Engineering Mathematics 2A
Mathematics is your toolbox to design, model, and control systems.
1 Course Outline
| School | School of Engineering | College | College of Science and Engineering |
|---|---|---|---|
| Credit level (Normal year taken) | SCQF Level 8 (Year 2 Undergraduate) | Availability | Available to all students |
| SCQF Credits | 10 | ECTS Credits | 5 |
2 Summary
Ordinary differential equations, transforms and Fourier series with applications to engineering. Linear differential equations, homogeneous and non-homogeneous equations, particular solutions for standard forcings; Laplace transforms and applications; standard Fourier series, half range sine and cosine series, complex form; convergence of Fourier series, differentiation and integration of Fourier series. Introduction to Partial Differential Equations.
3 Course description
3.1 Differential Equations
Linear Differential Equations 1 lecture
Linear constant coefficient Differential Equations 3 lectures
Second order linear constant coefficient differential equations, forcing and damping 2 lectures
3.2 Laplace Transforms
Definition, simple transforms, properties, inverse and shift theorem 3 lectures
Solution of ODEs 3 lectures
3.3 Fourier Series
Fourier series, coefficients, even/odd functions, linearity, convergence 2 lectures
Full range, half-range 2 lectures
Integration and differentiation of Fourier series 1 lecture
3.4 Partial Differential Equations
Wave equation, Heat or diffusion equation, Laplace equation 1 lecture
Solution of wave equation, D’alembert solution, separated solution 2 lectures
Additional Costs: Students are expected to own a copy of:
Modern Engineering Mathematics by Glyn James, Prentice Hall, ISBN 978-0-273-73413-X
Advanced Modern Engineering Mathematics by Glyn James, Prentice Hall, ISBN 978-0-273-71923-6
4 Total Hours: 100
- Lecture Hours 20,
- Seminar/Tutorial Hours 5,
- Formative Assessment Hours 2,
- Summative Assessment Hours 10,
- Programme Level Learning and Teaching Hours 2,
- Directed Learning and Independent Learning Hours 61
5 Assessment
- Written Exam 50 %,
- Coursework 50 %,
- 3 coursework:
- Differential Equations coursework due 13.10.2022 at 3 pm (37.5%)
- Laplace transform coursework with peer assessmentq
- 3 coursework:
- Practical Exam 0 %
6 Learning Outcomes
On completion of this course, the student will be able to:
- Calculate the solution of engineering problems described by linear, constant coefficient first and higher order differential equations
- Analyse and interpret the solutions to draw conclusions on the system behaviour
- Apply the Laplace transform to solve systems of linear, constant coefficient differential equations and to evaluate the stability of dynamic systems
- Use Fourier series analysis to approximate periodic functions, solve differential equations and analyse the response of systems to periodic forcing
- Distinguish between ordinary and partial differential equations and solve special cases of the wave equation
7 Course Contacts
| Course organiser | Dr Daniel Friedrich |
|---|---|
| Tel: | (0131 6)50 5662 |
| Email: | D.Friedrich@ed.ac.uk |
| Course secretary | Miss Mhairi Sime |
| Tel: | (0131 6)50 5687 |
| Email: | msime2@ed.ac.uk |