MATH3012 Numerical AnalysisBahçeşehir UniversityDegree Programs PHYSIOTHERAPY AND REHABILITATION (TURKISH)General Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
PHYSIOTHERAPY AND REHABILITATION (TURKISH)
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 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) To have theoretical and practical knowledge required to fulfill professional roles and functions of Physiotherapy and Rehabilitation field. 2
2) To act in accordance with ethical principles and values in professional practice. 1
3) To use life-long learning, problem-solving and critical thinking skills. 4
4) To define evidence-based practices and determine problem solving methods in Physiotherapy and Rehabilitation practices, using theories in health promotion, protection and care. 1
5) To take part in research, projects and activities within sense of social responsibility and interdisciplinary approach. 3
6) To have skills for training and consulting according to health education needs of individual, family and the community. 1
7) To be sensitive to health problems of the community and to be able to offer solutions. 3
8) To be able to use skills for effective communication. 5
9) To be able to select and use modern tools, techniques and modalities in Physiotherapy and Rehabilitation practices; to be able to use health information technologies effectively. 1
10) To be able to search for literature in health sciences databases and information sources to access to information and use the information effectively. 1
11) To be able to monitor occupational information using at least one foreign language, to collaborate and communicate with colleagues at international level. 1
12) To be a role model with contemporary and professional identity. 4