MATH3012 Numerical AnalysisBahçeşehir UniversityDegree Programs MEDICINEGeneral Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
MEDICINE
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) Integrates the knowledge, skills and attitudes acquired from basic and clinical medical sciences, behavioral sciences and social sciences, and uses them in health service delivery.
2) In patient management, shows a biopsychosocial approach that takes into account the socio-demographic and sociocultural background of the individual, regardless of language, religion, race and gender.
3) In the provision of health services, prioritizes the protection and development of the health of individuals and society.
4) Taking into account the individual, societal, social and environmental factors affecting health; does the necessary work to maintain and improve the state of health.
5) By recognizing the characteristics, needs and expectations of the target audience, provides health education to healthy/sick individuals and their relatives and other healthcare professionals.
6) Shows a safe, rational and effective approach in health service delivery, prevention, diagnosis, treatment, follow-up and rehabilitation processes.
7) Performs invasive and/or non-invasive procedures in diagnosis, treatment, follow-up and rehabilitation processes in a safe and effective way for the patient.
8) Provides health services by considering patient and employee health and safety.
9) In the provision of health services, takes into account the changes in the physical and socioeconomic environment on a regional and global scale, as well as the changes in the individual characteristics and behaviors of the people who apply to it.
10) Takes good medical practice into account while carrying out his/her profession.
11) Fulfills its duties and obligations within the framework of ethical principles, rights and legal responsibilities required by its profession.
12) Demonstrates decisive behavior in providing high-quality health care, taking into account the integrity of the patient.
13) Evaluates his/her performance in his/her professional practice by considering his/her emotions and cognitive characteristics.
14) Advocates improving the provision of health services by considering the concepts of social reliability and social responsibility for the protection and development of public health.
15) Can plan and carry out service delivery, training and consultancy processes related to individual and community health in cooperation with all components for the protection and development of health.
16) Evaluates the impact of health policies and practices on individual and community health indicators and advocates increasing the quality of health services.
17) The physician attaches importance to the protection of his/her own physical, mental and social health, and does what is necessary for this
18) Shows exemplary behavior and leads the healthcare team during service delivery.
19) Uses resources cost-effectively, for the benefit of society and in accordance with the legislation, in the planning, implementation and evaluation processes of health services in the health institution he/she is the manager of.
20) Establishes positive communication within the health team it serves and assumes different team roles when necessary.
21) Is aware of the duties and responsibilities of the health workers in the health team and acts accordingly.
22) In the professional practices, works in harmony and effectively with the colleagues and other professional groups.
23) Communicates effectively with patients, their relatives, healthcare professionals, other professional groups, institutions and organizations.
24) Communicates effectively with individuals and groups that require a special approach and have different socio-cultural characteristics.
25) In the diagnosis, treatment, follow-up and rehabilitation processes, shows a patient-centered approach that associates the patient with the decision-making mechanisms.
26) Plans and implements scientific research, when necessary, for the population it serves, and uses the results and/or the results of other research for the benefit of the society.
27) Reaches and critically evaluates current literature knowledge about his/her profession.
28) Applies the principles of evidence-based medicine in clinical decision making.
29) Uses information technologies to increase the effectiveness of its work on health care, research and education.
30) Effectively manages individual work processes and career development.
31) Demonstrates skills in acquiring and evaluating new knowledge, integrating it with existing knowledge, applying it to professional situations and adapting to changing conditions throughout professional life.
32) Selects the right learning resources to improve the quality of the health service it offers, organizes its own learning process