Ders Planı

Lesson Information

Course Credit	3.0
Course ECTS Credit	3.0
Teaching Language of Instruction	İngilizce
Level of Course	Bachelor's Degree, TYYÇ: Level 6, EQF-LLL: Level 6, QF-EHEA: First Cycle
Type of Course	Compulsory
Mode of Delivery	Face-to-face
Does the course require compulsory or optional work experience?	Z
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Purpose and Content

The aim of the course	This course introduces basic methods, algorithms and programming techniques to solve mathematical problems. The course is designed for students to learn how to develop numerical methods and estimate numerical errors using basic calculus concepts and results.
Course Content	This course covers the Round-off Errors and Computer Arithmetic: Binary Machine Numbers, Decimal Machine Numbers, Rate of Convergence,The Bisection Method; Fixed-Point Iteration The Newton's Method; The Secant Method,The Method of False Position; Error Analysis for Iterative Methods; Accelerating Convergence,Interpolation and the Lagrange Polynomial,Data Approximation and Neville's Method,Divided Differences: Forward, Backward and Centered Differences Numerical Differentiation: Three and Five Point Formulas Numerical Integration,Numerical Differentiation: Second Derivative Midpoint Formula; Round-Off Error Instability,Numerical Integration: the Trapezoidal and Simpson's Rule , Romberg Integration, Adaptive Quadrature Methods, Gaussian Quadrature,Numerical Integration: Open and Closed Newton-Cotes Formulas,Numerical Integration: Composite Numerical Integration and Round-Off Error Stability.

The aim of the course

This course introduces basic methods, algorithms and programming techniques to solve mathematical problems. The course is designed for students to learn how to develop numerical methods and estimate numerical errors using basic calculus concepts and results.

Course Content

This course covers the Round-off Errors and Computer Arithmetic: Binary Machine Numbers, Decimal Machine Numbers, Rate of Convergence,The Bisection Method; Fixed-Point Iteration The Newton's Method; The Secant Method,The Method of False Position; Error Analysis for Iterative Methods; Accelerating Convergence,Interpolation and the Lagrange Polynomial,Data Approximation and Neville's Method,Divided Differences: Forward, Backward and Centered Differences Numerical Differentiation: Three and Five Point Formulas Numerical Integration,Numerical Differentiation: Second Derivative Midpoint Formula; Round-Off Error Instability,Numerical Integration: the Trapezoidal and Simpson's Rule , Romberg Integration, Adaptive Quadrature Methods, Gaussian Quadrature,Numerical Integration: Open and Closed Newton-Cotes Formulas,Numerical Integration: Composite Numerical Integration and Round-Off Error Stability.

Learning Outcomes

Adequate knowledge in mathematics, physical sciences and the engineering subjects of individual branches; the ability to implement theoretical and practical knowledge in the respective areas to modeling and solving engineering problems.
Ability to identify, define, formulate and solve complex engineering problems; ability to select and implement the appropriate analysis and modeling methods in this respect.
Ability to design and conduct experiments for analyzing engineering problems or research subjects specific to the discipline, to collect data, to analyze and interpret the results.
Ability to use, choose and develop modern techniques and means required for engineering applications; ability to use information technologies effectively.
An ability to design and conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or discipline-specific research topics.
Awareness of the necessity of lifelong learning; ability to reach information, follow the latest developments in science and technology; ability to ensure self-renewal perpetually.
Acting in line with ethical principles, sense of professional and ethical responsibility; knowledge on the standards of engineering applications.
Ability to work effectively in interdisciplinary and multi-disciplinary teams and individual works.
Information about the effects of engineering applications on health, environment and safety in terms of universal and social aspects and information about the problems of the era; awareness about the legal results of engineering solutions.
Ability to communicate efficiently both in oral and written ways in Turkish; knowledge of at least one foreign language; ability to effectively prepare reports and understand written reports, prepare design and production reports, effective presentation, giving and receiving clear and understandable instructions.
Knowledge of business practices such as project management, risk management and change management; awareness of entrepreneurship, innovation; information about sustainable development.

Weekly Course Subjects

1	Round-off Errors and Computer Arithmetic: Binary Machine Numbers,
2	Decimal Machine Numbers, Rate of Convergence
3	The Bisection Method; Fixed-Point Iteration,The Newton's Method; The Secant Method.
4	The Method of False Position; Error Analysis for Iterative Methods; Accelerating Convergence
5	Interpolation and the Lagrange Polynomial
6	Data Approximation and Neville's Method,Divided Differences: Forward, Backward and Centered Differences
7	Numerical Differentiation: Three and Five Point Formulas Numerical Integration. Midterm.
8	Numerical Differentiation: Second Derivative Midpoint Formula.
9	Round-Off Error Instability.Meadterm exam.
10	Numerical Integration: the Trapezoidal and Simpson's Rule.
11	Numerical Integration:Romberg Integration.
12	Adaptive Quadrature Methods, Gaussian Quadrature.
13	Numerical Integration: Open and Closed Newton-Cotes Formulas.
14	Numerical Integration: Composite Numerical Integration and Round-Off Error Stability.

Resources

1.Çağal, B.,Sayısal Analiz,Birsen Yayın evi,1998.
2.Türker,E. S.,Bilgisayar Uygulamalı Sayısal Analiz Yöntemleri,Adapazarı,1997.
3.Cheney,W. & Kincaid, D.,Numerical Analysis,Brooks,1996.

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CLASS 4

Lesson Information

Purpose and Content

Learning Outcomes

Weekly Course Subjects

Resources

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