**Further Differential and Integral Calculus**

The Calculus of this module is a continuation of that of Engineering Mathematics 115. The following topics are covered: Hyperbolic functions; L’Hospital’s rule; more integration techniques; simple differential equations (separable and first order linear); parametric equations; polar coordinates and polar graphs; conic sections; quadratic surfaces and functions in two variables; complex numbers; matrix algebra.

**Module Information**

- 38571 145 (15) Engineering Mathematics 145
- Year 1, semester 2 of the Programmes in all engineering disciplines.
- Lecturing load: 5 lectures, 1 tutorial of 2 hours per week.
- Prerequisite: Engineering Mathematics 115.
- Language specification : A & E

**Lecturers**

- Ms L Wessels: Office 1009BD, Industrial Psychology/Mathematics Building (e-mail: lwessels@sun.ac.za)
- Dr C Naude: Office 1023A, Industrial Psychology/Mathematics Building (e-mail: cnaude@sun.ac.za
- Prof M Wild: Office 1023D, Industrial Psychology/Mathematics Building (email: mwild@sun.ac.za)
- Dr D Ralaivaosaona: Office 3004, Industrial Psychology/Mathematics Building (e-mail: naina@sun.ac.za)

**Study Material**

Prescribed textbooks:

- James Stewart,
*Calculus*(7^{th}Edition). Chapters 6,7,9,10,12,14 are covered. - Dennis G Zill/Warren S Wright,
*Advanced Engineering Mathematics*(4^{th}Edition). Chapters 8 and 17 (selected topics). - Class notes on Weierstrass substitution and rationalising substitution.

**Learning Opportunities**

- The learning material is fully covered during the lectures.
- During the tutorial periods students have the opportunity to solve problems under supervision and to obtain assistance with regard to aspects that may be unclear.
- Solutions to class problems or interesting and/or more difficult problems appear from time to time on SunLearn.

**Assessment**

- The assessment follows the general rules of the Faculty of Engineering. The final mark for this course consists of the following:
- Semester Mark (SM): Average mark of the tutorial tests that are written every Thursday.
- Assessment opportunity A1
- Assessment opportunity A2
- The mark is calculated as follows: Final mark (FM) = 0.2 x SM + 0.3 x A1 + 0.5 x A2
- A third assessment opportunity A3 is offered for students who miss opportunity A1 or A2 because of illness or some other valid reason, and for students with a final mark between 40 and 50.
- Students have to obtain at least 40 in either A2 or A3 to pass.

**General Information**

- Please note the following arrangements with regard to tutorials: (a) Attendance of all tutorials is compulsory, also for students who are repeating the course. (b) Students who are repeating the course and who have tutorial clashes with another (second-year) tutorial or practical class, must make arrangements to write the tutorial tests during the tutorial sessions.
- Pocket calculators may not be used in tests and examinations.

**Study Tips**

- It is important that you understand the basic theory well so that it can be applied. You should therefore first study the definitions and theorems thoroughly.
- In order to determine whether you have mastered the work, you should regularly do a variety of problems from the
*Exercises*in the textbook. The lecturer may highlight a number of these problems during the lectures, but they remain your own responsibility and will not be marked. - Feel free to ask your lecturer for assistance if you do not understand something or are stumped by a problem. The lecturer is available immediately after the end of each class, as well as in his/her office (preferably by appointment).
- Revise each paragraph fully after it has been dealt with in class. Make sure that you do not fall behind, as it is very hard to catch up later.

**Outcomes**

A student who has passed this module should possess the following skills:

- Is able to continue with ease with the Engineering Mathematics prescribed in the second year for the programmes concerned.
- Is able to recognise and apply indefinite integration techniques.
- Understands and can apply other aspects of Calculus, as set out in the module contents above.
- Understands complex numbers and complex functions.
- Is able to do matrix algebra and solve systems of linear equations.