HOLY ANGEL UNIVERSITY Graduate School of Engineering
Numerical Methods (GSNUMET)
Course Description
The course deals with the different techniques by which mathematical problems are formulated to solve with arithmetic operations. It covers the types of mathematical subject areas such as roots of equations, systems of linear algebraic equations, curve fitting, and numerical integration and differentiation.
Credit Units: 3 units Objectives:
At the end of the course, the students should be able to:
a. Have sufficient information to successfully approach a wide variety of engineering problems dealing with roots of equations.
b. Solve problems involving linear algebraic equations and appreciate the application of these equations in many fields of engineering.
c. Greatly enhance their capabilities to fit curves to data.
d. Solve many numerical integration and differentiation problems and appreciate their application for engineering problem solving.
e. Master the techniques and learn to assess the reliability, and be capable of choosing the best method/s for any particular problem.
Course Requirement/s: Term examinations, Portfolio, Literature surveys on numerical methods for engineering application to be presented in class at the end of the term.
Weeks Learning Content
1 Introduction: Mathematical Modeling and Engineering Problem-Solving, Computers and Software
2 Roots of Equations: Bracketing Methods (Graphical, Bisection)
3 Roots of Equations: Bracketing Methods (False Position, Problems)
4 Roots of Equations: Open Methods (Simple Fixed-Point Iteration, The Newton-Raphson Method)
5 Roots of Equations: Open Methods (The Secant Method, Multiple Roots)
6 Research Day
7 Linear Algebraic Equations: Gauss Elimination (Naïve Gauss Elimination, Gauss Jordan)
8 Linear Algebraic Equations: LU Decomposition 9 Linear Algebraic Equations: Matrix Inversion
10 Linear Algebraic Equations: Special Matrices and Gauss Seidel
11 Research Day
12 Curve Fitting: Least-Squares Regression 13 Curve Fitting: Interpolation
14 Curve Fitting: Fourier Approximation
15 Numerical Differentiation and Integration
16 Engineering Applications (Classroom presentations of literature surveys)
