Engineering Mathematics II
 
 
Subject Code: EEM1026
Aim of Subject: To provide various mathematical concepts and analysis methods in matrices, ordinary and partial differential equations and statistics in the engineering context.
Learning Outcome of Subject: At the completion of the subject, students should be able to:
  • Define and apply the concepts of sampling theory and central limit theorem
  • Perform statistical inference using estimation and hypothesis testing.
  • Define and apply basic matrix operations
  • Obtain the determinant of a square matrix and the inverse of an invertible matrix
  • Define and discuss the concepts of linear dependence and independence
  • Solve a system of linear equations using matrix method
  • Define the Fourier and Laplace transforms and their inverses
  • Apply Fourier and Laplace transforms to solve boundary value problems
  • Define -transform and apply it to solve difference equations
  • Solve first order ODE, in particular linear, separable and exact differential equations
  • Solve second order homogeneous and non-homogeneous ODEs with constant coefficients
  • Use series solution method to solve linear ODEs.
  • Classify basic PDEs, in particular classify second order linear PDEs as elliptic, hyperbolic or parabolic type (wave, diffusion and Laplace equations)
  • Discuss and apply the D’Alembert formula to solve the wave equation
  • Apply separation of variables method to solve linear homogeneous PDEs and transform the PDE using appropriate coordinate system that fits the boundary conditions
Programme Outcomes:
  • Ability to acquire and apply fundamental principles of science and engineering(80 %)
  • Capability to communicate effectively(10%)
  • Ability to identify, formulate and model problems and find engineering solutions based on a systems approach(10%)
Assessment Scheme:
  • Test/Quiz/Assignment - Written test, To enhance the understanding of basic concepts in lectures, To consolidate the concepts and techniques in lectures through problem solving. (40%)
  • Final Exam - Written exam(60%)
Teaching and Learning Activities: 50 hours (lectures and tutorials)
Credit Hours: 3
Pre-Requisite: EEM1016: Engineering Mathematics I
References:
  • Lecture Notes Series: Engineering Mathematics Volume 1 - 2nd edition, Pearson Prentice Hall, 2006. (Textbook)
  • Elementary Linear Algebra - 9th edition, Howard Anton, John Wiley & Sons, 2005.
  • Advanced Engineering Mathematics - 9th edition, Erwin Kreyszig, John Wiley & Sons, 2006.
  • Advanced Modern Engineering Mathematics - 3rd edition, Glyn James, Pearson Prentice Hall, 2004.
  • Further Engineering Mathematics - 3rd edition, Stroud, K.A., Macmillan, 1996.
  • Partial Differential Equations and Boundary-Value Problems with Applications - 3rd edition, Pinsky, M.A., McGraw-Hill, 1998.
  • Beginning Partial Differential Equations - 2nd edition, Peter V. O’Neil, John Wiley & Sons, 2008.
  • Calculus - 6th edition, James Stewart, BrooksCole, 2008.
  • Probability and Statistics for Engineers and Scientists - 8th edition, R.E.Walpole, R.H.Myers, S.L.Myres and K. Ye, Prentice Hall, 2007.

Subject Contents

  • Statistics
    Elementary sampling theory for normal population. Central limit theorem. Statistical inference (point and interval estimation and hypothesis testing) on means, proportions and variances. Chi-squares test of goodness of fit. Examples involving engineering applications.

     
  • Matrices and Determinants
    Matrices, some special matrices, matrix operations. Determinants and some useful theorems. Laplace’s development. Solution of system of linear equations by determinants. Linear dependence and independence, rank of a matrix. General system of linear equations, existence and properties of solution, Gaussian elimination.
     
  • Ordinary Differential Equations

    • Introduction and characteristics of a differential equation: definition, degree, order, linearity, homogeneity, concept of solution. First order equations, separable variables,exact equations, integrating factors, linear equations with applications (eg. radiocarbon dating, Newton’s law of cooling, etc.)
    Second order linear differential equations with constant coefficients.Homogeneous equations with applications such as electric circuits and mass-spring system, damping system. Non-homogeneous equations: complementary functions, particular integrals, method of undetermined coefficients. General linear second-order differential equations with variable coefficients. Elementary power series methods.
     
  • Integral Transform

    • Derivation of transforms and inverses (Fourier and Laplace). Applications of these transforms in boundary and initial value problems (eg. electrical circuits with a voltage source). -transform and its application to solve finite difference equations.
     
  • Partial Differential Equations

    • Basic concepts of partial differential equations. Classification of 2nd order linear partial differential equation into basic types. The principle of superposition. The wave, diffusion and Poisson’s equations. Boundary and initial-value problems. D’Alembert’s solution for wave equation. Method of separation of variables.