1 - Syllabus
Syllabus for SE 301 Numerical Methods for Semester 071
Catalog Description
Roots of nonlinear equations. Solutions of systems of linear algebraic equations. Numerical differentiation and integration. Interpolation. Least squares and regression analysis. Numerical solution of ordinary and partial differential equations. Introduction to error analysis. Engineering case studies.
Course Objectives
The course aims to introduce numerical methods used for the solution of engineering problems. The course emphasizes algorithm development and programming and application to realistic engineering problems.
Grading
Attendance 5% (-1 for each absence)
HW + Computer Homework 15%
Quizzes 20%
Midterm 25 % topics 1,2,3,4 (Nov. 3, 2007 7:00-9:00 PM)
Final 35 % topics 5,6,7,8,9 (Registrar)
Pre-Requisite
ICS 101 & MATH 201
Textbook
“Numerical Methods for Engineers”, Steven C. Chapra and Raymond P. Canale.
Other Reference:
"Numerical Mathematics and Computing." W. Cheney and Kincaid, 4th Edition.
Topics
1. Introductory material: 4 Lecturers
absolute and relative errors, Rounding and chopping, Computer
errors in representing numbers (sec 3.1-3.4)*.
Review of Taylor series (sec 4.1),
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2. Locating roots of algebraic equations: 6 Lectures
Graphical Methods ( Sec 5.1), Bisection method (Sec 5.2),
Newton method (sec 6.2), Secant method (sec 6.3),
Systems of nonlinear equations (6.5.2)*
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Systems of linear equations: 6 Lectures
Naïve Gaussian elimination (sec 9.2)
Gaussian elimination with scaled partial pivoting
and Tri-diagonal systems, Gauss-Jordan method (Sec 9.7)*
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4. The Method of Least Squares; 4 Lectures
Linear Regression (Sect 17.1), Polynomial Regression (17.2)
Multiple Linear Regression (Sec 17.3)*
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5. Interpolation: 4 Lectures
Newton’s Divided Difference method (Sec. 18.1),
Lagrange interpolation (Sec 18.2), Inverse Interpolation (Sec 18.4)
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6. Numerical Integration: 6 Lecturers
Trapezoid rule (sec. 21.1), Romberg algorithm (sec 22.2).
Gauss Quadrature (sec 22.3 )*
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7. Numerical Differentiation: 2.5 Lectures
Estimating derivatives and Richardson’s Extrapolation (sec. 23.1-23.2).
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8. Ordinary differential equations: 9 Lectures
Euler’s method (sec 25.1), Improvements of Euler’s method (sec 25.2),
Runge-Kutta methods (sec.25.3),
Methods for systems of equations (sec 25.4),
Multistep Methods (Sec 26.2),:
Boundary value problems (Sec. 27.1).
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9. Partial differential equations: 2.5 Lectures
Elliptic Equations (sec 29.1-29.2)and
Parabolic Equations (sec 30.1-30.4).
Revision 1 Lecture
