Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MTH101
Module Title: Engineering Mathematics I
Module Level: Level 1
Module Credits: 5.00
Semester: SEM1
Originating Department: Department of Pure Mathematics
Pre-requisites: N/A

 Aims The aims of this module are to:To give students advanced mathematical tools common to engineering applications. To demonstrate the physical origin of applied mathematics.To understand the basic concepts in vector analysis, complex functions and Laplace transformsTo be familiar with the equations of importance to engineering and science and their properties.To train the students' ability to think logically and independently and to acquire the skills of problem solving.
 Learning outcomes On successful completion of the module, the student is expected to have:A good understanding of the basics concepts of: A. Complex functions and their integrals.B. Laplace transforms.C. Series solutions of ODEs. D. Be able to solve problem by establishing appropriate mathematical models using the most relevant techniques.E. Have an appreciation of the importance of mathematics to engineering and science.
 Method of teaching and learning This module will be delivered by a combination of formal lectures, problem classes, case studies and revision seminars.
 Syllabus Complex Analysis (18 h)1.1 Revision of complex numbers1.2 Complex Functions1.3 Limit derivative, definition of analytic function, Cauchy-Riemann equations1.4 Rational function, exponential function, trigonometric and hyperbolic function, logarithmic function1.5 Complex integral: line integral, Cauchy's integral theorem 1.6 Laurent series1.7 Analyticity at infinity, zeros and singularities1.8 Integration by the method of residuesLaplace Transforms (9 h.)2.1 Definitions of Laplace transform and inverse transform, condition for existence.2.2 Properties and Laplace transform pairs2.3 Using residue theorem to obtain inverse Laplace transform2.4 Convolution and correlation2.5 Use of Laplace transform for the solution of ODEPower Series Solutions Of Ordinary Differential Equations (10 h)3.1 The power series methods and its theoretical basis 3.2 Legendre's equation and Legendre polynomials 3.3 Extended power series method and indicial equation3.4 Bessel's equation and Bessel functions of first kind3.5 Bessel functions of second kind 3.6 Orthogonal functions, orthogonality of Legendre's polynomials and Bessel function.2 hours Revision
Delivery Hours
 Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total Hours/Semester 39 13 98 150

## Assessment

 Sequence Method % of Final Mark 1 Formal Examination 80.00 2 Midterm 20.00
 Module Catalogue generated from SITS CUT-OFF: 12/5/2020 1:16:56 PM