**Mathematics for the Biological Sciences**

The aim of this module is to introduce the basic ideas behind differentiation and integration of functions. The first part of the module concerns functions in general, limits and continuity, derivatives, applications of derivatives (such as the sketching of graphs and optimisation) and the chain rule for derivatives. After that comes the exponential and logarithmic functions together with exponential growth models. Then the following topics are discussed: the definite integral and some of its applications, for example, the evaluation of areas and averages of populations, differential equations, with emphasis on separation of variables and logistic growth models. The techniques of integration discussed are substitution and integration by parts.

**Module Information**

- 21547 124 (16) Mathematics (Bio) 124
- Academic year 1, semester 1 of the Programme in the Biological Sciences.
- Lecture load: 4 lectures and one tutorial of 2 hours per week.
- Language specification : A & E
- There are three time table groups for Mathematics (Bio) 124:

**Group 1**, subdivided into 1A (Afrikaans) and 1B (English)

**Group 2**, subdivided into 2A (Afrikaans) and 2B (English)

**Group 3**, subdivided into 3A (Afrikaans) and 3B (English)

**Lecturers**

- Dr AP Keet, Industrial Psychology/Mathematics Building 1010A, keetap@sun.ac.za
- Dr C Naude, Industrial Psychology/Mathematics Building 1023A, cnaude@sun.ac.za
- Prof H Prodinger, Industrial Psychology/Mathematics Building 1028, hproding@sun.ac.za
- Ms LK Wessels, Industrial Psychology/Mathematics Building 1009B, lwessels@sun.ac.za

**Learning Material**

- L.D. Hoffmann and G.L. Bradley: APPLIED CALCULUS for Business, Economics, and the Social and Life Sciences (10th Expanded Edition), McGraw-Hill, 2010.

**Module Contents**

- Chapter 1, Functions, Graphs and Limits.
- Chapter 2, Differentiation; Basic Concepts.
- Chapter 2, Additional applications of the derivative.
- Chapter 4, The exponential and natural logarithmic functions.
- Chapter 5, Integration.
- Chapter 6, Additional Topics in Integration.
- Appendix A.
- Chapter 8.
- Chapter 11.

**Learning Opportunities**

- The learning material is completely 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.
- Method: Obtain class mark (CM40) and pass exam (final mark FM50).
- The class mark is determined by short compulsory tests at the end of the tutorial periods, a mini-class test, together with the official class test .
- Formula for final mark: FM= 0,4 CM + 0,6 EM, where EM is the exam mark.
- The dates and times of the class test and exam are published on Blackboard. For more information on exam regulations, see the Yearbook of the University, Parts 1 and 5.
- The short tutorial tests are graded and returned within one week, and the class test as soon as possible. Final marks (FM) are made known on the dates as officially determined by the Year Program of the University.

**General Information**

- Please note the following in connection with the tutorial classes: (a) Attendance at all tutorials is compulsory, also, in particular, for students repeating the course. (b) You may not make any other appointments (academic or otherwise) during tutorial periods. (c) Students who do not attend the tutorials in full or who do not write the tutorial tests, will not be allowed to write the examinations, unless they inform the lecturer beforehand of special circumstances and obtain the permission of the lecturer.
- Calculators are not allowed in the official class test and examinations.

**Hints for Studying**

- To succeed in this module it is essential that you work regularly on your own, practising the techniques and applying the results taught in lectures. Make sure that you understand and know the definitions on which the work is based.
- To test whether you are succeeding, you have to do a selection of problems from the
*Exercises*in the textbook regularly. - Ask the lecturer if you get stuck or do not understand. The lecturer is available after each lecture and in his/her office.
- Review each lecture in your textbook as soon as possible. It is difficult to catch up if you start lagging.

**Rationale**

This module is presented within the Programme in the Biological Sciences. It contributes to providing a basic training in Mathematics and is one of the core modules required in order to successfully complete the other modules in this Programme.

**Outcomes**

A student who has passed this module should:

- Understand the basic concepts of functions and limits, be able to use and apply differentiation, and know differentiation techniques such as the chain rule and implicit differentiation.
- Understand concepts regarding the exponential and logarithmic functions and be able to apply these functions in exponential growth and decay models.
- Be able to apply the definite integral in a variety of cases, and be able to handle integration techniques such as substitution and integration by parts.
- Be able to solve basic differential equations.