Applied Mathematics Option I - MAT00036I
- Department: Mathematics
- Credit value: 30 credits
- Credit level: I
- Academic year of delivery: 2022-23
Module summary
Module leads:
Dynamical Systems - George Constable
Newtonian Gravity - Ed Corrigan
Classical & Quantum Dynamics - Kasia Rejzner
Related modules
Additional information
For Natural Sciences students only.
Module will run
Occurrence | Teaching period |
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A | Autumn Term 2022-23 to Summer Term 2022-23 |
Module aims
The Applied Module in Stage 2 aims to introduce some of the main ideas and theories of modern applied mathematics and mathematical physics, along with some of the main mathematical methods that are used to study and solve problems in these theories. Rather than present the methods in isolation, the aim is to encounter them in the context of applications, so that theory and technique progress in tandem. The overall aim is to lay the foundations for the further study of applied mathematics and mathematical physics in Stages 3 and 4.
As part of these broad aims, this module has the following components:
- Introduction to Dynamical Systems and Newtonian Gravity (Autumn) provides an introduction to key methodological techniques for the analysis of dynamical systems, illustrated by examples, working up from low dimensions to implications in higher dimensions. It then moves on the the development of Newton’s theory of motion in vectorial form, leading up to the description of orbits in Newtonian gravity. Dynamical systems is further developed in the Waves and Fluids components as well as in various course in years 3 and 4, while Newtonian mechanics is further developed in the Classical Dynamics, Quantum Dynamics and Waves and Fluids components.
- Classical Dynamics (Spring) presents a sophisticated form of Newton’s laws known as analytical mechanics, which also forms an important component of modern theories of both classical and quantum physics.
- Quantum Dynamics (Spring/Summer) begins the development of quantum mechanics, and various relevant techniques of differential equations which have numerous other applications in pure and applied mathematics.
Studying these three components alongside each other during the course of the year will allow students to see the many connections across different areas of Applied Mathematics; understanding these connections and being able to use ideas and techniques across many contexts is an essential part of the modern mathematician’s toolkit.
Module learning outcomes
Subject content Introduction to Dynamical Systems:
Newtonian Gravitation ·Revision: Vectors, scalar and vector products and triple products, time-derivatives ·Frames of reference, Galilean relativity, Newton's laws. Energy, momentum, angular momentum. Circular motion and angular velocity. ·Many particles, two particles, Newton's law of gravity. Central forces and resulting planar motion in polar coordinates. The geometry of orbits: ellipses and Kepler's laws; parabolae, hyperbolae and scattering. Energy, effective potential, stability of orbits.
Classical Dynamics
Quantum Dynamics
Academic and graduate skills
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Indicative assessment
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 34 |
Closed/in-person Exam (Centrally scheduled) | 33 |
Closed/in-person Exam (Centrally scheduled) | 33 |
Special assessment rules
None
Additional assessment information
Students only resit components which they have failed.
Indicative reassessment
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 34 |
Closed/in-person Exam (Centrally scheduled) | 33 |
Closed/in-person Exam (Centrally scheduled) | 33 |
Module feedback
Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
Indicative reading
Steven Strogatz, Nonlinear dynamics and Chaos (CRC Press) M Lunn, A first course in Mechanics, Oxford University Press (U1 LUN) TWB Kibble and FH Berkshire, Classical Mechanics, Imperial College Press (U1 KIB) R Fitzpatrick, Newtonian Dynamics, Lulu (U1.3 FIT) R Douglas Gregory, Classical Mechanics Cambridge University Press (U1 GRE) P Smith and RC Smith, Mechanics John Wiley and Sons (U1 SMI ) H Goldstein, Classical Mechanics, Addison-Wesley, (U1 GOL). [Later editions in conjunction with C Poole and J Safko] LN Hand and JD Finch, Analytical Mechanics, Cambridge University Press (U1.017 HAN). NMJ Woodhouse, Introduction to Analytical Dynamics, Oxford University Press, (U1.3WOO) PCW Davies and DS Betts, Quantum Mechanics, Chapman and Hall (U 0.12 DAV) G F Simmons, Differential Equations, with Applications and Historical Notes, Tata McGraw-Hill (paperback) (S 7.38 SIM)
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