Differential Equations and Calculus for Engineers
| Code | School | Level | Credits | Semesters |
| MATH2025 | School of Mathematical Sciences | 2 | 10 | Autumn China |
- Code
- MATH2025
- School
- School of Mathematical Sciences
- Level
- 2
- Credits
- 10
- Semesters
- Autumn China
Summary
The majority of the module is concerned with providing techniques for solving selected classes of ordinary differential equations (ODEs) relevant to the analysis of engineering topics. This module also provides the basic calculus to help analyse engineering problems in two- or three-dimension and special solutions of partial differential equations relevant to engineering applications. The module will cover:
- Multiple integrals;
- Fourier series and Periodic Functions;
- Homogeneous (revision) and inhomogeneous second-order ODEs;
- Systems of ODEs;
- Application of Fourier Series;
- Laplace transform;
- Separation of Variable Technique for PDEs.
Target Students
BEng Architectural Environment Engineering students
Classes
- One 1-hour workshop each week for 12 weeks
- One 2-hour lecture each week for 12 weeks
Assessment
- 5% Coursework 1: Problems-based assignment
- 5% Coursework 2: Problems-based assignment
- 90% Exam 1 (2-hour): 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 module.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 module students will be able to:
- L01 - Evaluate two dimensional integrals;
- L02 – Solve a range of linear second-order ordinary differential equations;
- L03 - Understand and calculate the representation of a periodic function by a Fourier Series and use Fourier Series in solving differential equations;
- L04 - Apply separation of variables to relevant partial differential equations.