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| Unit name |
Applied Analysis 3 |
| Unit code |
MATH36203 |
| Credit points |
20 |
| Level of study |
H/6
|
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12)
|
| Unit director |
Dr. Slastikov |
| Open unit status |
Not open |
| Pre-requisites |
none
|
| Co-requisites |
none
|
| School/department |
School of Mathematics |
| Faculty |
Faculty of Science |
Description including Unit Aims
This unit introduces some of the main methods of modern analysis (focusing on partial differential equations and calculus of variations) along with some of the main problems in the physical sciences that have been solved using these methods, such as: 1. Pattern formation in elasticity and micromagnetics 2. The Allen-Cahn and Fokker-Plank equations 3. Optimal transportation
Aims
- To introduce some of the methods of modern analysis that are useful in solving applied problems.
- To introduce some of the major applications of modern analysis
Syllabus
- Preliminary results in analysis (functional spaces and basic theorems of PDEs and calculus of variations).
- Applications of analysis to important problems in materials science and physics.
Relation to Other Units
This unit uses some methods and ideas introduced in Analysis 2 and Calculus 2.
Intended Learning Outcomes
At the end of the course the student should be able to:
- Use, in simple situations, the basic tools of partial differential equations and the calculus of variations, and
- Understand some key examples in the physical sciences in terms of these tools.
Transferable Skills:
- Increased understanding of the relationship between mathematics and the natural sciences.
- Development of problem-solving and analytical skills.
Teaching Information
Lectures - 3 per week, in which the lecturer will present the course material on the blackboard. Students are expected to attend all lectures, and to prepare for them by reading notes, handouts or texts, as indicated by the lecturer.
Homework assignments - several problem sheets will be handed out.
Assessment Information
The final assessment mark for Applied Analysis 3 is calculated as follows:
- 100% from a 2½-hour written examination in May/June
- More information is given below.
Summer Examination
- The examination in May/June consists of a 2 ½-hour paper consisting of FIVE questions; you should attempt FOUR. If you attempt more than four, your best four answers will be used for assessment. Calculators may NOT be used.
Reading and References
- Gelfand, I. M. and Fomin, S. V., Calculus of variations, Dover publications
- Lawrence C. Evans, Partial Differential Equations, AMS
- Markowich, Peter A., Applied partial differential equations: A visual approach, Springer
- Dacorogna, B., Introduction to the calculus of variations, Imperial College Press.
