Computational Techniques 2

Semester 2, 2020

Staff

- Tony Downward
- Andreas Kempa-Liehr (director)
- Colin Simpson (coordinator)

Calendar notes

Methods for computing numerical solutions of mathematical models and data analytics problems with focus on translating algorithms to computer code. A selection of topics from numerical solution of linear and non-linear equations, eigen problems, ordinary and partial differential equations, databases, inverse problems and parameter estimation.

Prerequisite: ENGSCI 233Corequisite: ENGSCI 311 or 313 or 314

## Intended learning outcomes |
## Related graduate attributes |
## Related assessments |
---|---|---|

Non-Linear Equations: Formulate systems of non-linear equations as minimisation problems. Create code to implement root-finding methods including Bisection, Regula Falsi and Newton's method. Explain deflation of polynomials. |
ENGA02: problem analysis (4) ENGA03: design and solution development (1) ENGA05: modern tool usage (5) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (1) UOA_1: Disciplinary Knowledge and Practice (2) UOA_2: Critical Thinking (2) UOA_3: Solution Seeking (1) |
Lab - Nonlinear Equations and Univariate Minimisation Final Examination |

Finite Difference Methods: Derive finite difference representations of PDE problems and write code to solve these systems. |
ENGA03: design and solution development (1) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (1) UOA_1: Disciplinary Knowledge and Practice (2) UOA_3: Solution Seeking (1) |
Lab - Finite Differences Final Examination |

Ordinary differential equations: Transfer understanding of Improved Euler and Runge-Kutta from mathematics into code. Implement adaptive timestepping methods either from existing code or from scratch. Explain the pros and cons of higher order method. Explain the sources of error in lower order methods. Appreciate and discuss the trades-off between accuracy and computational expense. |
ENGA01: engineering knowledge (1) ENGA03: design and solution development (1) ENGA05: modern tool usage (5) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (1) UOA_1: Disciplinary Knowledge and Practice (2) UOA_3: Solution Seeking (1) |
Lab - ODEs Term Test Final Examination |

Univariate Minimization: Students will be able to compare numerical methods and select an appropriate method for minimization of a given problem. Generate code to apply methods and test success and speed of convergence. |
ENGA03: design and solution development (1) ENGA05: modern tool usage (5) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (1) UOA_1: Disciplinary Knowledge and Practice (2) UOA_3: Solution Seeking (1) |
Lab - Nonlinear Equations and Univariate Minimisation Final Examination |

Eigenvalues and eigenvectors: Write an algorithm that uses the Power Method, Deflation, Shifting and Inverse Iteration to find the eigenvectors and eigenvalues of a system. Identify and describe the sources of error and possible reasons why such algorithms may fail. |
ENGA03: design and solution development (1) ENGA05: modern tool usage (5) ENGK02: mathematical modelling (4) ENGK03: abstraction and formulation (1) UOA_1: Disciplinary Knowledge and Practice (2) UOA_3: Solution Seeking (1) |
Lab - Eigenproblems Term Test Final Examination |

Databases: Understand the fundamental concepts for modelling databases. Demonstrate the ability to query databases using SQL. |
ENGA01: engineering knowledge (1) ENGA03: design and solution development (1) ENGA05: modern tool usage (5) |
Lab - Databases Term Test Final Examination |

Coursework

No description given

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