 Credits:
| 6 |
| Level:
| Honours (FHEQ level 6) |
| Period: |
Semester 2
|
| Assessment:
| EX 100% |
| Supplementary Assessment: | MA30063 Mandatory Extra Work (where allowed by programme regulations) |
| Requisites:
| Before taking this unit you must take MA20223 and take MA30047 |
| Description:
| Aims & Learning Objectives:
Aims:
The aim of the course is to introduce students to applications of partial differential equations to model problems arising in biology. The course will complement Mathematical Biology I where the emphasis was on ODEs and Difference Equations.
Objectives:
Students should be able to derive and interpret mathematical models of problems arising in biology using PDEs. They should be able to perform a linearised stability analysis of a reaction-diffusion system and determine criteria for diffusion-driven instability. They should be able to interpret the results in terms of the original biological problem.
Content:
Topics will be chosen from the following:
Partial Differential Equation Models: Simple random walk derivation of the diffusion equation. Solutions of the diffusion equation. Density-dependent diffusion. Conservation equation. Reaction-diffusion equations. Chemotaxis. Examples for insect dispersal and cell aggregation.
Spatial Pattern Formation: Turing mechanisms. Linear stability analysis. Conditions for diffusion-driven instability. Dispersion relation and Turing space. Scale and geometry effects. Mode selection and dispersion relation.
Applications: Animal coat markings. "How the leopard got its spots". Butterfly wing patterns.
|
Programme availability:
|
MA30063 is Optional on the following programmes:
Department of Biology & Biochemistry
- RSBB-AFM07 : Integrated PhD Postgenomic Biosciences (Biosciences Route) (Full-time) - Year 1
- TSBB-AFM03 : MRes Biosciences (Full-time) - Year 1
Programmes in Natural Sciences
- UXXX-AFB01 : BSc (hons) Natural Sciences (Full-time) - Year 3
- UXXX-AKB02 : BSc (hons) Natural Sciences with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 4
- UXXX-AAB02 : BSc (hons) Natural Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- UXXX-AFM01 : MSci (hons) Natural Sciences (Full-time) - Year 3
- UXXX-AKM02 : MSci (hons) Natural Sciences with Professional Placement (Full-time with Thick Sandwich Placement) - Year 4
- UXXX-AAM02 : MSci (hons) Natural Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
Department of Mathematical Sciences
- USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
- USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
- USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 3
- USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 3
- USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
- USMA-AFM14 : MMath Mathematics (Full-time) - Year 4
- USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- TSMA-AFM09 : MSc Mathematical Sciences (Full-time) - Year 1
- TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 1
- TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 2
- TSMA-AFM08 : MSc Modern Applications of Mathematics (Full-time) - Year 1
- TSMA-AFL02 : PG Dip Modern Applications of Mathematics (Full-time) - Year 1
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