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
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.
Course description 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

Laplace Transforms:
- Definition, simple transforms, properties, inverse and shift theorem 3 lectures
- Solution of ODEs 3 lectures

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

Partial Differential Equations:
- Wave equation, Heat or diffusion equation, Laplace equation 1 lecture
- Solution of wave equation, D’alembert solution, separated solution 2 lectures
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Entry Requirements (not applicable to Visiting Students)
Pre-requisites It is RECOMMENDED that students have passed
<a “=”” href=“cxmath08060.htm” target=“_blank” title=“View Course details. Opens in a new window.”>Mathematics for Science and Engineering 1a (MATH08060) AND <a “=”” href=“cxmath08061.htm” target=“_blank” title=“View Course details. Opens in a new window.”>Mathematics for Science and Engineering 1b (MATH08061)
Co-requisites
Prohibited Combinations Other requirements None
Additional Costs Students are expected to own a copy of :

1. Modern Engineering Mathematics by Glyn James, Prentice Hall,
ISBN 978-0-273-73413-X

2. Advanced Modern Engineering Mathematics by Glyn James,
Prentice Hall, ISBN 978-0-273-71923-6
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Information for Visiting Students
Pre-requisites Mathematics units passed equivalent to Mathematics for Science and Engineering 1a and Mathematics for Science and Engineering 1b, or Advanced Higher Mathematics (A or B grade) or Mathematics and Further mathematics A-Level passes (A or B grade).
High Demand Course? Yes
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Course Delivery Information
Academic year 2022/23, Available to all students (SV1) Quota:��None
Course Start Semester 1
Timetable Timetable
Learning and Teaching activities (Further Info)

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 )
Assessment (Further Info) Written Exam 50 %, Coursework 50 %, Practical Exam 0 %
Additional Information (Assessment) Written Exam 50%:
Coursework 50%:

The School has a 40% Rule for 1st and 2nd year courses, i.e. you must achieve a minimum of 40% in coursework and 40% in written exam components, as well as an overall mark of 40% to pass a course. If you fail a course you will be required to resit it. You are only required to resit components which have been failed.
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S1 (December) 1:30
Resit Exam Diet (August) 1:30
Learning Outcomes
On completion of this course, the student will be able to:
  1. Calculate the solution of engineering problems described by linear, constant coefficient first and higher order differential equations
  2. Analyse and interpret the solutions to draw conclusions on the system behaviour
  3. Apply the Laplace transform to solve systems of linear, constant coefficient differential equations and to evaluate the stability of dynamic systems
  4. Use Fourier series analysis to approximate periodic functions, solve differential equations and analyse the response of systems to periodic forcing
  5. Distinguish between ordinary and partial differential equations and solve special cases of the wave equation
Reading List
Students are expected to own a copy of :
1. Modern Engineering Mathematics by Glyn James, Prentice Hall,
ISBN 978-0-273-73413-X
2. Advanced Modern Engineering Mathematics by Glyn James,
Prentice Hall, ISBN 978-0-273-71923-6
Additional Information
Graduate Attributes and Skills Not entered
Keywords Ordinary differential equations,Partial differential equations,Laplace transforms,Fourier series
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
,
Learning Outcomes
On completion of this course, the student will be able to:
  1. Calculate the solution of engineering problems described by linear, constant coefficient first and higher order differential equations
  2. Analyse and interpret the solutions to draw conclusions on the system behaviour
  3. Apply the Laplace transform to solve systems of linear, constant coefficient differential equations and to evaluate the stability of dynamic systems
  4. Use Fourier series analysis to approximate periodic functions, solve differential equations and analyse the response of systems to periodic forcing
  5. Distinguish between ordinary and partial differential equations and solve special cases of the wave equation
,
Reading List
Students are expected to own a copy of :
1. Modern Engineering Mathematics by Glyn James, Prentice Hall,
ISBN 978-0-273-73413-X
2. Advanced Modern Engineering Mathematics by Glyn James,
Prentice Hall, ISBN 978-0-273-71923-6
,
Additional Information
Graduate Attributes and Skills Not entered
Keywords Ordinary differential equations,Partial differential equations,Laplace transforms,Fourier series
,
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