12/08/2023, 16:53 EN1091: Engineering Analysis EN1091: Engineering Analysis School Cardiff School of Engineering Department Code ENGIN Module Code EN1091 External Subject Code 100184 Number of Credits 20 Level L4 Language of Delivery English Module Leader Dr Fei Jin Semester Double Semester Academic Year 2023/4 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 and to provide an introduction to numerical methods as a tool for solving engineering problems. 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 the concept of series expansions and convergence 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 Understand the scope offered by numerical techniques for the solution of engineering problems How the module will be delivered The module will be delivered through a blend of online teaching and learning material, guided study, and oncampus 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 Determine the series expansions of mathematical functions and the conditions under which they converge. 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 https://data.cardiff.ac.uk/legacy/grails/module/EN1091.html 1/3 12/08/2023, 16:53 EN1091: Engineering Analysis Apply basic numerical methods to solve engineering problems How the module will be assessed Students are assessed by two class tests, and by a 3-hour examination at the end of the Spring semester. Feedback is provided during example/tutorial classes. 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 1 N/A Exam - Spring Semester 80 Engineering Analysis 3 Class Test 10 Engineering Analysis Test 2 N/A Syllabus content Fundamentals of Algebra, Vectors & Function 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. Infinite series and expansion of functions Definition of series and simple concepts of convergence; ratio test for general series; power series and expansion of functions; Maclaurin`s and Taylor`s series; series for trigonometric, logarithmic and exponential functions; evaluation of functions. 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; theorems of Pappus; 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 https://data.cardiff.ac.uk/legacy/grails/module/EN1091.html 2/3 12/08/2023, 16:53 EN1091: Engineering Analysis of functions, chain rule, higher partial derivatives. Stationary values of a function of several variables. Fourier series Periodic Functions The Euler formulas and alternative formulas for Fourier coefficients. Half-Range expansions and simple applications of Fourier series. Numerical Methods Linear simultaneous equations - Gauss, Siedel, Jacobi Copyright Cardiff University. Registered charity no. 1136855 https://data.cardiff.ac.uk/legacy/grails/module/EN1091.html 3/3
