FACULTY of ENGINEERING / DEPARTMENT of ELECTRICAL and ELECTRONICS ENGINEERING (30%) English Course Catalog http://www.ktu.edu.tr/eee Phone: +90 0462 3253154 , 3772906

MF

FACULTY of ENGINEERING / DEPARTMENT of ELECTRICAL and ELECTRONICS ENGINEERING / (30%) English

Introduction of the Numerical Solutions and constructing a basis for the other numerical lectures.

Learning Outcomes

CTPO

TOA

Upon successful completion of the course, the students will be able to :

LO - 1 :

Know the differences between Numerical Analysis and Analytical Analysis.

2,3,4,12

1,

LO - 2 :

Calculate the roots of functions / polynomials.

2,3,4,12

1,

LO - 3 :

Numerically solve differential and integral calculation problems.

2,3,4,12

1,

LO - 4 :

Solve linear equation sets.

2,3,4,12

1,

LO - 5 :

Numerically solve solutions of ordinary differential equations.

2,3,4,12

1,

CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome

Contents of the Course

Chapt. -1: Introduction; Basic concepts and definitions
Chapt. -2: Errors in Numerical Analysis
Chapt. -3: Matrixes
Chapt. -4: Solutions of the Equations in One Variable and the Equation Systems
Chapt. -5: Taylor Series and Finite Differences
Chapt. -6: Interpolations, Extrapolations
Chapt. -7: Numerical Differentiation
Chapt. -8: Numerical Integration
Chapt. -9: Numerical Solutions of the Ordinary Differential Equations
Chapt. -10: Least Square Method and Curve Fitting

Course Syllabus

Week

Subject

Related Notes / Files

Week 1

Approximation and Round-off Errors, Significant Figures, Accuracy and Precision, Error Definitions, Round-Off Errors, The Taylor Series

Week 2

The Bisection Method, Simple Fixed-Point Iteration, The Newton-Raphson Method, The Secant Method, Multiple Roots

Week 3

Roots of Polynomials, Conventional Methods, Müllers Method, Bairstows Method

Week 4

Cramer's rule, Naive Gauss Elimination, Gauss-Jordan, The Matrix Inverse

Week 5

LU Decomposition, Gauss-Seidel, Cholesky decomposition

Week 6

Linear Regression, Polynomial Regression, General Linear Least Squares

Week 7

Newtons Divided-Difference Interpolating Polynomials, Lagrange Interpolating Polynomials, Coefficients of an Interpolating Polynomial, Inverse Interpolation

Week 8

High-Accuracy Differentiation Formulas, Richardson Extrapolation, Derivatives of Unequally Spaced Data

Week 9

Mid-term exam

Week 10

The Trapezoidal Rule, Simpsons Rules, Integration with Unequal Segments, Open Integration Formulas

Week 11

Multiple Integrals, Newton-Cotes Algorithms for Equations, Improper Integrals

Week 12

Ordinary Differential Equations, Eulers Method, Improvements of Eulers Method

Week 13

Runge-Kutta Methods, Adaptive Runge-Kutta Methods

Week 14

Partial Differential Equations

Week 15

The Laplace Equation, Solution Technique, Boundary Conditions

Week 16

End-of-term exam

Textbook / Material

1

Chapra, Steven,Canale Raymond,1985,Numerical Methods For Engineers,McGrawHill,İSBN 0 07 010664-9

Recommended Reading

1

Akpınar, A.Sefa,2008,Sayısal Çözümleme,KTÜ Mühendislik Fakültesi Fakülte Ders Notları Serisi No::2,Trabzon