# KC4010 - Engineering Mathematics

## What will I learn on this module?

The module will provide you with a first level course in engineering mathematics. Fundamentals of algebra, trigonometry and calculus are reviewed. Your knowledge of calculus will be extended, and complex numbers, matrices, vectors and differential equations are studied.

Outline Syllabus
Basic algebra and trigonometry
Transposition, simplification, quadratic equations, simultaneous equations, functions sin, cos, tan, inverses, sec, cosec, cot; identities.

Basic calculus
Derivative as slope and rate of change, standard derivatives; product, quotient and function of a function rules; integration
as reverse of differentiation, standard integrals, area under a curve; solution of simple differential equations by direct integration.

Complex numbers
Addition, subtraction, multiplication, complex conjugate and division in algebraic form. The Argand diagram. Polar form and
exponential form, with multiplication and division. De Moivre's theorem (powers and roots). Locus problems.

Calculus
Implicit, parametric and logarithmic differentiation. Maxima and minima. MacLaurin's series. Partial differentiation, first order change, analysis of errors, method of least squares. Integration techniques (substitution, partial fractions, by parts) and simple applications of integration.

Matrices and Determinants
Second and third order determinants, evaluation, properties, Cramer's Rule for solution of simultaneous equations; matrices, addition, subtraction, multiplication, transpose, inverse (via adjoint), solution of simultaneous linear equations by matrix inversion.

Vectors
Sum, difference, magnitude, components, Cartesian representation in three dimensions; scalar and vector products, angle between vectors, application to simple geometrical and physical problems.

Differential Equations
Solution of first order by separation of variables and integrating factor; second order with constant coefficients, auxiliary
equation, complementary function, particular integral by substitution, applications to, for example, mass-spring-damper and/or L-C-R circuits.

### How will I learn on this module?

The module is taught via a wide range of learning and teaching approaches, especially through a combination of lectures and seminars focussing on problem solving where you will be able to obtain help. Lectures will allow you to experience and understand the formalism of the required mathematical techniques as well as include relevant engineering examples and guided in-class exercise-solving sessions between more theoretical expositions. You will have an opportunity to enhance your understanding of the subject through seminars which promote both independent learning and problem solving within peer groups. Through small group teaching you will be instructed in the use of appropriate software (such as MATLAB and Microsoft Excel) which will then allow you to define and solve mathematical problems specifically related to engineering applications. You will receive formative feedback in the seminars. The mathematical rigour and critical thinking associated with this module will develop your proficiency in tackling engineering problems, which is a highly-demanded skill by employers. All the abilities that you will develop in this module are also highly transferable across other engineering and scientific disciplines.

The module learning outcomes will be assessed by an examination worth 100% of the mark at the end of semester one. Written feedback will be provided individually on the exam scripts. All feedback will be provided within 20 working days of the date of the assessment.

### How will I be supported academically on this module?

In addition to direct contact with the module team during lectures and seminars, you will be encouraged to develop your curiosity by making direct contact with the module team through email or a blackboard discussion forum in which you can actively engage with the staff and student peers in a dynamic learning space enabling you to clarify and resolve issues of concern. You will also be regularly directed to supporting resources including relevant texts, student software downloads and relevant multimedia materials, accessible via eLP. References to these resources will be made available through the e-learning portal and in lectures and seminars.

### What will I be expected to read on this module?

All modules at Northumbria include a range of reading materials that students are expected to engage with. The reading list for this module can be found at: http://readinglists.northumbria.ac.uk

### What will I be expected to achieve?

MLO1 Use and apply the basic skills of algebraic and trigonometric manipulation to gain confidence with complex numbers in algebraic, polar and exponential form, de Moivre's theorem, calculus, determinants and matrices, linear simultaneous equations, vectors and differential equations.

Intellectual / Professional skills & abilities:
MLO2 Use derivatives and partial derivatives to solve minimisation problems and estimate measurement errors.

MLO3 Employ techniques of differentiation, integration and differential equations to model simple mechanical systems and electrical circuits.

MLO4 Understand the principles of linear regression and apply it to statistics problems.

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):

MLO5 Increases awareness and proficiency in exploiting mathematical techniques to solve physical and engineering problems.

### How will I be assessed?

SUMMATIVE

1. Examination (100%): MLO1, 2, 3, 4

Feedback given to students on their exam script within 20 working days of the exam.

FORMATIVE
1. Tutorials and workshops – MLO1,2,3,4

Continuous feedback will be provided on seminar work. This work will include problems designed to aid student understanding

None

None

### Module abstract

This module deals with learning the mathematical skills required for your programme and future career path. The module is designed to provide content which is delivered by analytical problem solving as well as by using state of the art mathematical software and will equip you with the skills to solve challenging problems in later years in the chosen discipline. The context of the problems to be solved will include practical and real-life problems from a wide range of engineering applications to demonstrate the relevance of the various mathematical tools taught in the whole year. Teaching methods will include lectures, small group seminars and tutorials where you can interact with your classmates as well as tutors. Regular continuous feedback on your learning will be provided during seminars online discussions while formal feedback is provided through coursework and final assessment.

### Course info

UCAS Code H600

Credits 20

Mode of Study 3 years full-time or 4 years with a placement (sandwich)/study abroad

Department Mathematics, Physics and Electrical Engineering

Location City Campus, Northumbria University

City Newcastle

Start September 2022 or September 2023

## Electrical and Electronic Engineering BEng (Hons)

All information on this course page is accurate at the time of viewing.

Our Campus based courses starting in 2022 and 2023 will be delivered on-campus with supporting online learning content. We continue to monitor government and local authority guidance in relation to Covid-19 and we are ready and able to adjust the delivery of our education accordingly to ensure the health and safety of our students and staff.

On-campus contact time is subject to increase or decrease in line with any additional restrictions, which may be imposed by the Government or the University in the interest of maintaining the health and safety and wellbeing of students, staff, and visitors. This could potentially mean increased or fully online delivery, should such restrictions on in-person contact time be required.

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