Differential Equations and Calculus for Engineers
| Code | School | Level | Credits | Semesters |
| MTHS2004 | Mathematical Sciences | 2 | 10 | Autumn UK |
- Code
- MTHS2004
- School
- Mathematical Sciences
- Level
- 2
- Credits
- 10
- Semesters
- Autumn UK
Summary
The majority of the course is concerned with providing techniques for solving selected classes of ordinary differential equations (ODEs) relevant to the analysis of engineering topics. This course also provides the basic calculus to help analyse engineering problems in two- or three-dimensions and special solutions of partial differential equations relevant to engineering applications. The course will cover:
- Multiple integrals;
- Fourier series and Periodic Functions;
- Homogeneous (revision) and inhomogeneous second-order ODEs;
- Systems of ODESs;
- Application of Fourier Series;
- Laplace transform;
- Separation of Variable Technique for PDEs.
Target Students
Available to BSc, BEng and MEng students in the Faculty of Engineering and the School of the Built Environment.
Classes
- One 1-hour workshop each week for 11 weeks
- One 2-hour lecture each week for 11 weeks
Each week there will normally be 2 lectures to introduce key mathematical knowledge/ideas/techniques on module topics. Alternate weeks 1 hr of worked examples to facilitate solving of problems/tutorial/problem class or provide students with the opportunity to gain individual help understanding module topics, clarification of lecture notes or support in developing problem solving skills.
Assessment
- 5% Coursework 1: Problems-based assignment
- 5% Coursework 2: Problems-based assignment
- 90% Exam 1 (2-hour): Written examination
Assessed by end of autumn semester
Educational Aims
To introduce multiple integrals in cartesian and polar coordinates used in the fundamental analysis of two dimensional advanced engineering problems. To understand, apply and manipulate standard techniques for solving important classes of ordinary differential equations and the calculus relevant to analysing core engineering models. The fundamental concepts for solving partial differential equations relevant to modelling of thermodynamic, fluid or elastic problems is introduced and illustrated by obtaining fundamental solutions using techniques developed within the course.Learning Outcomes
Knowledge and understanding of mathematics necessary to support application of key engineering principles.
To apply mathematical methods, tools and notations proficiently in the analysis and solution of engineering problems.
On successful completion of this course students will be able to:
Evaluate two dimensional integrals;
Solve a range of linear second-order linear ordinary differential equations;
Understand and calculate the representation of a periodic function by a Fourier Series and use Fourier Series in solving differential equations;
Apply separation of variables to relevant partial differential equations.