Applied Mathematics
| Code | School | Level | Credits | Semesters |
| MATH1029 | School of Mathematical Sciences | 1 | 20 | Full year China |
- Code
- MATH1029
- School
- School of Mathematical Sciences
- Level
- 1
- Credits
- 20
- Semesters
- Full year China
Summary
This is a year-long module that introduces students to mathematical modelling and simulation using difference equations and ordinary differential equations. The module also introduces classical and quantum mechanics. Students who have studied this module will have the basis for further study of more advanced topics in applied mathematics, mathematical physics and scientific computing.
•Modelling with differential equations: difference equations; linear constant coefficient ordinary differential equations; second order nonlinear ordinary differential equations; the phase plane; equilibrium points; limit cycles and the Poincaré-Bendixson theorem; Lotka-Volterra equations.
•Mechanics: Newton’s Laws and point particles; systems of particles; oscillations; work and energy; planetary orbits; introduction to quantum mechanics.
Target Students
Single Honours students from the Department of Mathematical Sciences.
Classes
- Three 1-hour workshops each week for 24 weeks
Component No1 - Number of Sessions Per Week - 6 – weeks 1 to 6 – shared with Probability and Statistics 1
Assessment
- 40% Coursework 1: Summative assessment based on tasks distributed through the year.
- 20% Class Test 1 (1-hour): Written class test - Autumn
- 40% Exam 1 (2-hour): Written examination - Spring
Assessed by end of spring semester
Educational Aims
The overall aims are to give students an introduction to mathematical modelling using a variety of techniques, including simulation in Python, with a focus on ordinary differential equations, and a particular emphasis on classical mechanics. This provides students with a good foundation for studying more advanced topics in applied mathematics, mathematical physics and scientific computing.Learning Outcomes
A student who completes this module successfully should be able to:
L1 – Define the essence of real-world problem and use the mathematical modelling cycle to create a plan to solve it;
L2 – Make effective use of Python to investigate mathematical models based on difference equations and ordinary differential equations;L3 – Determine properties of solutions of second order, autonomous ordinary differential equations using phase plane techniques;
L4 – Apply Newtons Laws to simple mechanical systems;
L5 – Understand the basic formalism of quantum mechanics;
L6 - Take an inclusive and ethical approach to collaborating with peers to give and receive feedback on work.
Conveners
- Dr Mainul Haque