Mathematics 5B

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Laurent series, region of convergence. Residue theorem. Laplace transforms. Fourier transforms. Z-transforms. Difference equations. Convolution of sequences, using Z-transform to solve difference equations. Wave equation and its solution on a half-line. Laplace and Poisson equation. Bessel functions. Introduction to statistics. Histogram, empirical distribution functions. Means and variance, correlation and covariance.

Requirements:

Syllabus of lectures:

1. Laurent series, region of convergence

2. Residue theorem

3. Laplace transforms

4. Fourier transforms

5. Z-transforms

6. Difference equations

7. Convolution of sequences, using Z-transform to solve difference equations

8. Wabe equation and its solution on a half-line

9. Laplace and Poisson equation

10. Bessel functions

11. Introduction to statistics

12. Histogram, empirical distribution functions

13. Means and variance, correlation and covariance

Syllabus of tutorials:

1. Laurent series, region of convergence

2. Residue theorem

3. Laplace transforms

4. Fourier transforms

5. Z-transforms

6. Difference equations

7. Convolution of sequences, using Z-transform to solve difference equations

8. Wabe equation and its solution on a half-line

9. Laplace and Poisson equation

10. Bessel functions

11. Introduction to statistics

12. Histogram, empirical distribution functions

13. Means and variance, correlation and covariance

Study Objective:

Study materials:

[1] There is no text-book covering the course completely. The lecturer will hint resources to particular topics.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: