COURSE SYLLABUS

Course Number: MATH6630
Course Title: Introduction to Numerical Analysis I
Credit Hours: 3
Prerequisites: Math2650 and the ability to program in a high level language
Corequisite: 

Objectives:
To present the following topics in Numerical Analysis:Numerical solution of equations in one variable, polynomial interpolation and approximation, numerical differentiation and integration, numerical solutions of ordinary differential equations, error analysis. Students will be expected to write computer programs using the algorithmsdiscussed.

Course Content (typical):
Mathematical Preliminaries---calculus, roundoff error, computer arithmetic. (1 week)

Solution of Equations in One Variable (3 weeks)
-- Bisection method
-- Fixed-point iteration
-- Newton-Raphson and the secant method
-- Steffensen's method

Interpolation and Polynomial Interpolation and Approximation (3 weeks)
-- Lagrange interpolation and Neville's method
-- Cubic spline interpolation

Numerical Differentiation and Integration (3 weeks)
-- Numerical differentiation
-- Newton-Cotes quadrature formulas
-- Adaptive quadrature (optional)
-- Romberg integration

Initial-Value Problems for Ordinary Differential Equations (4 weeks)
-- Euler's method
-- Runge-Kutta methods
-- Multi-step predictor-corrector methods
-- Higher order equations and systems of differential equations
-- Stability analysis and stiff differential equations

Introduction to Boundary-value Problems for Ordinary Differential Equations --- Shooting Method (optional, 1 week)

Assign around 5 -- 6 programs from the algorithms above to be programmed and tested by the students.
Assign at least one retrieval from "net lib" for comparison of the codes and results.

Possible Textbooks:
-- K. E. Atkinson, An introduction to Numerical Analysis, Wiley
-- Richard L. Burden and J. Douglas Faires, Numerical Analysis, 5th Edition, Prindle, Weber and Schmidt.

Grading and Evaluation Procedures:
Homework, programming assignments, tests and final exam at the instructor's discretion.
 
Statement related to policies on unannounced quizzes and class attendance and participation:
Individual instructors have different policies concerning pop quizzes, class participation, homework grades, and attendance, which are announced at the beginning of the semester.