# COMO303 Numerical Methods

Develops the theory and techniques required to apply computational methods in modelling, applied mathematics, and data analysis. Topics include matrix computation, data fitting, and the numerical solution of differential equations.

This paper introduces methods and theory for computational applied mathematics and modelling, with an emphasis on practical applications and modelling. You will learn a useful collection of numerical techniques for solving a wide variety of mathematical problems. In particular, we discuss solving systems of equations, matrix decompositions, curve fitting, numerical integration and differential equations. For some methods, detailed derivations are given, so you will also obtain an understanding of why the methods work, when they will not work and of difficulties that can arise. For other methods, the focus will be on applying them in practical situations. For the computational side, we will use the numerical computing environment MATLAB. Previous experience with MATLAB is useful, but not required. An introduction will be provided in the first labs. At the end of this paper, you will have a good understanding of how to solve various problems numerically, choose the best method for a given problem, and to interpret the solutions found in the context of error bounds and stability.

Paper title Numerical Methods COMO303 Computational Modelling 0.15 18 points Semester 1 (On campus) \$1,110.75 Tuition Fees for international students are elsewhere on this website.
Prerequisite
MATH 202
Restriction
MATH 361
Recommended Preparation
COMO 204
Schedule C
Science
Eligibility
This paper should appeal to a wide group of students, including those majoring in Mathematics, Statistics, Computational Modelling, Physics, Engineering, Computer Science, Economics or any other field in which one often needs to use numerical approximations to solve real world problems.
Contact
jhennig@maths.otago.ac.nz
Teaching staff

Lecturer: Dr Jörg Hennig

Paper Structure
This paper covers four key themes:
• Introduction to numerical algorithms
• Matrix decompositions and their uses
• Least-squares fitting and applications
• Modelling with ordinary differential equations
Teaching Arrangements
Each week there are 2 or 3 lectures (alternating) and 2 hours of supervised labs.
Textbooks

Textbooks are not required for this paper.

A useful reference is Cleve B. Moler, Numerical Computing with MATLAB, SIAM (2008). A free web edition is available.

Course outline
View the course outline for COMO 303
Interdisciplinary perspective, Critical thinking, Information literacy.
Learning Outcomes

Students who successfully complete this paper will develop

• Information and computational literacy
• Interdisciplinary thinking
• Communication and writing skills

## Timetable

### Semester 1

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
Other

#### Lecture

Stream Days Times Weeks
Attend
A1 Monday 13:00-13:50 9-15, 18-22
Wednesday 13:00-13:50 9-15, 17-22
Friday 13:00-13:50 9-10, 12, 14, 17, 19, 21

#### Tutorial

Stream Days Times Weeks
Attend
A1 Monday 15:00-16:50 9-15, 18-22

Develops the theory and techniques required to apply computational methods in modelling, applied mathematics, and data analysis. Topics include matrix computation, data fitting, and the numerical solution of differential equations.

This paper introduces methods and theory for computational applied mathematics and modelling, with an emphasis on practical applications and modelling. You will learn a useful collection of numerical techniques for solving a wide variety of mathematical problems. In particular, we discuss solving systems of equations, matrix decompositions, curve fitting, numerical integration and differential equations. For some methods, detailed derivations are given, so you will also obtain an understanding of why the methods work, when they will not work and of difficulties that can arise. For other methods, the focus will be on applying them in practical situations. For the computational side, we will use the numerical computing environment MATLAB. Previous experience with MATLAB is useful, but not required. An introduction will be provided in the first labs. At the end of this paper, you will have a good understanding of how to solve various problems numerically, choose the best method for a given problem, and to interpret the solutions found in the context of error bounds and stability.

Paper title Numerical Methods COMO303 Computational Modelling 0.15 18 points Not offered in 2023 (On campus) Tuition Fees for 2023 have not yet been set Tuition Fees for international students are elsewhere on this website.
Prerequisite
MATH 202
Restriction
MATH 361
Recommended Preparation
COMO 204
Schedule C
Science
Eligibility
This paper should appeal to a wide group of students, including those majoring in Mathematics, Statistics, Computational Modelling, Physics, Engineering, Computer Science, Economics or any other field in which one often needs to use numerical approximations to solve real world problems.
Contact

Dr Jörg Hennig

Teaching staff

Lecturer: Dr Jörg Hennig

Paper Structure
This paper covers four key themes:
• Introduction to numerical algorithms
• Matrix decompositions and their uses
• Least-squares fitting and applications
• Modelling with ordinary differential equations
Teaching Arrangements
Each week there are 2 or 3 lectures (alternating) and 2 hours of supervised labs.
Textbooks

Textbooks are not required for this paper.

A useful reference is Cleve B. Moler, Numerical Computing with MATLAB, SIAM (2008). A free web edition is available.

Interdisciplinary perspective, Critical thinking, Information literacy.
Learning Outcomes

Students who successfully complete this paper will develop

• Information and computational literacy
• Interdisciplinary thinking
• Communication and writing skills

## Timetable

### Not offered in 2023

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
Other