35335 Mathematical Methods
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particular session, location and mode of offering is the authoritative source
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Subject handbook information prior to 2023 is available in the Archives.
Credit points: 6 cp
Result type: Grade and marks
Requisite(s): 35231c Differential Equations
The lower case 'c' after the subject code indicates that the subject is a corequisite. See definitions for details.
Description
This subject introduces students to the advanced techniques that are used to formulate and solve problems in the physical and biological sciences, as well as problems in finance and economics, in the form of partial differential equations and boundary value problems. Topics include: Sturm–Liouville theory; vector integral theorems; special functions; Bessel and Legendre equations with applications to boundary value problems; integral transform methods; and Green's functions.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | proficiency in solving problems in pure and applied mathematics by vector calculus methods; |
|---|---|
| 2. | proficiency in the mathematical techniques needed in solving boundary value problems for differential equations; |
| 3. | an understanding of the Sturm-Liouville approach to differential equations and how it leads to eigenfunction expansions for solutions of boundary value problems, including the role played by special functions; |
| 4. | the ability to model physical problems in terms of differential equations and an appreciation of the role of integral transform theory in the solution of differential equations; |
Contribution to the development of graduate attributes
By giving a broad introduction to the most important and widely used concepts in mathematics, this subject links directly to the graduate attribute “Disciplinary knowledge and its appropriate applications”. Throughout the course mathematics is presented as a tool, which students are invited to use in the solution to real-world problems. This subject thereby contributes to the graduate attributes “An Inquiry-oriented approach” and “Professional skills and their appropriate application”.
Teaching and learning strategies
Lectures: two hours/week
Problem Class: two hours/week
Content (topics)
A flexible selection from the following topics, dependent on students' interests and depth of coverage
- Sturm-Liouville theory
- Solution of PDEs by characteristics
- Vector calculus and PDEs
- Series solutions of linear equations: Bessel's equation and Legendre's equation, Review of orthogonal functions and Fourier series.
- Continuous eigenvalues and Fourier Integrals
- Integral transform methods for PDEs
- Green's function methods for PDEs
Assessment
Assessment task 1: Assignment 1
| Intent: | To develop ability in modelling physical problems and competence in using computer code to solve problems. This assessment task contributes to the development of the following graduate attributes: 1. disciplinary knowledge and its appropriate application 2. an inquiry-oriented approach |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 2 and 4 This assessment task contributes to the development of course intended learning outcome(s): .0 and .1 |
| Type: | Project |
| Groupwork: | Individual |
| Weight: | 15% |
| Criteria: | correct choice and use of problem solving strategies and procedures, accurate mathematical reasoning |
Assessment task 2: Assignment 2
| Intent: | To develop ability in modelling physical problems and competence in using computer code to solve problems. This assessment task contributes to the development of the following graduate attributes: 1. disciplinary knowledge and its appropriate application 2. an inquiry-oriented approach |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 2, 3 and 4 This assessment task contributes to the development of course intended learning outcome(s): .0, .1 and .2 |
| Type: | Project |
| Groupwork: | Individual |
| Weight: | 15% |
| Criteria: | correct choice and use of problem solving strategies and procedures, accurate mathematical reasoning |
Assessment task 3: Assignment 3
| Intent: | To develop ability in modelling physical problems and competence in using computer code to solve problems. This assessment task contributes to the development of the following graduate attributes: 1. disciplinary knowledge and its appropriate application |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1 and 3 This assessment task contributes to the development of course intended learning outcome(s): .0 and .2 |
| Type: | Project |
| Groupwork: | Individual |
| Weight: | 15% |
| Criteria: | correct choice and use of problem solving strategies and procedures, accurate mathematical reasoning |
Assessment task 4: Assignment 4
| Intent: | To develop ability in modelling physical problems and competence in using computer code to solve problems. This assessment task contributes to the development of the following graduate attributes: 1. disciplinary knowledge and its appropriate application 3. professional skills and their appropriate application |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1 and 2 This assessment task contributes to the development of course intended learning outcome(s): .0 and .4 |
| Type: | Project |
| Groupwork: | Individual |
| Weight: | 15% |
| Criteria: | correct choice and use of problem solving strategies and procedures, accurate mathematical reasoning |
Assessment task 5: Final Examination
| Intent: | To test the ability gained to correctly formulate and solve unseen problems. This assessment task contributes to the development of the following graduate attributes: 1. disciplinary knowledge and its appropriate application 3. professional skills and their appropriate application |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 3 and 4 This assessment task contributes to the development of course intended learning outcome(s): .0 and .4 |
| Type: | Examination |
| Groupwork: | Individual |
| Weight: | 40% |
| Criteria: | correct use of terminology, correct choice and use of problem solving strategies and procedures, accurate mathematical reasoning |
Minimum requirements
Any assessment task worth 40% or more requires the student to gain at least 40% of the mark for that task. If 40% is not reached, an X grade fail may be awarded for the subject, irrespective of an overall mark greater than 50.
Recommended texts
Advice on textbooks will be given in the initial lecture. The following texts are recommended for additional reference:
- Kreyzig, E. Advanced Engineering Mathematics, 9th edition, John Wiley and Sons, 2006.
- Salas, S. L, Hille, E. & Etgen, G. J. Calculus: One and Several Variables, 10th edition, John Wiley & Sons, 2007. (ISBN 9780470132203)
- J Stewart, Calculus: Concepts and Contexts, 3rd ed., ISBN 0534 409830. Thomson Brooks/Cole Publishing Company, 2006 (Metric ed.) or ISBN 0534 409865 (non-metric edition published in 2005).