Numerical Analysis (ENS 409)

2024 Spring
Faculty of Engineering and Natural Sciences
Engineering Sciences(ENS)
3
6
Melih Türkseven melih.turkseven@sabanciuniv.edu,
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English
Undergraduate
CS201 DSA201
Formal lecture
Interactive,Project based learning,Simulation
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Programs\Type Required Core Elective Area Elective
Computer Science and Engineering *
Computer Science and Engineering *
Data Science and Analytics *
Electronics Engineering *
Electronics Engineering *
Industrial Engineering *
Industrial Engineering (Previous Name: Manufacturing Systems Engineering) *
Materials Science and Nano Engineering *
Materials Science and Nano Engineering (Previous Name: Materials Science and Engineering) *
Mathematics Minor *
Mechatronics Engineering *
Mechatronics Engineering *
Molecular Biology, Genetics and Bioengineering *
Molecular Biology, Genetics and Bioengineering (Pre. Name: Biological Sciences and Bioengineering) *

CONTENT

This course covers the use of numerical computing techniques for mathematical and scientific problems. Topics include: floating-point representation, approximations and computer arithmetic, error analysis, conditioning and stability, Taylor series, roots of nonlinear equations, Newton's method, curve fitting and interpolation solution to systems of linear equations using techniques such as LU decomposition, Gaussian elimination, Jacobi, Gauss-Seidel Iteration, eigenvalue problems, numerical integration and solutions to differential equations.

OBJECTIVE

To provide a solid background for understanding and implementing numerical analysis and related algorithms.

LEARNING OUTCOMES

  • Perform error analysis; compute absolute and relative errors, round-off and truncation errors; identify subtractive cancellation and error magnification in numerical computations
  • Implement various root finding algorithms for the solution of nonlinear equations
  • Interpolate data using Lagrange and Newton polynomials
  • Approximate noisy data using least squares regression techniques
  • Develop computational algorithms for direct and iterative solutions of system of linear equations
  • Compute numerical derivatives and integrals using various approximations and improve the estimates using Richardson extrapolation
  • Solve ordinary differential equations numerically using Euler, second and fourth order Runge-Kutta methods
  • Gain hands on experience by developing Matlab programs for numerical problems.

ASSESSMENT METHODS and CRITERIA

  Percentage (%)
Final 30
Midterm 25
Participation 5
Individual Project 30
Homework 10

RECOMENDED or REQUIRED READINGS

Textbook

Numerical Analysis, J. Douglas Faires and Richard L. Burden, Thomson Press, 2004 (9th edition is available as pdf)
Optional Readings

- Applied Numerical Methods with MATLAB for Engineers and Scientists, S. C. Chapra, 3rd Edt., Tufts University, McGraw-Hill, 2012.
- Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, 6th Edition, McGraw-Hill, 2010
- Numerical Methods using MATLAB, J.H. Mathews & K.D. Fink, 4th Edt., Pearson, 2004.