Chemical Engineering Preview
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course General Introduction Information

Course Code:

MAT202

Course Name:

Numerical Analysis

Course Semester:

Spring

Course Credits:

ECTS

Language of instruction:

Course Requirement:

Does the Course Require Work Experience?:

Type of course:

Necessary

Course Level:

Bachelor

TR-NQF-HE:6. Master`s Degree

QF-EHEA:First Cycle

EQF-LLL:6. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator :

Assoc. Prof. HATİCE ESRA ÖZKAN UÇAR

Course Lecturer(s):

Dr. Öğr. Üyesi M. Fatih UÇAR

Course Assistants:

Course Purpose and Content

Course Objectives:	Basic numerical methods, algorithms and programming techniques used to find solutions to mathematical problems are explained. At the end of this course, the student learns how to approach a given problem numerically with numerical methods developed using basic analysis techniques.
Course Content:	Approaching methods to problems with basic numerical algorithms.

Learning Outcomes

The students who have succeeded in this course;
1) It understands standard IEEE binary floating point arithmetic, machine precision, and calculates its error.
2) It approximates functions using Taylor polynomials and calculates an upper limit for the resulting error.
3) It solves the equation f(x)=0 using the bisection algorithm and calculates the number of steps required for a given precision.
4) Calculates the fixed points of the f(x) function using an iterative method.
5) For a given ratio range, it finds the solutions of the equation f(x)=0 using Newton, Newton-Raphson and secant methods.
6) Performs polynomial interpolation for curve fitting using Lagrange polynomials, learns and applies the Neville method, and uses the Newton divided difference algorithm.
7) It deduces the difference formulas used to approximate the derivative of a function and calculates the error in the approximation using Lagrange polynomials.
8) Performs numerical definite integration calculations using open-closed Newton-Cotes formulas, trapezoidal and Simpson rules, and obtains and uses compound integration formulas.
9) Calculates generalized integrals using numerical methods.

Course Flow Plan

Week	Subject	Related Preparation
1)	Preliminary Information: Limits and Continuity, Differentiability, Integration, Taylor Polynomials and Series	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
2)	Rounding Errors, Decimal Machine Numbers, and Convergence Speed	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
3)	Bisection Method; Fixed Point Iteration	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
4)	Newton and Secant Methods	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
5)	Regula False Method, Interpolation	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
6)	Lagrange Interpolation Polynomials, Neville Method	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
7)	Inverse Interpolation, Split Differences	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
7)	Inverse Interpolation, Split Differences	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
8)	Forward, Reverse Differences	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
9)	Central Differences	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
10)	Numerical Differential: Richardson Extrapolation	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
11)	Numerical Integration: Explicit and Implicit Newton-Cotes Formulas	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
12)	Rounding Errors Occurring in Compound Numerical Integration and Compound Integral Calculation	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
13)	Romberg Integration, Numerical Solutions of Initial Value Problems: Euler, Mid-Point Method	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
14)	Modified Euler, Heun and Runge-Kutta Methods	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
15)	final exam
16)	final exam

Sources

Course Notes / Textbooks:	-J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. -Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. -K. Atkinson and W. Han, Elementary Numerical Analysis, John Wiley, 3rd edition. -Cheney,W.,-Kincaid,D., Numerical Mathematics and Computing,Brooks,1985
References:	-J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. -Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. -K. Atkinson and W. Han, Elementary Numerical Analysis, John Wiley, 3rd edition. -Cheney,W.,-Kincaid,D., Numerical Mathematics and Computing,Brooks,1985

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Medium	3 Highest

	Program Outcomes	Level of Contribution
1)	To be able to use advanced theoretical and practical knowledge acquired in the field	2
2)	To be able to interpret and evaluate data using advanced knowledge and skills acquired in the field, to be able to identify and analyze problems, to be able to develop solutions based on research and evidence.	1
3)	To be able to plan and manage activities for the development of employees under his/her responsibility within the framework of a project.	1
4)	To act in accordance with social, scientific, cultural and ethical values in the stages of collecting, interpreting, applying and announcing the results of data related to the field.	2
5)	To be able to carry out an advanced level study related to the field independently.	1
6)	To be able to take responsibility individually and as a team member to solve complex and unforeseen problems encountered in applications related to the field.	2
7)	To have advanced theoretical and practical knowledge supported by textbooks, application tools and other resources containing up-to-date information in the field.	1
8)	To have sufficient awareness of the universality of social rights, social justice, quality culture and protection of cultural values, environmental protection, occupational health and safety.	1
9)	To be able to inform the relevant people and institutions about the issues related to the field; to be able to convey his / her thoughts and suggestions for solutions to problems in written and orally.	1
10)	To be able to share his/her thoughts and suggestions for solutions to problems related to his/her field with experts and non-experts by supporting them with quantitative and qualitative data.	1
11)	To be able to organize and implement projects and activities for the social environment in which he/she lives with a sense of social responsibility	1
12)	To be able to evaluate the advanced knowledge and skills acquired in the field with a critical approach	2
13)	To be able to identify their learning needs and direct their learning	2

Learning Activity and Teaching Methods

Course
Homework
Problem Çözme

Measurement and Evaluation Methods and Criteria

Yazılı Sınav (Açık uçlu sorular, çoktan seçmeli, doğru yanlış, eşleştirme, boşluk doldurma, sıralama)
Homework

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Homework Assignments	1	% 20
Midterms	1	% 30
Final	1	% 40
Kanaat Notu	1	% 10
total		% 100
PERCENTAGE OF SEMESTER WORK		% 60
PERCENTAGE OF FINAL WORK		% 40
total		% 100

İş Yükü ve AKTS Kredisi Hesaplaması

Activities	Number of Activities	Aktiviteye Hazırlık	Aktivitede Harçanan Süre	Aktivite Gereksinimi İçin Süre	Workload
Course Hours	17	2			34
Study Hours Out of Class	1	6			6
Midterms	1	48			48
Final	1	48			48
Total Workload					136