**Galerkin Finite Element Method**

The module provides an introduction to weighted residual methods which form the basis of the finite element method which is extensively used in Civil Engineering practice. One- and two-dimensional heat conduction problems are used to explain the principles of weighted residuals and the problems are solved by means of finite elements. The first part of the module is a short introduction to Taylor polynomials, Taylor’s theorem and some applications.

**Module Information**

- 38571 252 (8) Engineering Mathematics 252
- Second year, second semester of the Program in Civil Engineering.
- Two lectures and one tutorial of 1 hour per week.
- Prerequisite pass modules (PP³50): Engineering Mathematics 145 or Engineering Mathematics 214; Prerequisite module (KP³40): Engineering Mathematics 214.

**Lecturer**

- Dr A Keet: Office: 1010A , Industrial Psychology/Mathematics Building: (e-mail: keetap@sun.ac.za)

**Learning Material**

- Class notes are provided.

**Module Content**

- Class notes: Taylor’s Theorem
- Class notes: Methods of weighted residuals and Finite Elements.

**Learning Opportunities**

- The course material is dealt with in detail during the lectures. Tutorials provide the opportunity to work on problems and discuss coursework under supervision of the lecturer.

**Assessment**

- Method: Obtain class mark (KP³40) and pass exam (final mark PP³50).
- The class mark is determined by short tests during the tutorial periods (30%), and the class test (70%). An additional test will take place during the fourth term; the mark obtained for this test is averaged with that of the formal class test.
- Formula for final mark: PP = 0,4 KP + 0,6 EP.
- The date and time of the class test and the additional test are determined by the Faculty of Engineering (http://www.eng.sun.ac.za), and those of the examination are published on the University’s website (myMaties). For more information on exam regulations see the University Calendar, Parts 1 and 11.
- Tutorial tests are graded and returned within one week, and the class test is returned during the week following the mid-semester break.

**Study Hints**

- It is important that you understand the basic concepts very well, so that you are able to apply the theory.
- To determine whether you have mastered the course material, you must complete all homework problems as well as all tutorial exercises.
- You are welcome to consult your lecturer if there is anything which you do not understand, or if you get stuck with a problem. The lecturer will be available right after each lecture, as well as in his/her office (preferably by appointment).
- Revise each section completely as soon as it has been discussed in class. It is important that you do not fall behind, since it is very difficult to catch up.

**Rationale**

The module is presented as part of the Program in Civil Engineering and offers basic training in Mathematics which is necesary for the successful completion of other modules within this Program. The module supports the Program outcome that graduates should be able to use their knowledge of mathematics to solve engineering problems.

**Learning Outcomes**

After completing this course, students should be able to:

- Find the Taylor polynomials of elementary functions; is acquainted with Taylor’s theorem and some elementary applications.
- Understand weighted residual techniques, in particular the Galerkin method, to solve boundary value problems for ordinary and simple partial differential equations; can set up die Galerkin equations using first-order basis functions.