### EN1090: Engineering Analysis

 School Cardiff School of Engineering Department Code ENGIN Module Code EN1090 External Subject Code H100 Number of Credits 20 Level L4 Language of Delivery English Module Leader Dr Emmanuel Brousseau Semester Double Semester Academic Year 2021/2

#### Outline Description of Module

To develop the basic mathematical knowledge and intellectual skills appropriate for a modern engineering degree scheme, and the ability to apply such knowledge and skills in an engineering context.

#### On completion of the module a student should be able to

• Demonstrate knowledge and understanding of differential and integral calculus
• Display an understanding of matrices and matrix algebra
• Understand basic complex numbers and their applications
• Understand elementary statistical analysis and probability, via the interpretation, formulation and solution of mathematical and engineering problems.
• Demonstrate the ability to apply integration to solve a variety of engineering problems
• Understand the concepts and techniques required for solving differential equations
• Understand the concept and application of Fourier series

#### How the module will be delivered

The module will be delivered through a blend of online teaching and learning material, guided study, and on-campus face-to-face classes (tutorials, examples classes).

Students are expected to devote a minimum of three hours per week to private study and attempting a comprehensive set of tutorial problems, which form the basis of the example / tutorial classes.

#### Skills that will be practised and developed

• Apply the basic principles of differential and integral calculus in the solution of mathematical and engineering problems.
• Apply matrix algebra in the solution of simultaneous equations
• Apply basic complex numbers in the solution of numerical problems
• Apply the basic principles of probability theory and statistical analysis in an engineering context.
• Application of integration in solving variety of numerical/engineering problems
• Apply partial differentiation to find stationary values of functions with more than one variable
• Solve first and second order differential equations
• Calculate Fourier series representation of standard waveforms

#### How the module will be assessed

Students are assessed by 4 short class tests, two of them taking place during the Autumn semester and the other two during the Spring semester, circa weeks 4 and 8 for both semesters, and by a formal three-hour examination at the end of the Spring semester.

The class tests takes the form of several compulsory questions, covering the material taught to date, and is designed to enable students to evaluate their progress in relation to the specified learning outcomes.

The formal examination consists of one compulsory question and three from five optional questions, covering all the material taught.

There is a potential for re-assessment in this module which may result in a 100% written assessment during the August Resit period.

#### Assessment Breakdown

Type % Title Duration(hrs)
Class Test 10 Engineering Analysis Test N/A
Exam - Spring Semester 90 Engineering Analysis 3

#### Syllabus content

Fundamentals of Algebra, Vectors & Functions
Expansion and simplification of algebraic expressions. Introduction to vector addition and multiplication. Review of single and multivariable functions such as polynomials, trigonometry and inverse functions.
Differentiation
Definition as a limit; product, quotient and chain rules; differentiation of algebraic, trigonometric, exponential, hyperbolic, logarithmic, inverse, implicit and parametric functions; higher derivatives.
Integration
Definition of indefinite integral; standard forms, integration by substitution and by parts; rational and irrational functions; algebraic, trigonometric and hyperbolic substitutions; definite and improper integrals.
Matrices
Introduction to matrices and matrix algebra. Solving simultaneous equations using matrix algebra.
Complex Numbers
Complex numbers, rectangular and polar forms, Argand diagrams, principal values, conjugates, exp(jq) = cos q + j sinq, De Moivre`s theorem, roots of complex numbers.

Probability and Statistics
Graphical representation of data; measures of location and dispersion; discrete and continuous frequency distributions; probability and probability distributions; Binomial, Poisson and Normal distributions; basic ideas of significance and confidence limits.
Application of integration
Multiple integrals; areas and moments of area, centroid, radius of gyration; parallel and perpendicular axes theorems; polar co-ordinates; lengths and moments of arcs; surface and volumes of revolution; moments of inertia.
Hyperbolic Functions
Hyperbolic functions, inverse hyperbolic functions and their properties.

Ordinary differential equations
Ordinary differential equations, directly integrable, variable separable, homogeneous and linear equations of first order and degree. Integrating factors. Linear differential equations with constant coefficients, complementary functions and particular integrals.

Partial differentiation
Functions of several variables; partial differentiation, the total derivative, partial differentiation of a function of functions, chain rule, higher partial derivatives. Stationary values of a function of several variables.

Fourier series
Periodic Functions.

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