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General Information
The class grade is determined as the follow percentages. The grade follows
the standard method 90-100 A , 80-89 B , 70-79 C ,
60-69 D , and below 60 F .
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Percentage of Final
Grade |
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Homework |
15 % |
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Exam 1 |
25 % |
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Exam 2 |
25 % |
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Final |
35 % |
Homework will be assigned every class and will be collected at the
two class period later. This is a problems course, and you are
going to do problems. However, you can work in groups on the homework. I
want you to learn the material.
Textbook: Fausett , Applied Numerical Analysis, Using Matlab
, 1999
Outline
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Date |
Topic |
Reading |
May 28 -
June 1 |
Syllabus & grading; Introduction and
overview of the class; Numerical Analysis and Computers; Introduction to
Matlab
Matlab introduction continue; Matlab files and data files; Input/Output
files: Relative/Logistic/Arithmetic Operations; Operational Precedence:
Program flow controls:"if", "switch", "for", and "while" ; Designing a
program; Debug techniques;
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Chap. 1
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June 4 -
June 8 |
Numerical Errors; Computer problems; Introduction to 1 variable methods;
Bisection method, linear interpolation, Secant method, Newton's method, and
Muller's method. Begin with systems of equations, Gauss elimination, etc.
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Chap 2 & 3
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June 11 -
June 15 |
The material covers the
systems of equations and setting them up in matrix format. Discuss the
solving systems of equations using Gaussian elimination, Gauss-Seidel, and
Gauss-Jordan.
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Chap. 3 & 4
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June 18 -
June 22 |
Discussion on how to handle nonlinear numerical problems using succcessive
over relaxation, newton method, and problems with the stability of
nonlinear problems. The lectures cover the topics of LU decomposition,
Cout's method, Doolittle method, Cholesky's method and how to solve
problems using the techniques.
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Chap. 5 & 6
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June 25 -
June 29 |
Exam 1 will be open book and open notes, however you are going to need
know the material. The lectures will continue with LU decomposition and start
the discussion on eigenvalues and eigenvectors.
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Chap. 6 & 7
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July 2 -
July 6 |
The lectures introduce the topic of eigenvalues and eigenvectors and how
to determine them using Power method, Inverse Power methods and QR techniques
Introduction of interpolation between points using Lagrange, Newton
and linear interpolation. Using interpolation techniques to analysis
data points between values.
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Chap. 7 & 8
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July 9 -
July 13 |
The introduction of
Rational function, Hermite polynomials and Cubic splines. The lecture
dealt with least square techniques to find the best curve fit for the data.
Discussed nonlinear least square techniques (log-log), quadratic and Legrende
polynomials to model the space.
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Chap. 8 & 9
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July 16 -
July 20 |
Discussion on how to
do simple derivatives using Taylor series to obtain the formulas, estimating
the error and how to refine the derivatives. The integration techniques using
Trapezoidal, Simpson's method 1/3 and 3/8, Gaussian Quadrature and Romberg
refinements.
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Chap. 11 & 12
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July 23 -
July 27 |
Exam 2 is to be given in class and will be open notes and open
book. Discussion on how to
do initial value problems with Taylor series, Euler, Modified Euler/Midpoint
method/Linear Runge Kutta, Classic (4th order) Runge Kutta, Adam
Bashford and Predictor Corrector techniques.
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Chap. 12 & 13
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July 30 -
Aug. 3 |
Discussion of systems of ODEs and discussion of BVP.
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Chap. 13 & 14
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Aug. 6 -
Aug. 10 |
Final Exam - August 7 from 1:00pm-3:00pm
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