MATH270-22S2 (C) Semester Two 2022

# Mathematical Modelling and Computation 2

15 points

Details:
 Start Date: Monday, 18 July 2022 End Date: Sunday, 13 November 2022
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Sunday, 31 July 2022
• Without academic penalty (including no fee refund): Sunday, 2 October 2022

## Description

Numerical methods and stochastics: solving nonlinear equations; solving systems of linear equations; interpolation; initial value and boundary value problems for ordinary differential equations; Monte Carlo simulation and applications. Programming and problem solving using MATLAB and the application of these ideas.

PLEASE NOTE: The above description is incorrect as the course now uses Python, not MATLAB.  For bureaucratic reasons this cannot be fixed for 2022.  Here is what it should say:

Use of the language Python for numerical methods, including solutions of systems of linear equations, solution of ordinary differential equations and systems of differential equations, boundary value problems, approximation techniques, area integration, statistics, random number generation, and Monte Carlo integration.  Modelling projects and engineering applications.

The use of mathematical modelling and computation in science. Numerical methods with strong emphasis on applications in physical and natural sciences. The course has a strong programming component done in Python. Case studies with scientific applications will reinforce the theory seen in class.

Course Information:
An application-oriented course in mathematical modelling and scientific computation. Numerical methods and approximations underlie much of modern science, such as bioinformatics, fluid dynamics, climate change prediction, analysis of large data sets and creation of special effects in movies. The course will cover a range of techniques from calculus and linear algebra, together with algorithmic and programming considerations. Programming exercises will be conducted using Python. The methods covered will be applied in case studies in the physical and life sciences.

Topics covered:
Mathematical modelling methods and techniques. Iterative methods for nonlinear equations; numerical solution of linear and nonlinear systems; interpolation and approximation; numerical quadrature; numerical solution of ordinary differential equations; random number generation and Monte Carlo integration. Python: matrix algebra; structured programming; writing Jupyter notebooks; user-defined functions; visualisation techniques.

## Learning Outcomes

• Students will be able to:

• Develop and critically assess mathematical models of problems in the physical and life sciences.
• Implement numerical algorithms in Python in order to solve mathematical models.
• Use commercially available computer programs with enough theoretical knowledge to make intelligent decisions about the outputs.

## Prerequisites

(MATH170 or EMTH171 or MATH280 or COSC121 or Head of School approval) and (EMTH119 or MATH103 or MATH199)

EMTH271, MATH271

## Indicative Fees

Domestic fee \$802.00

International fee \$4,563.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

## All MATH270 Occurrences

• MATH270-22S2 (C) Semester Two 2022