogeneous, exact, linear. Second order linear equations, reducible to first order, with constant coefficients, with series solution. Damped and forced oscillations. Simple non linear ODEs: critical points and stability, qualitative nature of the solutions.

Textbooks for reference

Glyn James: Modern Engineering Mathematics, 3rd edition, Pearson, 2003.
Dominic Jordan and Peter Smith: Mathematical Techniques, Oxford University Press, 2002.
Ken Stroud: Engineering Mathematics, 5th edition, Palgrave MacMillan, 2001.

Last updated 03/06/04