Applied Mathematics

Code

MATH1103

School

Mathematical Sciences

Level

1

Credits

20

Semesters

Full Year UK

Summary

This is a year-long module that introduces students to mathematical modelling and simulation using difference equations, random walks and ordinary differential equations. The module also introduces classical and quantum mechanics. In the first five weeks of the module, students will be introduced to Python, and learn how to write code to simulate a variety of simple mathematical models. 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 and simulation: Introduction to Python; difference equations; random walks; ordinary differential equations.
•    Modelling with 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 and Joint Honours students from the School of Mathematical Sciences.

Co-requisites

Modules you must take in the same academic year, or have taken in a previous year, to enrol in this module:

• Core Mathematics (MATH1101)

Classes

• Six 1-hour workshops each week for 6 weeks
• Sixteen 1-hour workshops each week for 3 weeks

Assessment

• 40% Coursework 1: Summative assessment based on tasks distributed through the year.
• 40% Exam 1 (2-hour): Written examination. Assessed at the end of the Spring semester.
• 20% Exam 2 (1-hour): Class test

Assessed by end of spring semester

Educational Aims

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, random walks 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 - Collaborate effectively with peers in a group setting and present conclusions both verbally and in writing.

Conveners

• Dr Rachel Nicks