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COURSE OUTLINE
KMU 206
- NUMERICAL ANALYSIS WITH MATLAB®
SPRING SEMESTER, 2007-2008 |
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INSTRUCTOR: |
Dr. ÖNEL, Selis
| selis@hacettepe.edu.tr
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TEACHING ASSISTANT: |
PAŞAOĞLU, Gökhan
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gpasa@hacettepe.edu.tr |
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COURSE GOALS: |
- Teach fundamentals of numerical
methods
- Enhance students' programming skills using the MATLAB
environment to implement algorithms
- Teach the use of MATLAB as a tool (using built-in functions)
for solving problems in science and engineering |
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COURSE MAIN TEXTBOOK: |
Currently, a main course textbook
is not assigned and the students have the option to choose any
of the supplementary textbooks for the course. |
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SUPPLEMENTARY TEXTBOOKS: |
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S.
Nakamura, Numerical Analysis and Graphic Visualization with
MATLAB® , 2/e, Prentice Hall, 2002, ISBN:01306548921
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A.
Gilat and V. Subramaniam, Numerical Methods for Engineers and
Scientists, John Wiley & Sons, Inc., 2008, ISBN:
9780471734406
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C. Moler, Numerical Computing with MATLAB®,
Electronic edition: The MathWorks, Inc., Natick, MA, 2004,
http://www.mathworks.com/moler. Print
edition: SIAM, Philadelphia, 2004.http://ec-securehost.com/SIAM/ot87.html
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J.
H. Mathews and K. D. Fink, Numerical Methods Using MATLAB®,
3rd ed, Upper Saddle River, NJ: Prentice Hall, 2004, ISBN:
0130652482
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L.
v. Fausett, Applied Numerical Analysis Using MATLAB® 2/E,
Prentice Hall, ISBN: 0132397285
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J.
Kiusalaas, Numerical Methods in Engineering with MATLAB® ,
Cambridge University Press, 2005, ISBN: 0521852889
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SCHEDULE: |
KMU 206-21
Monday............. 12:30-14:20 (Class D3)
Friday............... 13:30-15:20 (Class D3)
KMU 206-22
Wednesday........ 13:30-15:20 (Class D3)
Friday............... 09:30-11:20 (Class D3) |
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CONTENT: |
Fundamental formulation, methodology and techniques for
numerical solution of engineering problems, fundamental
principles of digital computing and the implications for
algorithm accuracy and stability, error propagation and
stability analysis. |
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OBJECTIVES: |
Increase the numerical problem solving and computational skills
of engineering students; Implement an understanding of the
numerical methods based on their relevance to engineering
problems; Instill the abilities of both hand computation and
programming. |
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COURSE FORMAT:
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The course will consist of classroom instruction including
lectures using classical lecture style, power point slides, and
simultaneous Matlab applications via projection. Additional
computer lab and tutorial hours will be held by the course
assistant. |
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DATE OF MIDTERM:
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1st
Midterm:
March 24-30
2nd
Midterm:
April 28-May 4 |
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GRADING:
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Quizes Homeworks........... ....................................10%
Midterm I
............................................................15%
Midterm II............................................................30%
Final
Exam...........................................................
45%
Total...................................................................100%
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Course Outline
(click here for
detailed version) |
Week# |
Topics |
1 |
PPt Slides |
Course
objectives, MATLAB® environment & programming (Application in the
computer lab) |
2
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Introduction to
numerical methods; background for matrix and vector operations;
Systems of linear equations:
Unsolvable and
ill-conditioned systems, condition number |
3
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PPt Slides |
Solving systems
of Linear Equations: Background,
Gauss
elimination method, Pivoting, Gauss-Jordan method, LU
decomposition method, inverse of a matrix, brief MATLAB® review |
4
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PPt Slides |
Solving systems
of Linear Equations: Iterative methods, use of MATLAB® built-in
functions |
5
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PPt Slides |
Matrix
eigenvalues and eigenvectors;
Power method |
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Midterm |
6
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PPt Slides |
Nonlinear
equations; background, estimation of error;
Solving nonlinear equations;
Fixed-point
iteration method, Bisection method, Regula Falsi method, Secant method |
7
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PPt Slides |
Systems of
nonlinear equations; Successive substitution method, Newton’s method,
use of MATLAB built-in functions; equations with multiple
solutions |
8
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PPt Slides |
Curve Fitting
and interpolation; interpolation using a single polynomial,
Lagrange and Newton’s polynomials, piecewise interpolation,
linear, quadratic, and cubic splines, use of MATLAB built-in
functions for curve fitting and interpolation |
9 |
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Midterm |
10
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Numerical
differentiation; Differentiation using Lagrange polynomials, use
of MATLAB built-in functions for numerical differentiation |
11 |
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Numerical
differentiation; Richardson’s extrapolation, error in numerical
differentiation, numerical partial differentiation |
12 |
PPt Slides |
Numerical
Integration; background, rectangle and midpoint methods,
trapezoidal method, Simpson’s methods; use of MATLAB built-in
functions for integration, Richardson extrapolation, Romberg
integration |
13 |
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ODE initial
value problems; Runge-Kutta methods, multistep methods,
predictor-corrector methods, system of first-order ODEs,
higher-order IVP; local truncation error in 2nd-order
Runge-Kutta method, step size for desired accuracy, stability,
stiff ODEs |
14 |
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ODE boundary
value problems; background, shooting methods, finite difference
method |
