**Analysis and Linear Algebra**

The course material is divided into two sections:

**Section A: Analysis**

- Improper integrals
- Sequences and series
- Ordinary differential equations

**Section B: Linear Algebra **

A follow-up to the Linear Algebra part of Mathematics 214, concentrating on the theory and applications of eigenvalues, quadratic forms and linear transformations.

**Module Information**

- 21539 244 (16) Mathematics 244
- Academic year 2, Semester 2 of the Programme in the Mathematical Sciences.
- Lecture load: 4 lectures and one tutorial of 2 hours per week.
- Module prerequisites: A class mark of at least 40% for Mathematics 214.
- Language specification : A

**Lecturers**

- Prof L van Wyk: Office 1023E, Industrial Psychology/Mathematics Building (e-mail: lvw@sun.ac.za)
- Prof S Mouton: Office 1023B, Industrial Psychology/Mathematics Building (e-mail: smo@sun.ac.za)

**Learning Material**

- Section A: Calculus, Seventh Edition. J. Stewart. Brooks/Cole Cengage Learning, 2012 (as well as notes on the Web).
- Section B: Elementary Linear Algebra: Applications Version, 11th Edition. Anton, Rorres. John Wiley, New York, 2015.

**Module Contents**

See summary.

**Learning Opportunities**

The learning material is covered during the lecture periods. During the tutorial periods problems are solved under supervision. The solutions of tutorial problems are made available within one week after the tutorial.

**Assessment**

Your class mark will be the average of your marks for the two midsemester tests. There will be no opportunity to rewrite a test (i.e. there will be no “valskermtoetse”). To obtain permission to write the exams, you require a class mark of at least 40%. To pass the course, you need a final mark of at least 50%.

**General Information**

- Please take note: (a) It is compulsory to attend all tutorials. (b) Do not make other appointments during tutorial periods.
- No scientific calculators will be allowed in tests and exams.

**Rationale**

This module is presented within the Programme in the Mathematical Sciences. It contributes to providing a basic training in Mathematics, and is one of the core modules that is a prerequisite for some other modules.

**Outcomes**

A student who passed this module should be equipped with the following skills:

Section A:

- A basic knowledge of improper integrals of the first and second kind; convergence tests for improper integrals, application thereof in the theory of gamma and beta functions.
- A basic understanding of sequences and series: limits, convergence, convergence tests, Taylor’s theorem, power series.
- Properties and techniques of solving elementary first and second order differential equations. Applications of differential equations in practical problems.

Section B:

- Understands basic principles of eigenvalues, eigenvectors, simultaneous orthogonal bases, quadratic forms;
- Can compute eigenvalues and eigenvectors of small matrices;
- Can solve constant-coefficient systems of differential equations;
- Can diagonalize symmetric matrices;
- Can express and manipulate a quadratic form in matrix notation.

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