Mathematical Methods for Chemical and Environmental Engineering
| Code | School | Level | Credits | Semesters |
| MTHS1008 | Mathematical Sciences | 1 | 20 | Full Year UK |
- Code
- MTHS1008
- School
- Mathematical Sciences
- Level
- 1
- Credits
- 20
- Semesters
- Full Year UK
Summary
A key aspect of the course is the modelling of Chemical Engineering situations in terms of mathematical problems.
The complexity of solving general (large) systems of equations is introduced and their study using matrix techniques. The calculus of a single variable is reviewed and extended to develop techniques used in the analysis of engineering problems:
- matrix algebra and its applications to systems of equations and eigenvalue problems;
- functions and their properties;
- advanced differential and integral calculus of one variable.
Furthermore, this course introduces the techniques for solving selected first-order differential equations relevant to the analysis of generic engineering problems. The course also provides mathematical tools in terms of advanced differential calculus and vectors for modelling of generic engineering situations given in terms of multi-dimensional models:
- first-order ordinary-differential equations;
- vector spaces and their applications;
- differential calculus of functions of several variables;
- vector calculus.
Basic numerical methods for solving equations involving functions, and for differential equations are introduced.
Target Students
Available to BSc, BEng and MEng students in the Faculty of Engineering.
Classes
- One 1-hour workshop each week for 11 weeks
- One 2-hour lecture each week for 11 weeks
These activities are taken together with students on MTHS1003 (Autumn) and MTHS1004 (Spring). Weekly: Normally 2 lectures to introduce key mathematical knowledge, ideas and techniques. Alternate weeks: 1 hour of worked examples for solving of problems or a tutorial/problem class for provision of individual help with understanding module topics, clarification of lecture notes or support in developing problem solving skills. Optional weekly 1-hr (clinic) sessions for individual support.
Assessment
- 5% Coursework 1: Problems-based assignment
- 5% Coursework 2: Problems-based assignment
- 5% Inclass Exam 1 (Written): Written inclass assessment, 45 minutes
- 5% Inclass Exam 2 (Written): Written inclass assessment, 45 minutes
- 80% Exam 1 (3-hour): Written exam
Assessed by end of spring semester
Educational Aims
The course provides a qualifying year provision for Chemical and Environmental engineers, to equip students with both the confidence and competence in a range of fundamental elementary mathematical techniques and basis for advanced mathematical methods used in the quantitative study and analysis of engineering problems. This includes the modelling of Engineering situation in mathematical terms. There is a strong emphasis of enabling transition to a university qualifying level environment.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:
L1 - Find suitable mathematical models for typical Engineering applications;
L2 - Apply matrix algebra techniques to analyse efficiently and solve systems of equations and algebraic eigenvalue problems;
L3 - Identify properties and characteristics of standard mathematical functions used in engineering and their differential and integral evaluation and features;
L4 - Use extended techniques of differential and integral calculus, typically used in solving engineering problems;
L5 - manipulate vectors to solve geometric problems in engineering;
L7 - understand and apply basic differential calculus associated with functions of several variables;
L10 - apply suitable numerical methods to finding zeros of functions and to solving first order differential equations.
L6 - classify and solve a range of standard-type first-order ordinary differential equations;
L8 - apply several variable calculus to applications in simplified engineering contexts;
L9 - apply differential operators to scalar and vector fields relevant to engineering problems;