## MAS156 Mathematics (Electrical and Aerospace)

 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.

Prerequisites: B Tech or A-level mathematics or equivalent

The following modules have this module as a prerequisite:
 MAS241 Mathematics II (Electrical)

## Aims

1. To reinforce previous mathematical knowledge.
2. To develop new mathematical concepts needed to support engineering at Level 1.
3. To provide a foundation for the Level 2 mathematics courses for engineers.

## Learning outcomes

Semester 1:
1. Ability to sketch functions and evaluate simple limits using algebraic techniques.
2. Ability to differentiate, find maxima and minima and apply this technique to curve sketching.
3. Ability to find 1st and 2nd order partial derivatives.
4. An understanding of hyperbolic functions.
5. Ability to apply l'Hôpital's rule.
6. Ability to manipulate complex numbers.
7. Knowledge of the basic properties of vectors.

Semester 2:
1. Ability to evaluate indefinite and definite integrals using the techniques of substitution and integration by parts.
2. Ability to manipulate matrices, evaluate determinants and find the inverse of a non-singular square matrix.
3. Ability to apply matrix methods to the solution of systems of simultaneous linear equations.
4. Ability to find eigenvalues and corresponding eigenvectors of a square matrix
5. Ability to solve first order ordinary differential equations which are (i) variables separable, (ii) linear,
6. Ability to solve second order linear homogeneous ordinary differential equations with constant coefficients.
7. Ability to solve second order linear inhomogeneous ordinary differential equations with constant coefficients, using a trial technique for the particular integral.
8. 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.

Semester 2:
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.

Type Author(s) Title Library Blackwells Amazon
B A. Croft, R. Davison and M. Hargreaves Engineering Mathematics: a foundation for electronic, electrical, communications and systems engineer 510.2462 (C) Blackwells Amazon
B C. W. Evans Engineering Mathematics 510.2462 (E) Blackwells Amazon
B G. James and D. Burley Modern Engineering Mathematic 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 12:00 - 12:50 lecture Diamond Building LT1 Tue 09:00 - 09:50 tutorial (group EE1s) 9 Mappin Street G14 Tue 09:00 - 09:50 tutorial (group EE2s) DIA-WR3 Tue 09:00 - 09:50 tutorial (group EE3s) 38 Mappin Street, Workroom 4 Tue 15:00 - 15:50 tutorial (group AE1s) Hicks Lecture Theatre 10 Tue 15:00 - 15:50 tutorial (group AE2s) Hicks Lecture Theatre B Tue 15:00 - 15:50 tutorial (group AE3s) Hicks Lecture Theatre D Tue 15:00 - 15:50 tutorial (group AE4s) Arts Tower Lecture Theatre 8 Thu 11:00 - 11:50 lab session (group ae1s) Arts Tower Lecture Theatre 7 Thu 11:00 - 11:50 lab session (group ee1s) Hicks Lecture Theatre 4 Thu 11:00 - 11:50 lab session (group ee2s) 9 Mappin Street G14 Thu 11:00 - 11:50 lab session (group ee3s) Richard Roberts Room B79 Thu 12:00 - 12:50 lab session (group ae2s) DIA-WR1 Thu 12:00 - 12:50 lab session (group ae3s) DIA-WR3 Thu 12:00 - 12:50 lab session (group ae4s) 38 Mappin Street, Workroom 4