School of Engineering \ Mechanical Engineering
Course Credit
ECTS Credit
Course Type
Instructional Language
Programs that can take the course
Mathematical modeling and programming. Approximations, error analysis, rounding and truncation errors, Taylor series. Numerical methods for solving algebraic equations: Implicit and explicit methods. Linear equation system solutions: Gaussian elimination, LU discretization and iterative methods. Curve fitting, regression and interpolation: Lagrange, Newton and Gaussian formulations. Numerical integration: Trapezoid and Simpson rules. Numerical methods for solving ordinary differential equations: Euler and Runge-Kutta methods.
Textbook and / or References
StevenCChapraandRaymondP.Canale, "NumericalMethodsforEngineers",6thedition, McGraw-Hill, 2010, ISBN: 978-007-126759-5.
To acquire knowledge about numerical methods used to solve engineering problems and the skills to apply this knowledge to engineering problem solving.
1. Realize the need for numerical methods, understand their capabilities and weaknesses.
2. Practice algorithmic thinking.
3. Learn fundamental numerical techniques that are used in engineering calculations.
4. Learn how to implement these techniques on computer, be aware of built-in functionalities of computer algebra software.
Week 1: Introduction: Mathematical modeling and programming
Week 2: Approaches and error analysis, Taylor series
Week 3: Finding roots of equations: Bracketing methods
Week 4: Finding roots of equations: Explicit methods, Solutions of linear algebraic equations: Gaussian elimination
Week 5: Solutions of linear algebraic equations: LU discretization and Matrix inverse
Week 6: Solutions of linear algebraic equations: Iterative methods, Gauss-Seidel
Week 7: Curve fitting, regression: Linear, 2nd degree, other degree polynomials and Least Squares regression methods
Week 8: Interpolation
Week 9: Numerical integration: Newton Cotes integral formulations, Trapezoid rule
Week 10: Numerical integration: Simpson's rule and Romberg's method
Week 11: Numerical differentiation, methods for numerical solution of ordinary differential equations: Euler's method
Week 12: Methods for numerical solution of ordinary differential equations: Runge Kutta method
Tentative Assesment Methods
Homework 10%
Midterm Exams 40%
Quiz 10%
Final 40%
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