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COURSE OUTLINE
KMU 206
- NUMERICAL ANALYSIS WITH MATLAB®
SPRING SEMESTER |
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INSTRUCTOR: |
Dr.
Selis ÖNEL
| selis@hacettepe.edu.tr
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TEACHING ASSISTANT: |
Erhan
Þenlik|
erhansnk@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: |
The book written by L.v. Fausett's
is recommended as the main textbook for this course. Yet,
students have the option to choose any of the supplementary
textbooks for the course. |
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SUPPLEMENTARY TEXTBOOKS: |
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L.
v. Fausett, Applied Numerical Analysis Using MATLAB® 2/E,
Prentice Hall, ISBN: 0132397285
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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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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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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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J.
Kiusalaas, Numerical Methods in Engineering with MATLAB® ,
Cambridge University Press, 2005, ISBN: 0521852889
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SCHEDULE: |
Joint classes for KMU 206 sections 21
and 22
Monday.....................2 PM - 4 PM (Class D6)
Friday.......................9 AM - 11 PM (Class D6)
KMU 206
Office hours
Thursday...................1 PM - 2 PM
Friday.......................11 AM - 11.45 AM |
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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
26
2nd
Midterm:
April
30 |
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GRADING:
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Quizes & Homeworks..............................................25%
Midterm I
............................................................25%
Midterm
II...........................................................(20%)
Final
Exam + 20% Exam .........................................50%
Total..................................................................100%
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Course Outline
(click here for
detailed version) |
Subject# |
Topics |
1 |
Html Pdf |
Course
objectives, MATLAB® environment & programming |
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Pdf Slides |
Introduction to Matlab
Applications;
Background for matrix and vector operations |
2
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Pdf Slides |
Introduction to
mathematical modeling and numerical methods;
Systems of linear equations:
Unsolvable and
ill-conditioned systems, condition number |
3
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Pdf 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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Pdf Slides |
Solving systems
of Linear Equations: Iterative methods, use of MATLAB® built-in
functions |
5
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Pdf 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 |
6 |
Pdf Slides |
Matrix
eigenvalues and eigenvectors;
Power method |
7
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Pdf Slides |
Nonlinear
equations; background, estimation of error;
Solving nonlinear equations;
Fixed-point
iteration method, Bisection method, Regula Falsi method, Secant method |
8
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PdfSlides |
Systems of
nonlinear equations; Successive substitution method, Newton’s method,
use of MATLAB built-in functions; equations with multiple
solutions |
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 |
Pdf 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 |
