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ZUG2025 - Differential and Integral Calculus

Undergraduate – Module

Refer to the specific census and withdrawal dates for the semester(s) in which this module is offered.


Business, Engineering and Technology


South Africa

  • Semester 1, 2019
    On-campus block of classes
    (Mainstream & Extended Programme)

12 credits, NQF Level 6


The module aims to provide the students with an ability to work with the methods and applications of multi variable differential and integral calculus such as vector calculus, differential equations and linear algebra so that they can be able to apply these concepts successfully in solving simple to complex engineering problems. In addition this module equips the students with the ability to interpret and apply directional derivatives, as well as double, triple, line and surface integrals, including the basic integral theorems of multi-variable functions.


On completion of the module, students will be expected to be able to:

1Understand the use of complex variables and functions
2Find bases for spaces arising from matrices or linear equations
3Understand and apply the theory of diagonalisation
4Perform calculations on differential equations
5Apply the theory of series, power series and Fourier series
6Understand the differential operators: grad, div and curl and some applications
7Apply tangent planes and normal vectors to surfaces
8Understand multiple integrals
9Apply appropriate theorems in integral equations


Coursework assessment: 30%
Examination: 70%

Workload requirements

The objective of this module is to enable the students to have a very good conceptual and visual understanding of the fundamentals of the mathematics of multi-variable functions and vector calculus. It provides them with the skill to have a professional approach in solving mathematical problems so that they can be able to perform calculations with the logic and precision that is often required in complicated engineering problems. There will be a combination of lectures, that will include interactive elements, and tutorial work that will be done on an individual basis. All outcomes will be assessed by means of tutorials, class tests and a final examination.

Chief examiner(s)





Basic Mathematical Concepts, Advanced Mathematical Concepts