Text and Reference Books

- P. V. O’Neil, Advanced Engineering Mathematics, Latest or Any Ed., PWS.

- E. Kreyszig, Advanced Engineering Mathematics, Latest or Any Ed., Wiley.

Lectures

- Lectures will follow closely (but not 100%) the materials in the lecture notes, which are available at this web site.

- However, certain parts of the materials will not be covered and examined and this will be made known during the classes.

- Attendance is essential.

- ASK any question at any time during the lecture.

Tutorials

- The tutorials will start on Week 4 of the semester.

- Although you should make an effort to attempt each question before the tutorial, it is NOT necessary to finish all the questions.

- Some of the questions are straightforward, but quite a few are difficult and meant to serve as a platform for the introduction of new concepts.

- Tutorial Set 2 is an interactive one. You are required to come out with your own solutions.

- ASK your tutor any question related to the tutorials and the course.

Examination

- The examination paper is 2-hour in duration.

- You will be allowed to bring with you an A4 sheet (both sides) of formulae into the exam hall.

- To prepare for the examination, you may wish to attempt some of the questions in exams held in previous years (no solutions to these problems will be given out to the class).

- However, note that the topics covered may be slightly different and some of the questions may not be revelant. Use your own judgement to determine the questions you should attempt.

Interactive Tutorial

- Your performance in
the interactive tutorial will consists 10% of your final grade.

Final Grade

- Your final grade in
the Part 1 (FG1) of this course will be computed as follows:

- FG1 = Interactive
Tutorial Marks (max. = 5) + 90% of Exam Marks (max. = 50)

FG (Grand Total) = FG1 + Your score from Part 2

Course Outlines

Sequences and series; convergence and divergence; a test for divergence; comparison tests for positive series; the ratio test for positive series; absolute convergence; power series.

Bessel’s equation and Bessel functions; the Gamma function; solution of Bessel’s equation in terms of Gamma function; Modified Bessel’s equations; Applications of Bessel’s functions;

**3. Legendre's Equation
and Legendre Polynomials**

Legendre’s equation;
Legendre polynomials and their properties.

**4. Partial Differential
Equations**

Boundary value problem
in partial differential equations; wave equation; heat equation; Laplace
equation; Poisson’s equation; Dirichlet and Nuemann Problems. Solutions
to wave and heat equations using method of separation of variables.