1. To provide a detailed introduction to techniques (change of variable, integration by parts and partial fractions) for and applications of one-dimensional integrals.

2. To introduce partial derivatives of functions of two variables and their applications, e.g., for linear approximations.

3. To comprehensively introduce matrices, determinants and several techniques for solving systems of linear equations; to introduce eigenvalues and eigenvectors for 2x2 matrices.

4. To briefly revise or introduce the scalar and cross products of vectors and their basic applications.

5.To give a comprehensive introduction to first-order ordinary differential equations (ODEs), including systems of two ODEs with constant coefficients, and second-order ODEs with constant coefficients.

6.To introduce, time permitting, the Fourier expansion of periodic functions.

(LO1) Learning outcomes  After completing the module students should be able to  *  evaluate a range of one-dimensional integrals using standard techniques  *  calculate partial derivatives and find the tangent plane to a surface  *  invert 3x3 matrices and solve systems of linear equations   *  solve basic (systems of) ODEs relevant to electrical engineering

Methods and applications of integration: 8 lectures

Partial differentiation and applications: 3 lectures

Matrices, determinants, linear equations: 8 lectures

Products and applications of vectors: 3 lectures

Basic ordinary differential equations: 8 lectures

Fourier expansion of periodic functions: 3 lectures

Tutorials, class test, exam revision: 15 hours