ODEs, Curves and Dynamics
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.
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
Reading and References
- 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
- William E Boyce and Richard C DiPrima, Elementary Differential Equations and Boundary Value Problems, 9th Edition, Wiley
A in A Level Mathematics or equivalent
Methods of teaching
Lectures, supported by lecture notes with problem sets and model solutions, problems classes and small group tutorials.
Methods of Assessment
The pass mark for this unit is 40.
- Problem sheets set by the lecturer and marked by the students’ tutors.
- Two 1.5h exams (45% each)
- Coursework (10%)
For information resit arrangements, please see the re-sit page on the intranet.
Further exam information can be found on the Maths Intranet.