Undergraduate Course: Mathematics for Science and Engineering 2b (MATH08070)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Not available to visiting students |
| Credit level (Normal year taken) | SCQF Level 8 (Year 2 Undergraduate) |
Credits | 10 |
| Home subject area | Mathematics |
Other subject area | None |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | This course is aimed at second year Engineering students :
Multivariate integration, vector calculus and partial differential equations for engineering. Gradient, tangent plane, normals; Scalar and vector fields; divergence and curl; conservative fields and potential; vector differential identities; simple applications from properties of continua and electromagnetism. Repeated multiple integration (change of order of integration); integration in non-cartesian coordinates, Jacobian; line integrals (link to potential and work); surface integrals (flux); divergence, Green's and Stokes' theorems; applications and physical interpretations; standard partial differential equations, wave equation, heat equation and Laplace's equation, solution of standard equations, D'Alembert solution for wave equation, separation of variables with Fourier series, Laplace transform methods. |
Course Delivery Information
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| Delivery period: 2012/13 Semester 2, Not available to visiting students (SS1)
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Learn enabled: Yes |
Quota: None |
| Location |
Activity |
Description |
Weeks |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| King's Buildings | Lecture | Swann , Main Lecture Theatre | 1-11 | 10:00 - 10:50 | | | | | | King's Buildings | Lecture | Swann , Main Lecture Theatre | 1-11 | | | | 10:00 - 10:50 | |
| First Class |
Week 1, Monday, 10:00 - 10:50, Zone: King's Buildings. Swann, Main Lecture Theatre |
| No Exam Information |
Summary of Intended Learning Outcomes
1. An understanding of vector fields, their divergence and curl.
2. An ability to use the basic vector differential identities.
3. A competence in evaluating repeated and multiple integrals.
4. An understanding of line integrals, their calculation and relation to the potential of a conservative field.
5. An ability to calculate integrals, such as flux, over simple curved surfaces.
6. An ability to use the divergence theorem and Stokes's theorem in simple situations, and a realization of their great practical importance.
7. An understanding of the importance of the standard partial differential equations.
8. The ability to solve the standard partial differential equations using separation of variables and Laplace transforms.
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Assessment Information
| Coursework 20%; examination 80%. |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Vector Calculus :
- Basic concepts, Transformations [1 lecture]
- Gradient [0.5 lecture]
- Divergence and curl [1.5 lectures]
Integration :
- Double Integrals [3 lectures]
- Line integrals [2 lectures]
- Green's Theorem [1 lecture]
- Surface Integrals [2 lectures]
- Volume Integrals [1 lecture]
- Gauss' Theorem [1 lecture]
- Stokes' Theorem [1 lecture]
PDEs (analytically, no numerical) :
- Wave equation, Heat or diffusion equation, Laplace equation [1 lecture]
- Solution of wave equation, D¿Alembert solution, separated solutions, Laplace transform [3 lectures]
- Solution of Heat or diffusion equation, separated solutions, Laplace transform [2 lectures]
- Solution of Laplace equation, separated solutions [2 lectures] |
| Transferable skills |
Not entered |
| Reading list |
Students would be expected to own a copy of :
Modern Engineering Mathematics by Glyn James, Prentice Hall
Advanced Modern Engineering Mathematics by Glyn James, Prentice Hall |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | mse2b |
Contacts
| Course organiser | Dr Noel Smyth
Tel: (0131 6)50 5080
Email: N.Smyth@ed.ac.uk |
Course secretary | |
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