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

## Timetable 2022

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 12:00 - 13:00 C3 Lecture Theatre 18 Jul - 28 Aug 12 Sep - 23 Oct Lecture B 01 Tuesday 10:00 - 11:00 C3 Lecture Theatre 18 Jul - 28 Aug 12 Sep - 23 Oct Lecture C 01 Wednesday 12:00 - 13:00 C3 Lecture Theatre 18 Jul - 28 Aug 12 Sep - 23 Oct Computer Lab A 01 Thursday 08:00 - 10:00 Jack Erskine 001 Computer Lab 18 Jul - 28 Aug 12 Sep - 23 Oct 02 Thursday 14:00 - 16:00 Eng Core 342 CAD Lab 18 Jul - 28 Aug 12 Sep - 23 Oct 03-P1 Friday 11:00 - 13:00 Eng Core 216 CAD Lab 18 Jul - 14 Aug 12 Sep - 23 Oct 03-P2 Friday 15:00 - 17:00 Eng Core 342 CAD Lab 15 Aug - 28 Aug 04 Friday 15:00 - 17:00 Eng Core 342 CAD Lab 18 Jul - 28 Aug 12 Sep - 23 Oct

## Examination and Formal Tests

Activity Day Time Location Weeks Test A 01 Tuesday 19:00 - 20:30 Jack Erskine 033 Lab 1 26 Sep - 2 Oct 02 Tuesday 19:00 - 20:30 Jack Erskine 035 Lab 2 26 Sep - 2 Oct 03 Tuesday 19:00 - 20:30 Jack Erskine 038 Lab 4 26 Sep - 2 Oct 04 Wednesday 19:00 - 20:30 Jack Erskine 033 Lab 1 26 Sep - 2 Oct 05 Wednesday 19:00 - 20:30 Jack Erskine 035 Lab 2 26 Sep - 2 Oct 06 Wednesday 19:00 - 20:30 Jack Erskine 038 Lab 4 26 Sep - 2 Oct

## 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