Overview
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.
About this paper
| Paper title | Numerical Methods |
|---|---|
| Subject | Computational Modelling |
| EFTS | 0.15 |
| Points | 18 points |
| Teaching period | Semester 1 (On campus) |
| Domestic Tuition Fees ( NZD ) | $1,318.20 |
| International Tuition Fees | 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
For more information, contact MATH and COMO 200-300 Level Advisor, Dr Jörg Hennig at joerg.hennig@otago.ac.nz
- Teaching staff
Teaching staff to be advised.
- 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.- Graduate Attributes Emphasised
- Interdisciplinary perspective, Critical thinking, Information literacy.
View more information about Otago's graduate attributes. - Learning Outcomes
Students who successfully complete this paper will develop:
- Information and computational literacy
- Interdisciplinary thinking
- Communication and writing skills
Overview
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 interpret the solutions found in the context of error bounds and stability.
About this paper
| Paper title | Numerical Methods |
|---|---|
| Subject | Computational Modelling |
| EFTS | 0.15 |
| Points | 18 points |
| Teaching period | Semester 1 (On campus) |
| Domestic Tuition Fees | Tuition Fees for 2027 have not yet been set |
| International Tuition Fees | 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, Physics, Engineering, Computer Science or Economics, as well as students with an interest in Computational Modelling, or in any other field where numerical approximations are used to solve real-world problems.
- Contact
Associate Professor Jörg Hennig (MATH and COMO 200-300 Level Advisor): joerg.hennig@otago.ac.nz
- Teaching staff
Teaching staff to be advised.
- 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 two or three lectures (alternating) and two hours of supervised labs.
- Textbooks
Textbooks are not required for this paper, however, a useful reference is:
- Cleve B. Moler, Numerical Computing with MATLAB, SIAM (2008).
A free web edition is available.
- Graduate Attributes Emphasised
- Interdisciplinary perspective, Critical thinking, Information literacy.
View more information about Otago's graduate attributes. - Learning Outcomes
Students who successfully complete this paper will develop:
- Information and computational literacy
- Interdisciplinary thinking
- Communication and writing skills