《Numerical Analysis》Syllabus

一．Course Description

二. Course Objectives

The course will introduce the fundamentals of numerical methods for engineering and applied science streams. The goal of the course is to provide a broad background in numerical methods with theoretical discussion. Topics include errors in numerical computation, root finding for algebraic (linear and non-linear equations) and transcendental equation, interpolation, Curve Fitting, Numerical Differentiation, Numerical Integration and Eigenvalues and Eigenvectors.

三．Textbook

J. H. Mathews and K. D. Fink: Numerical Methods using MATLAB, Prentice Hall of India (PHI), 4th Edition, 2005

四．Course Contents

1. Preliminaries

1.1 ReviewofCalculus

1.2 Binary Numbers

1.3 ErrorAnalysis

2. The Solution of Nonlinear Equations f(x)=0

2.1 Iteration for Solving x=g(x)

2.2 Bracketing Methods for Locating a Root

2.3 Newton-Raphson and Secant Methods

3. The Solution ofLinear Systems AX=B

3.1 Upper-Triangular Linear Systems

3.2 Gaussian Elimination and Pivoting

3.3 Triangular Factorization

3.4 Iterative Methods for Linear Systems

4. Interpolation and Polynomial Approximation

4.1 Taylor Series and Calculation of Functions

4.2 Introduction to Interpolation

4.3 Lagrange Approximation

4.4 Newton Polynomials

5. Curve Fitting

5.1 Least-squares Line

5.2 Curve Fitting

5.3 Interpolation by Spline Functions

5.4 Fourier Seriesand Trigonometric Polynomials

6. Numerical Differentiation

6.1 Approximating The Derivative

6.2 Numerical Differentiation Formulas

7. Numerical Integration

7.1 Introduction to Quadrature

7.2 Composite Trapezoidal and Simpson's Rule

7.3 Recursive Rules and Romberg Integration

7.4 Adaptive Quadrature

8. Eigenvalues and Eigenvectors

8.1 Homogeneous Systems: The Eigenvalue Problem

8.2 Power Method

8.3 Jacobi's Method

8.4 Eigenvalues of Symmetric Matrices

五．Recommended Textbooks

[1] S. S. Sastry: Introductory Methods of Numerical Analysis, Prentice Hall of India (PHI), 4th Edition, 2005

[2] C. B. Moler, Numerical Computing with MATLAB, Society for Industrial & Applied ,2004

[3] K. E. Atkinson, An Introduction to Numerical Analysis, Wiley India Pvt. Limited, 2th Edition, 2008

六．Evaluation Scheme and Course Grade

Homework assignment will be given over the course of the semester after the end of each chapter. These will serve primarily for helping students to practice theoretical components of the course material. Homework will be due one week after it is assigned.

Course Grade: Homework 40% + Final Exam 60%