comutational course

1. University ofGondar
Institute ofTechnology
Department ofElectrical and Computer Engineering
Computational Methods course outline
Course Code ECEg2113
Course Title Computational Methods
Degree Program B. Sc. in Electrical and Computer Eng.
Module Name Advanced Engineering Mathematics
Module Code ECEg-M2101
Lecturers Temesgen G. (sec1&2) & Wondimu B. (sec3)
E-mail: temesgengeta13@gmail.com
ECTS Credits 5
Students Workload Lecture Tutorial Practice or Laboratory Home study
48 - 48 48
Course Objectives
& Competences to
be Acquired
Students shall learn basics of mathematical modeling, different numerical methods
for determination of roots of equations, fundamentals of linear algebraic equations,
least square regressions and interpolation methods, numerical differentiation and
integration, and solving ordinary differential equations numerically
Course Description This course is aimed at introducing the students with Number System, Numerical
Error Analysis and Solution of Nonlinear Equations. In addition, it will cover revision
of matrices, interpolation & approximation, numerical differentiation & integration.
And finally, it will introduce them with FEM & FDTD.
Week Contact
Hours
Course Contents
1st
,2nd
6 hrs 1Number System and Numerical Error Analysis
 The Error Problem;
 Representation of Integers and Fractions;
 Number Representation and Storage in Computers;
 Rounding Off Problem;
 Numerical Errors; Significant Digits; Numerical Cancellation;
 Algorithm for Conversion from one base to another;
 Computational Problems and Algorithms;
 Computational Efficiency;
 Computational Methods for Error Estimation
3rd
,4th
,5th
9 hrs 2. Solution ofNonlinear Equations
 Methods used in Root Finding;
 Summary of the Solutions of Nonlinear Equations;
 Fixed Point Iteration;
 RealRoots of Polynomial Equations;
 Iterative Methods for Finding RealZeros of a Polynomial;
 Order of Convergence
6th
,7th
6 hrs 3. ReviewMatricesand its Computation
 Elementary Properties of Matrices;
 Orthogonality and Ortho normality of Vectors and Matrices;
 Norm of Vectors and Matrices, System of Linear Equations
 Existence and Uniqueness of Solutions;
 Methods of Solution of Linear Equations,

2. 8th
3 hrs 4. Solution ofSystems ofNonlinear Equations
 The Iterative Method; The Newton-Raphson Method
9th
Uniform exam week
10th
,11th
,
12th
9 hrs 5. Interpolation and Approximation
 Class of Common Approximation Functions;
 Criteria for the Choice of the Approximate Function;
 Finite Differences;
 Divided Differences;
 Interpolation by Polynomials;
 Least Square Approximation by Polynomials;
 Piecewise Polynomial Approximation;
 Cubic Spline Interpolation
13th
,14th
6 hrs 6. Numerical Differentiation and Integration
 Numerical Differentiation;
 Numerical Integration, numerical Solutions of Differential Equations
 Ordinary Differential Equations;
 Partial Differential Equations
15th
3 hrs 7. Introduction to FEM and FDTD Methods
16th
Final exam
Pre-requisites Applied mathematics-III & Introduction to computing
T. & learning
Methodology
Lectures,tutorials, assignments, laboratory and paper work
Assessment Exams, Quiz’s, Assignments and simulation and laboratory evaluation
Course policy All students are expected to abide by the code of conduct of students Senate
Legislation of our University throughout this course.
 Academic dishonesty, including cheating, fabrication, and plagiarism will not
be tolerated.
 Class activities will vary day to day, ranging from lectures to discussions.
Students will be active participants in the course.
 You are required to submit and present the assignments provided according to
the time table indicated.
 80 % of class attendance is mandatory! Please try to be on time for class. I
will not allow you enter if you are late more than five minutes.
 Active participation in class is essential and it will have its own value in your
grade
 Cell phones MUST be turned off before entering the class
Books &References [1] Chapra C.S. and Canale P.R.,“Numerical Methods for Engineers with
Programming and Software Application”
[2] Recktenwald, Gerald. Numerical Methods with Matlab, Prentice Hall, 2000.
[3] Erwin Kreysizg (2005), Advanced Engineering Mathematics, 9th edition, Wiley.
[4] Stewart,J. (2002), Calculus, 5th edition, Brooks Cole.
[5] Brown, J. W. & Churchill, R. V. (2003), Complex Variables and Applications,
7th edition