MATH3012 Numerical AnalysisBahçeşehir UniversityDegree Programs PERFORMING ARTSGeneral Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
PERFORMING ARTS
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MATH3012 Numerical Analysis Spring
Fall
2 2 3 6
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: English
Type of course: Non-Departmental Elective
Course Level: Bachelor’s Degree (First Cycle)
Mode of Delivery: Face to face
Course Coordinator :
Recommended Optional Program Components: None
Course Objectives: Numerical Analysis is concerned with the mathematical derivation, description and analysis of obtaining numerical solutions of mathematical problems. We have several objectives for the students. Students should obtain an intuitive and working understanding of some numerical methods for the basic problems of numerical analysis. They should gain some appreciation of the concept of error and of the need to analyze and predict it. And also they should develop some experience in the implementation of numerical methods by using a computer.

Learning Outcomes

The students who have succeeded in this course;

The students who succeeded in this course;
o will be able to define Errors, Big O Notation, Stability and Condition Number, Taylor’s Theorem.
o will be able to solve Nonlinear Equations.
o will be able to solve Linear Systems.
o will be able to use Iterative Methods for Linear Systems.
o will be able to calculate Eigenvalues and Eigenvectors.
o will be able to solve System of Nonlinear Equations.
o will be able to calculate Interpolating and Polynomial Approximation.

Course Content

In this course the solution of linear and nonlinear systems will be discussed numerically. Also iterative methods for linear systems will be taught.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Errors, Big O Notation, Stability and Condition Number, Taylor’s Theorem.
2) The Solution of Nonlinear Equations in the form of f(x)=0: Bisection Method, Fixed Point Iteration.
3) Newton-Rapson Method, Secant Method.
4) The Solution of Linear System : Solving Triangular System, Gauss Elimination and Pivoting.
5) LU Factorization, Tridiagonal System, Vector and Matrix Norms
6) Sensitivity of Linear Equations. Condition Number and Stability.
7) Iterative Methods for Linear Systems: Jacobi Method.
8) Gauss Seidel Method. Diagonally Dominant Matrix. Errors in Solving Linear Systems.
9) Eigenvalues and Eigenvectors: The Power Method. The Inverse Power Method.
10) System of Nonlinear Equations: Newton’s Method.
11) Interpolating and Polynomial Approximation: Lagrange interpolation polynomial, Newton Interpolation.
12) Piecewise Linear Interpolation, Cubic Spline.
13) Least Square Approximation: Curve Fitting.
14) Inconsistent System of Equations. Errors in Interpolation .

Sources

Course Notes / Textbooks: Numerical Methods Using MATLAB (Fourth Edition), John H. Mathews and Kurtis D. Fink, Pearson Prentice Hall
References:

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Attendance 16 % 0
Laboratory 16 % 5
Quizzes 5 % 10
Midterms 2 % 45
Final 1 % 45
Total % 105
PERCENTAGE OF SEMESTER WORK % 60
PERCENTAGE OF FINAL WORK % 45
Total % 105

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 16 3 48
Laboratory 14 1 14
Study Hours Out of Class 16 2 32
Quizzes 3 5 15
Midterms 2 5 10
Final 1 5 5
Total Workload 124

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) They acquire theoretical, historical and aesthetic knowledge specific to their field by using methods and techniques related to performing arts (acting, dance, music, etc.). 2
2) They have knowledge about art culture and aesthetics and they provide the unity of theory and practice in their field. 2
3) They are aware of national and international values in performing arts. 2
4) Abstract and concrete concepts of performing arts; can transform it into creative thinking, innovative and original works. 1
5) They have the sensitivity to run a business successfully in their field. 3
6) Develops the ability to perceive, think, design and implement multidimensional from local to universal. 3
7) They have knowledge about the disciplines that the performing arts field is related to and can evaluate the interaction of the sub-disciplines within their field. 2
8) They develop the ability to perceive, design, and apply multidimensionality by having knowledge about artistic criticism methods. 3
9) They can share original works related to their field with the society and evaluate their results and question their own work by using critical methods. 1
10) They follow English language resources related to their field and can communicate with foreign colleagues in their field. 1
11) By becoming aware of national and international values in the field of performing arts, they can transform abstract and concrete concepts into creative thinking, innovative and original works. 3
12) They can produce original works within the framework of an interdisciplinary understanding of art. 2
13) Within the framework of the Performing Arts Program and the units within it, they become individuals who are equipped to take part in the universal platform in their field. 3
14) Within the Performing Arts Program, according to the field of study; have competent technical knowledge in the field of acting and musical theater. 2
15) They use information and communication technologies together with computer software that is at least at the Advanced Level of the European Computer Use License as required by the field. 3