 # Module IEA-1002:Mathematics 2

### Module Facts

Run by School of Computer Science and Electronic Engineering

10 Credits or 5 ECTS Credits

Semester 2

Organiser: Dr Zengbo Wang

### Overall aims and purpose

To equip students with the mathematical skills required for Year 1 Engineering courses and for progressing successfully to Year 2 Courses.

### Course content

• Differentiation: Revision of notation for sets and functions. Revision of basic algebra techniques. The limit of a real function at a point. Derivative as gradient: tangent lines. Rules of differentiation. Polynomial, exponential, logarithmic, and inverse functions. Local maxima, minima, points of inflection. Using MATLAB to sketch graphs of functions. Parametric curves; polar coordinates. Solution of equations by iteration

• Integration: Integration as anti-differentiation. The area under a curve. Integration by parts and by substitution. Methods of numerical integration. Mean and root-mean-square values. The method of partial fractions. Integrals of the form f’(x)/f(x) and f’(x).f(x). Distance, velocity and acceleration. Parametric curves: arc length and area. Maclaurin and Taylor series expansions. Arithmetic with Maclaurin series.

• Number Systems: Integers, rationals and real numbers. Fractions ↔ infinite decimal expansions. j = √( -1), solving quadratic equations. Complex arithmetic; Argand diagram. Revision of trigonometric functions. Complex functions: bilinear; exp; log. exp(jθ) = cos(θ) + j.sin(θ). De Moivre’s theorem: n-th roots

• Functions of two variables: Examples of real functions of two variables. Using MATLAB to sketch surfaces. Partial differentiation and tangent planes. Maxima, minima and saddle points. Solution of exact differential equations. Maclaurin series for f(x,y).

### Learning outcomes mapped to assessment criteria

threshold

40%

good

60%

excellent

70%

Know and understand the basis, rules and techniques of differential calculus and its application in engineering.

Has basic knowledge and understanding of differential calculus. Able to apply this knowledge to simple functions found in the electronic engineering course. Has knowledge and understanding of most of the material covered. In addition to the threshold requirements, understands the implications of the theory and is able to apply this to most functions found in the electronic engineering course. In-depth understanding of all areas covered. Able to apply theory to unseen problems.

Know and understand the basis, rules and techniques of integral calculus and its application in engineering.

Has basic knowledge and understanding of the integral calculus. Able to apply the theory to simple functions found in the electronic engineering course. Has knowledge and understanding of most of the material covered. In addition to the threshold requirements, understands the implications of the theory and is able to apply this to most functions found in the electronic engineering course. In-depth understanding of all areas covered. Able to apply theory to unseen problems.

Know and understand the basis, rules and techniques of complex number algebra and its application in engineering.

LO3) Know and understand the basis, rules and techniques of complex number algebra and its application in engineering. Has knowledge and understanding of most of the material covered. In addition to the threshold requirements, understands the implications of the theory and is able to apply this to most functions found in the electronic engineering course. In-depth understanding of all areas covered. Able to apply theory to unseen problems.

Know and understand the basis, rules and techniques for partial differentiation.

LO4) Know and understand the basis, rules and techniques for partial differentiation. Has basic knowledge and understanding of real functions of two variables and the methods of partial differentiation. Able to apply to simpler functions found in the electronic engineering course. In-depth understanding of all areas covered. Able to apply theory to unseen problems.

### Assessment Methods

Type Name Description Weight
Examination 70
Test Week 5 10
Test Week 8 10
Test Week 12 10

### Teaching and Learning Strategy

Hours
Lecture

2 x 2 hours Lectures (lecturing+ student in-class practice style), over 12 weeks

48
Private study

Exercise questions and solutions are available to student for private study after each lecture.

52

### Transferable skills

• Literacy - Proficiency in reading and writing through a variety of media
• Numeracy - Proficiency in using numbers at appropriate levels of accuracy
• Exploring - Able to investigate, research and consider alternatives
• Critical analysis & Problem Solving - Able to deconstruct and analyse problems or complex situations. To find solutions to problems through analyses and exploration of all possibilities using appropriate methods, rescources and creativity.
• Argument - Able to put forward, debate and justify an opinion or a course of action, with an individual or in a wider group setting

### Subject specific skills

• Apply underpinning concepts and ideas of engineering;
• Solve problems logically and systematically;
• Use both verbal and written communication skills to different target audiences;
• Analyse and display data using appropriate methods and mathematical techniques;
• Demonstrate familiarity with relevant subject specific and general computer software packages.

### Courses including this module

#### Compulsory in courses: 