# KC4018 - Engineering Analytics

## What will I learn on this module?

Basic algebra and trigonometry
Transposition, simplification, quadratic equations, simultaneous equations, functions and 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.

# 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 allow students 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. Students 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. You will have an opportunity to carry out relevant engineering problems and will be provided with formative feedback in seminars. 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. The mathematical rigour and critical thinking associated with this module will develop your ability to tackle engineering problems which is skill demanded by employers. All the skills 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 a formal class test worth 20% of the mark in early semester two and a closed book written examination worth 80% of the mark at the end of the year. Written feedback will be provided to the cohort in class for the MCQ test and 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 ed to supporting resources including relevant texts, student software downloads and relevant multimedia materials.

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?

Knowledge & Understanding:
1) 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:
2) Use derivatives and partial derivatives to solve minimisation problems and estimate measurement errors.
3) Employ techniques of differentiation, integration and differential equations to model simple mechanical systems. Include MLO’s being assessed eg.. MLO 2 & 3

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
4) Increases awareness and proficiency in exploiting mathematical techniques to solve physical and engineering problems.

# How will I be assessed?

1. MCQ Class Test (20%)
KU-F4, IP F1 PVA F5 You will receive feedback in class as a group within 20 working days of the class

2. Examination (80%)
KU-F4, IP-F1, PVA-F5
Feedback given to students on their exam script within 20 working days of the exam

As above.

1. Seminars (problem solving sessions)
Continuous feedback will be provided on seminar work. This work will include problems designed to aid student understanding

N/A

N/A

# 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 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 on line discussions while formal feedback is provided through coursework and final assessment.

# What will I learn on this module?

Basic algebra and trigonometry
Transposition, simplification, quadratic equations, simultaneous equations, functions and 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.

### Course info

UCAS Code H201

Credits 20

Mode of Study 4 years full-time or 5 years with a placement (sandwich)/study abroad

Department Mechanical and Construction Engineering

Location City Campus, Northumbria University

City Newcastle

Start September 2020

### Current, Relevant and Inspiring

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