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# Introduction to Applied Mathematics - MAT00003C

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• Department: Mathematics
• Module co-ordinator: Prof. Martin Bees
• Credit value: 20 credits
• Credit level: C
• Academic year of delivery: 2023-24

## Module summary

This module introduces students to Newtonian mechanics and mathematical modelling, developing a range of techniques that form the foundation of the applied mathematician’s toolbox.

## Related modules

### Prohibited combinations

• None

Pre-requisite modules:
Foundations & Calculus

Co-requisite modules:
Multivariable Calculus & Matrices

## Module will run

Occurrence Teaching period
A Semester 2 2023-24

## Module aims

This module is split into two parts.

In part I, students explore Newton’s application of calculus to describe the motion of objects in space and time, learning how to construct the equations of motion for a body subject to forces that may depend on time, position or velocity, and then using a variety of techniques to understand the solution behaviour.

In part II, the students learn the process of building and analysing a mathematical model to answer a range of real-world questions, introducing them to the applied mathematician’s toolkit, used to obtain various types of solutions to a variety of mathematical models, and developing the intuitive aspects of applied mathematics

## Module learning outcomes

By the end of the module, students will be able to

1. Solve problems using Newton’s Laws of Motion in one and two dimensions.

2. Solve problems using the equations of motion in polar coordinates, including planetary motion.

3. Use dimensional analysis to discover scaling laws and dependence on dimensionless numbers.

4. Analyse 1st order ODEs and coupled pairs thereof in applied contexts.

5. Solve simple Partial Differential Equations including wave and heat equations

## Module content

• Newtonian mechanics and motion in one dimension, including time- and position-dependent force

• Motion in two dimensions.

• Equations of motion in polar coordinates

• Dimensional analysis and scaling

• 1st order ODEs in an applied context

• Coupled pairs of 1st order ODEs in applied contexts

• The heat and wave equations

## Assessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Introduction to Applied Mathematics
2 hours 90
Essay/coursework
Coursework
N/A 10

None

### Additional assessment information

Due to the pedagogical desire to provide speedy feedback in seminars, extensions to the written coursework are not possible.

To mitigate for exceptional circumstances, the written coursework grade will be the best 4 out of the 5 assignments. If more than one assignment is affected by exceptional circumstances, an ECA claim must be submitted (with evidence)

### Reassessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Introduction to Applied Mathematics
2 hours 90
Essay/coursework
Coursework
N/A 10

## Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy

The module will draw from a wide variety of sources. Many of them will be available online and on the VLE. There is no one book covering everything. Good sources include:

D. Edwards and M. Hamson, Guide to mathematical modelling (Palgrave, 2001).

K K Tung, Topics in Mathematical Modelling, Princeton 2007.

C.D. Collinson and T. Roper, Particle Mechanics, Arnold (London 1995)/Elsevier (2004);

J. Berry and K. Houston, Mathematical Modelling, Arnold (London 1995).

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.