To give fundamental methods of numerical analysis.

Learning Outcomes

CTPO

TOA

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

LO - 1 :

Understand about the errors resulting from the making of approximations while applying various numerical methods, and the ways to minimizing of these errors.

1,2

1,

LO - 2 :

Understand about the weak and powerful sides, and skills of numerical methods and the computers.

1,2

1,

LO - 3 :

Choose the appropriate numerical method depend on the problem to be

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1,

LO - 4 :

Obtain the basic numerical solution of ordinary differential equations.

1,2

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

Mathematical modeling concept, approximations and errors. Roots of equations. Systems of algebraic equations. Curve fitting. Interpolations. Tables of Finite Differences.Numerical differentiation and numerical integration. Solution of ODE's.

Course Syllabus

Week

Subject

Related Notes / Files

Week 1

Motivation. Numerical methods and engineering practice. Mathematical modeling concept.

Week 2

Taylor series. Approximations and error definitions. Numerical errors; relative, absolute, approximation, truncation and truncation errors.

Week 3

Roots of equations. Barcketing methods: Bisection and false-position methods.

Week 4

Open methods: Simple iteration, Newton-Raphson and Secant methods. Multiple roots. Comparison of various methods.

Week 5

Lineer cebirsel denklemler. Küçük denklem sistemlerinin çözümü: Grafik yöntemler, Cramer kuralı ve bilinmeyenlerin yok edilmesi.

Week 6

Gauss elimination, Gauss-Jordan, Matrix inverse methods. Gauss-Saidel method. Weak and powerful sides of solution methods.

Week 7

Table of Finite Differences. Forward finite differences, backward finite differences and central differences.

Week 8

Interpolation. Linear and higher order interpolations with Newton and Lagrange interpolating polynomials.

Week 9

Mid-term Exam

Week 10

Numerical differentiation. Forward, backward and central approximations of differentiations. High order differentiation formulas.