MAS151 Civil Engineering Mathematics
| Both semesters, 2017/18 | 20 Credits | ||||
| Lecturer: | Prof Koji Ohkitani | Home page (also MOLE) | Timetable | Reading List | |
| Aims | Outcomes | Teaching Methods | Assessment | Full Syllabus | |
This module aims to reinforce students' previous knowledge and to develop new basic mathematical techniques needed to support the engineering subjects taken at Levels 1 and 2. It also provides a foundation for the Level 2 mathematics courses in the appropriate engineering department. The module is delivered via online lectures, reinforced with 2 weekly interactive problem classes.
There are no prerequisites for this module.
The following modules have this module as a prerequisite:
| MAS252 | Further Civil Engineering Mathematics and Computing |
Aims
- To reinforce previous mathematical knowledge.
- To develop new mathematical concepts needed to support engineering at Level 1.
- To provide a foundation for the Level 2 mathematics courses for engineers.
Learning outcomes
Semester 1:- Ability to sketch functions and evaluate simple limits using algebraic techniques.
- Ability to differentiate, find maxima and minima and apply this technique to curve sketching.
- Ability to find 1st and 2nd order partial derivatives.
- An understanding of hyperbolic functions.
- Ability to apply l'Hôpital's rule.
- Ability to manipulate complex numbers.
- Knowledge of the basic properties of vectors.
Semester 2:
- Ability to evaluate indefinite and definite integrals using the techniques of substitution and integration by parts.
- Ability to manipulate matrices, evaluate determinants and find the inverse of a non-singular square matrix.
- Ability to apply matrix methods to the solution of systems of simultaneous linear equations.
- Ability to find eigenvalues and corresponding eigenvectors of a square matrix
- Ability to solve first order ordinary differential equations which are (i) variables separable, (ii) linear,
- Ability to solve second order linear homogeneous ordinary differential equations with constant coefficients.
- Ability to solve second order linear inhomogeneous ordinary differential equations with constant coefficients, using a trial technique for the particular integral.
- Ability to apply Laplace Transforms and use them to solve linear differential equations.
Teaching methods
Online video lectures, online tests, problem classes, problem solving.
5 lectures, 40 tutorials
Assessment
One three-hour exam at the end of the year (85%). Online tests (15%).
Full syllabus
Semester 1:
1. Functions of a real variable and limits:
The concept
of a function and simple limits, continuity.
2. Differentiation:
Basic rules of differentiation:
maxima, minima and curve sketching. Inverse functions.
3. Partial differentiation:
1st and 2nd derivatives,
geometrical interpretation.
4. Hyperbolic functions:
Definitions and derivatives
of hyperbolic functions and their inverses.
5. Series:
Taylor and Maclaurin series, L'Hôpital's rule.
6. Complex numbers:
basic manipulation,
Argand diagram, de Moivre's theorem, Euler's relation.
7. Vectors:
Vector algebra, dot and cross
products, differentiation.
1. Integration:
Indefinite integrals of simple functions. Simple substitutions. Standard forms involving inverse trigonometric and inverse hyperbolic functions. Examples using completing the square and partial fractions. Integration by parts. Definite integrals: properties, evaluation, application to area.
2. Matrices and linear equations:
Definition of an m ×n matrix. Special matrices (identity, zero, square etc.). Matrix algebra. Transpose. Symmetric and skew-symmetric matrices, and the decomposition of square matrices. Determinants. Inverse of a non-singular matrix. Use of matrices to solve systems of linear equations (homogeneous and nonhomogeneous). Gaussian elimination. Eigenvalues and eigenvectors.
3. Ordinary differential equations:
First order differential equations: variables separable, linear with integrating factor, general solution, solution satisfying given initial conditions. Second order linear differential equations with constant coefficients: auxiliary equation, complementary function. Particular integral for polynomials, exponentials, trigonometric functions and products of polynomials and exponential/trigonometric functions on right-hand side. Laplace Transforms and their use in the solution of linear differential equations.
Reading list
| Type | Author(s) | Title | Library | Blackwells | Amazon |
|---|---|---|---|---|---|
| B | C. W. Evans | Engineering Mathematics | 510.2462 (E) | Blackwells | Amazon |
| B | G. James and D. Burley | Modern Engineering Mathematics | 510.2462 (J) | Blackwells | Amazon |
| B | K. A. Stroud and D. J. Booth | Engineering Mathematics | 510.2462 (S) | Blackwells | Amazon |
(A = essential, B = recommended, C = background.)
Most books on reading lists should also be available from the Blackwells shop at Jessop West.
Timetable (semester 2)
| Mon | 09:00 - 09:50 | tutorial | (group CV1s) | 38 Mappin Street, Workroom 3 | |||
| Mon | 09:00 - 09:50 | tutorial | (group CV2s) | 38 Mappin Street, Workroom 4 | |||
| Mon | 09:00 - 09:50 | tutorial | (group CV3s) | Hicks Lecture Theatre 4 | |||
| Mon | 09:00 - 09:50 | tutorial | (group CV4s) | Hicks Lecture Theatre 10 | |||
| Mon | 09:00 - 09:50 | tutorial | (group CV5s) | K14 Hicks Building | |||
| Thu | 13:00 - 13:50 | lecture | Richard Roberts Auditorium | ||||
| Fri | 12:00 - 12:50 | lab session | (group cv1s) | Hicks Lecture Theatre 4 | |||
| Fri | 12:00 - 12:50 | lab session | (group cv2s) | Hicks Lecture Theatre 10 | |||
| Fri | 12:00 - 12:50 | lab session | (group cv3s) | Hicks Lecture Theatre D | |||
| Fri | 12:00 - 12:50 | lab session | (group cv4s) | Hicks Lecture Theatre 9 | |||
| Fri | 12:00 - 12:50 | lab session | (group cv5s) | 9 Mappin Street G14 |