Course Title: Numerical Solutions of DEs

Part A: Course Overview

Course Title: Numerical Solutions of DEs

Credit Points: 12.00

Course Code




Learning Mode

Teaching Period(s)


City Campus


145H Mathematical & Geospatial Sciences


Sem 1 2006,
Sem 1 2007,
Sem 1 2008,
Sem 1 2009,
Sem 2 2010,
Sem 2 2011,
Sem 2 2012,
Sem 2 2013,
Sem 2 2014,
Sem 2 2015

Course Coordinator: Dr John Gear

Course Coordinator Phone: +61 3 9925 2589

Course Coordinator Email:

Course Coordinator Location: Building 8, level 9, room 21

Pre-requisite Courses and Assumed Knowledge and Capabilities

MATH1142 Calculus 1
MATH1144 Calculus 2
Or equivalent first year university mathematics courses.
MATH2109 or any equivalent course that gives basic knowledge in programming with Maple, Mathematica or MatLab.


Assumed Knowledge:

  • Ability to formulate and solve differential equations.
  • Ability to recognize the properties of matrices; solve linear systems; calculate determinants of matrices; find eigenvalues and eigenvectors.
  • Ability to create a Taylor series approximation to a function of one variable.
  • Knowledge of one of the following symbolic manipulation packages: Maple or Mathematica or knowledge of MatLab.
  • Skill in writing a simple program in either: Maple or Mathematica or MatLab.

Course Description

This course introduces and studies advanced numerical techniques used in the solution of Partial Differential Equations. The course introduces the methods and tools necessary for the Finite Difference Method (FDM) solution and the Finite Element Method (FEM) solution of real world problems from various scientific and engineering fields.

Modern mathematics software packages, such as Maple or Mathematica or Matlab and industrial engineering simulation software ANSYS will be used in the computing laboratory to support the course.

Objectives/Learning Outcomes/Capability Development

This course contributes to the following Program Learning Outcomes for BP083 Bachelor of Science (Mathematics):

Knowledge and technical competence

  • use the appropriate and relevant, fundamental and applied mathematical and statistical knowledge, methodologies and modern computational tools.


  • synthesize and flexibly apply knowledge to characterize, analyze and solve a wide range of problems
  • balance the complexity / accuracy of the mathematical / statistical models used and the timeliness of the delivery of the solution.


  • communicate both technical and non-technical material in a range of forms (written, electronic, graphic, oral) and tailor the style and means of communication to different audiences. Of particular interest is the ability to explain technical material, without unnecessary jargon, to lay persons such as the general public or line managers.

On successful completion of this course you should be able to:  

  1. Implement a variety of explicit and implicit finite difference methods/schemes (FDM) for solving parabolic, elliptic and hyperbolic partial differential equations; identify efficient ways of structuring computations and  explain the impact of criteria such as convergence, consistency and stability for evaluating the usefulness of a scheme.
  2. Elaborate the theoretical basis of the Finite Element Method (FEM) and employ a range of techniques to validate finite element simulations.
  3. Solve a variety of typical scientific and engineering problems using ANSYS to build the FEA (finite element analysis) and CFD (computational fluid dynamics) models and
  4. Implement a variety of numerical methods for the solution of Partial Differential Equations using Maple or Mathematica or Matlab and ANSYS,
  5. Report in concisely in written form the method used, the implementation and the results obtained.
  6. Discuss the accuracy of technical computations and results and describe the relevance of issues such as appropriateness of the mathematical model, sources of error in the numerical simulations and computational efficiency. 

Overview of Learning Activities

This course is presented using a mixture of classroom instruction; problem-based tutorial classes; exercises; WebLearn quizzes and tests and programming assignments.

Primarily you will be learning in face-to-face lectures.  An online course site will be used to disseminate course materials, and to provide you access to self-assessment quizzes and tests. Five topics will be featured: Direct solution of systems of linear equations; Iterative solution of systems of linear equations; Solution of partial differential equations: finite difference methods; Solution of partial differential equations: finite element methods; and Introduction to ANSYS.

The underlying theories and their applications will be explained and illustrated in lectures. Computational laboratory sessions will reinforce the material covered in lectures and in each student’s personal study. The laboratory sessions are designed to assist understanding. Computer programming tasks will reinforce the theory presented in lectures. Practice and example worksheets will support the programming tasks and facilitate the skills required to complete these tasks. Programming assignments will be completed using the symbolic manipulation package Maple or Mathematica or Matlab and the industrial engineering FEA & CFD package: ANSYS.

WebLearn quizzes are designed to provide instant feedback and can be attempted repeatedly until proficiency in the learning objectives is achieved. You should aim to master each WebLearn quiz before attempting the corresponding WebLearn test.WebLearn quizzes are provided for formative assessment purposes. WebLearn tests are for summative assessment purposes (counted towards your overall assessment result).

Programming assignments are designed to make you aware of efficient ways to structure your computations and appreciate criteria such as convergence, rate of convergence and accuracy. The programming assignments will be supported by Mathematica notebooks, Maple worksheets, Matlab example sheets and guides on how to use ANSYS.

Topic based exercises are available to help you obtain proficiency in the course content.

Typical exam style questions are provided to assist in your preparation for the final examination.

Overview of Learning Resources

The blackboard site links to the Googlesite where you will find:

  1. Teaching schedule and guide to WebLearn tests.
  2. Assessment guide and assessment schedule.
  3. Programming Assignments
  4. Course notes.
  5. Recommended references
  6. Topic exercises and answers
  7. Sample exam papers
  8. Maple demonstration documents, worksheets and introductory worksheet.
  9. Matlab demonstration documents and videos
  10. Mathematica demonstration documents and introductory notebook

A library guide is available at

Overview of Assessment

Assessment Tasks:


Assessment Task 1:  Web Learn Tests (x 4 on-line)

Weighting 15 %

This assessment task supports CLOs 1, 2, 3 & 4.


Assessment Task 2: Open Book Mid-semester Test

Weighting 15%

Textbooks, lecture notes, exercise solutions and sample test solutions allowed.

This assessment task supports CLOs 1, 2, 3 & 4.

Assessment Task 3: Assignments (x4)

Weighting 2 x 6% and 2 x 9% = 30%

This assessment task supports CLOs 1, 2, 3, 4, 5,6

Assessment Task 4: Final Examination (Open Book) 
Weighting 40%
This assessment supports CLOs 2, 3 & 4.