The University of Southampton
Courses

# MATH1055 Mathematics for Electronic and Electrical Engineering

## Module Overview

Feedback and student support during module study (formative assessment) • Examples and specimen test in each set of self-study notes, with solutions, for self-assessment. • Test at end of each topic is marked one-to-one with immediate feedback, at the rate of about two tests in three weeks. • Twice weekly timetabled workshops available. • Past examination papers and solutions. Relationship between the teaching, learning and assessment methods and the planned learning outcomes. The end of module examination is structured into two parts. The first part contains 20 multiple choice questions which test basic knowledge of all topics and whether simple calculations can be performed successfully. The second part consists of longer questions which test the depth of understanding of topics on the syllabus and the ability to carry out longer pieces of work. The general skills elements are not explicitly assessed, but their development will reflect on the quality of the overall outcomes.

### Aims and Objectives

#### Module Aims

To present, after some preparation and revision, the basic mathematical methods of differential and integral calculus, complex numbers, vectors and matrices, ordinary differential equations and statistics

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• Critically analyse and solve some mathematical problems
• Work more effectively with self-study material
• Demonstrate knowledge and understanding of basic differential and integral calculus, complex numbers, vectors and matrices, statistics and differential equations, and be familiar with partial differentiation and some more advanced techniques of calculus
• Show logical thinking in problem solving
• Demonstrate organisational and time-management skills
• Perform calculations in simple situations and work through some longer examples

### Syllabus

A-Level Revision Algebra: simplification of expressions and functions; indices; linear and quadratic equations; simultaneous linear equations; inequalities; partial fractions. Trigonometry: solution of triangles; multiple angle formulae; trigonometric equations. The following topics are studied and tested over two semesters: 1. Differentiation: basic rules; differentiation of standard functions; Newton's method for finding roots; partial differentiation. 2. Integration: definition of integral; standard integrals; substitution; integration by parts; numerical integration. 3. Complex numbers: graphical representation; algebra; polar form; Euler's formula and exponential form. 4. Differential equations : classification; simple first and second order differential equations. 5. Functions: inverse; trigonometric; exponential, logarithmic and hyperbolic. 6. Differentiation: maxima, minima and points of inflection; curve sketching; parametric, implicit and logarithmic differentiation; Taylor and Maclaurin series. 7. Integration: substitution; applications to centroids, volumes of revolution, etc. 8. Integration: rational functions; improper integrals. 9. Integration: double integrals; polar coordinates; triple integrals. 10. Differential equations: solution of first order ODEs (separable, homogenous, linear and exact). 11. Differential equations: linear operators; linear inhomogeneous second order ODEs; free and forced oscillators. 12. Vectors: basic properties; Cartesian components, scalar and vector products. 13. Vectors: triple products; differentiation and integration of vectors; vector equations of lines and planes. 14. Matrix algebra: terminology; addition, subtraction and multiplication of matrices; determinants. 15. Matrix algebra: inverse of a matrix using cofactors; systems of linear equations; inverse of a matrix using the elimination method. 16. Matrix algebra: rank; eigenvalues and eigenvectors. 17. Further calculus: chain rule for partial derivatives; higher partial derivatives; total differentials and small errors. 18. Laplace transforms: definition; standard functions; inverse transforms; solution to second order ODEs. 19. Complex numbers: trigonometric and hyperbolic functions; logarithm of a complex number; De Moivre's theorem; roots; simple loci in the complex plane. 20. Fourier series: periodic signals; whole-range Fourier series; even and odd functions.

#### Special Features

This is a self-study course: there are no lectures except an introductory lecture on the first session in Week 1. The other sessions are testing and marking sessions, which the student attends at their own pace.

### Learning and Teaching

#### Teaching and learning methods

Teaching methods include • Self-study notes for each topic, including examples and specimen test (with solutions). Learning activities include • Individual study of identified sections in course textbook. • Working through examples and specimen test for each topic in the set of self-study notes, with solutions provided.

TypeHours
Teaching1
Independent Study149
Total study time150

K A Stroud (2007). Engineering Mathematics.

Glyn James (2015). Modern Engineering Mathematics.

### Assessment

#### Summative

MethodPercentage contribution
Class Test  (1 hours) 5%
Coursework 20%
Written exam  (2 hours) 75%

#### Referral

MethodPercentage contribution
Exam 100%

#### Repeat Information

Repeat type: Internal & External

### Costs

#### Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

##### Books and Stationery equipment

The core textbook (James, 5th edition) is provided by the Faculty. Theare are copies of the alternative core textbook (Stroud, 6th edition) in the Hartley library (8 copies, 2 in short loan, library code QA100 STR). Older versions of the core textbooks (James 4th or 3rd edition, Stroud 5th edition) can also be used, and the library holds several copies.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.