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# Unit information: ODEs, Curves and Dynamics in 2018/19

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Unit name ODEs, Curves and Dynamics MATH10012 20 C/4 Teaching Block 4 (weeks 1-24) Professor. Linden Not open A in A Level Mathematics or equivalent none School of Mathematics Faculty of Science

## Description

This unit aims to provide the essential tools, concepts and skills for Applied Mathematics at undergraduate level. The first part will expose students to the basic theory of ordinary differential equations. The second part will cover gradients, the mathematical description of curves, as well as double and triple integrals. Important examples and motivation will be provided by applications of these techniques to elementary Newtonian mechanics, taught from a mathematical perspective.

## Intended learning outcomes

At the end of this unit the student should:

• be able to solve simple first and second order differential equations
• be able to use partial derivatives and the gradient vector
• be able to work with curves (e.g. parametrise them, express them in different systems of coordinates, and evaluate line integrals)
• be able to evaluate integrals in two and three dimensions
• understand the basic principles of Newtonian mechanics, and be able to apply the theory of ordinary differential equations as well as the above techniques to mechanical problems
• understand the connection of the course material to other areas of Mathematics including Analysis
• have developed the skills required for further study in Applied Mathematics, including theoretical understanding, the ability to perform relevant calculations with confidence, the ability to model phenomena of the physical world using mathematical techniques, and geometric intuition

## Teaching details

Lectures, supported by lecture notes with problem sets and model solutions, problems classes and small group tutorials.

## Assessment Details

Formative assessment:

• problem sheets set by the lecturer and marked by the students’ tutors.

Summative assessment:

• Two 1.5h exams (45%) after each teaching block
• Coursework (10%)

## Reading and References

Recommended reading:

• Schaum's Outline of Calculus (Fourth Edition) by Frank Ayres Jr and Elliott Mendelson. Schaum's Outline Series, McGraw-Hill, 1999. ISBN 0070419736
• D. Kleppner & Robert J. Kolenkow, An Introduction to Mechanics, McGraw-Hill, 1973
• Martin Braun 'Differential Equations and Their Applications' 4th Edition, Springer
• Serge Lang 'Calculus of Several Variables' Springer

Further reading and references are available at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html