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
MAT2062 Differential Equations Fall 3 0 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 : Dr. Öğr. Üyesi GÜLSEMAY YİĞİT
Course Lecturer(s): Prof. Dr. NAFİZ ARICA
Recommended Optional Program Components: None
Course Objectives: This course covers the fundamental concepts of an introductory level of elementary differential equations with basic concepts, theory, solution methods and applications. Main goal is to develop the basics of modeling at an introductory level and connect this step to the theoretical and methodological resource of mathematics.

Learning Outcomes

The students who have succeeded in this course;
1. Classify differential equations and determine the existence and uniqueness of solutions of Initial Value Problems
2. Solve first order separable and linear differential equations
3. Use substitution methods to solve homogeneous and Bernoulli equations
4. Solve exact differential equations
5. Solve the higher order linear homogeneous and nonhomogeneous differential equations
6. Solve the systems of linear differential equations
7. Solve differential equations by using Laplace transform method

Course Content

In this course basic concepts of elementary differential equations will be covered. The solution techniques for the different types of first order differential equations will be given and the solution methods will be taught. The higher order linear differential equations and solution methods will be discussed. The systems of linear equations will be covered with different techniques. Finally, the Laplace Transform method will be taught to solve linear differential equations.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Classification of differential equations, Explicit solution, implicit solution, Initial Value Problems, Integrals as General and Particular Solutions.
2) Existence and Uniqueness of Solution. Separable Differential Equations.
3) First Order Linear Differential Equations.
4) Substitutions methods. Homogeneous Differential Equations. Bernoulli Differential Equations.
5) Exact Differential Equations.
6) Population models. Reducible second order equations.
7) Theory of Higher Order Linear Differential Equations, Existence and Uniqueness Theorem, Linear Dependence and Independence, Representation of Solutions for Homogeneous and Nonhomogeneous Cases.
8) Homogeneous Linear Equations with Constant Coefficients. Euler Equations.
9) Solution of Nonhomogeneous Linear Differential Equations. Method of Undetermined Coefficients.
10) Solution of Nonhomogeneous Linear Differential Equations. Method of Variation of Parameters.
11) Theory of Systems of Linear Differential Equations.
12) The Eigenvalue Method for Systems of Linear Differential Equations.
13) Laplace Transforms: Definition of the Laplace Transform, Properties of the Laplace Transform. Inverse Laplace Transform.
14) Solution of Differential Equations by using Laplace Transform.

Sources

Course Notes / Textbooks: Differential Equations with Boundary Value Problems by C. Henry Edwards & D. E.Penney, sixth edition

References: Introduction to Ordinary Differential Equations” by Shepley L. Ross. Fourth Edition, John Wiley and Sons.

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Quizzes 2 % 20
Midterms 1 % 35
Final 1 % 45
Total % 100
PERCENTAGE OF SEMESTER WORK % 55
PERCENTAGE OF FINAL WORK % 45
Total % 100

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