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ZUG2031 - Advanced 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 2, 2019
    On-campus block of classes
    (Mainstream & Extended Programme)

12 credits, NQF Level 6


This module is a continuation of the Differential and Integral Calculus module, offered in semester 1, and it aims at providing students with advanced knowledge of the theory and application of Laplace and Fourier transforms, special and analytic functions, boundary value problems involving partial differential equations. It further enhances the students’ knowledge of integral calculations by introducing him to complex variables, surface and volume integrals as well as integral theorems of Gauss and Stokes.


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

1Understand and apply theory of Laplace transforms
2Understand and apply theory of Fourier transforms
3Understand the meaning of special functions and analytic functions
4Solve boundary value problems
5Understand complex variables involving conformal transformations & Ideal flow in the plane
6Solve problems involving surface and volume integrals
7Perform calculations on integral theorems like Gauss’ and Stokes’ theorems


Coursework assessment: 30%
Examination: 70%

Workload requirements

The module equips the students with an ability to use the mathematics of Transforms and Special Functions, including complex variable and integral theorems to formulate and solve problems in calculus in a way that will enable them to extend the application of these transforms, functions and theorems to advanced and specialist modules in engineering.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 tutorial work, class tests and a final examination.

Chief examiner(s)





Differential and Integral Calculus