Department of Mathematical Sciences



Introductory Differential and Integral Calculus

This module deals mainly with Calculus. The following topics are covered: Number systems; inequalities and absolute values; functions; mathematical induction; the binomial theorem; differentiation and applications (graphs, optimisation, Newton’s method, etc.); indefinite and definite integrals; integration techniques (substitution); inverse functions; exponential and logarithmic functions.

Module Information

  • 38571 115 (15) Engineering Mathematics 115
  • Year 1, semester 1 of the programmes in all Engineering disciplines.
  • Lecturing load: 5 lectures, 1 tutorial of 2.0 hours per week.
  • Language specification : A & E


  • Prof W Wagner, Office 1008D, Industrial Psychology/Mathematics Building (e-mail:
  • Dr C Naude Office 1023C, Industrial Psychology/Mathematics Building (e-mail:
  • Prof M Wild, Office 1023D, Industrial Psychology/Mathematics Building  (e-mail:
  • Dr D Ralaivaosaona, Office 3004, Industrial Psychology/Mathematics Building (e-mail:

Learning Material

  • Prescribed textbook: James Stewart, Calculus (7th Edition).
  • Additional class notes on certain topics.
  • Selected paragraphs from Appendices A and D and Chapters 1 to 7 are covered.

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 tutorials appear from time to time on SunLearn.

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 × SM + 0,3 × A1 + 0,5 × 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.  Failing to do so will result in the student not being allowed to write the examinations.
  • 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 will 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 usually available immediately after the end of each class, as well as in his/her office (preferably after an 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.


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

  • Understands the basic concepts of interval notation, absolute values, solving inequalities of real numbers.
  • Must be able to do demonstrations by means of induction and to handle the binomial theorem.
  • Understands concepts relating to functions of one variable: definition sets, limits of functions, continuity of functions.
  • Is able to induce and to apply all differentiation rules and formulas.
  • Knows and is able to apply indefinite integration techniques (substitution).
  • Is able to perform applications of both differentiation and integration (see the Module Contents above in this regard).