MATHEMATICS | |||||
Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT4065 | Partial Differential Equations II | Fall | 3 | 0 | 3 | 6 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Language of instruction: | English |
Type of course: | Departmental Elective |
Course Level: | Bachelor’s Degree (First Cycle) |
Mode of Delivery: | Face to face |
Course Coordinator : | |
Recommended Optional Program Components: | None |
Course Objectives: | 1. Find the Green’s function of a PDE using Fourier methods. 2. Transform a PDE into an integral equation. 3. Determine the existence and uniqueness of solutions of PDEs and integral equations. 4. Determine the salient features of the spectrum of PDEs and integral equations. |
The students who have succeeded in this course; Explain the basic concepts of Partial Differential Equations. Obtain and Explain the Fundamental Definitions, Concepts, Theorems and Applications of Partial Differential Equations. Gain Experience on Partial Differential Equations. Generalize, Emphasize and Apply the concept of Theory of Ordinary Differential Equations to the Partial Differential Equations. Explain and Apply the principles of Theory of Ordinary Differential Equations to the Partial Differential Equations. Interpret the Stability results and Applications of Partial Differential Equations. Distinguish the difference between Partial Differential Equations and Fractional order Partial Differential Equations. Develop awareness for the Partial Differential Equations. |
Week 1: Classification and characteristics of PDEs; Week 2: Transform method,Green’s function methods; Week 3: Eliptic problems; Week 4: Parabolic problems; Week 5: Hyperbolic problems; Week 6: Nonvariational techniques; Week 7: Hamilton-Jacobi equation; Week 8: Systems of conservation laws and shocks; Week 9: MIDTERM Week 10: Fourier Transform; Week 11: Laplace Transform Week 12: Weak derivatives; Week 13: Sobolev Spaces; Week 14: Sobolev Inequalities; Week 15: General review Week 16: Final |
Week | Subject | Related Preparation |
1) | Classification and characteristics of PDEs; | |
1) | Review | |
2) | Transform method,Green’s function methods; | |
3) | Eliptic problems; | |
4) | Parabolic problems; | |
5) | Hyperbolic problems; | |
6) | Nonvariational techniques; | |
7) | Hamilton-Jacobi equation; | |
8) | Systems of conservation laws and shocks; | |
10) | Fourier Transform; | |
11) | Laplace Dönüşümü | |
12) | Weak derivatives; | |
13) | Sobolev Spaces; | |
14) | Sobolev Inequalities; |
Course Notes / Textbooks: | |
References: | 1. Partial Differential Equations: An Introduction / W. A. Strauss. 2. An Introduction to Partial Differential Equations / Y. Pinchover and J. Rubinstein. 3. Partial Differential Equations of Mathematical Physics and Integral Equations / R. B. Guenther and J. W. Lee. 4. Partial Differential Equations / L. C. Evans. |
Semester Requirements | Number of Activities | Level of Contribution |
Homework Assignments | 3 | % 10 |
Midterms | 1 | % 40 |
Final | 1 | % 50 |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 50 | |
PERCENTAGE OF FINAL WORK | % 50 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Study Hours Out of Class | 14 | 2 | 28 |
Homework Assignments | 3 | 10 | 30 |
Midterms | 1 | 10 | 10 |
Final | 1 | 15 | 15 |
Total Workload | 125 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution | |
1) | To have a grasp of basic mathematics, applied mathematics and theories and applications in Mathematics | 5 |
2) | To be able to understand and assess mathematical proofs and construct appropriate proofs of their own and also define and analyze problems and to find solutions based on scientific methods, | 5 |
3) | To be able to apply mathematics in real life with interdisciplinary approach and to discover their potentials, | 4 |
4) | To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, | 4 |
5) | To be able to tell theoretical and technical information easily to both experts in detail and non-experts in basic and comprehensible way, | 4 |
6) | To be familiar with computer programs used in the fields of mathematics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level, | 4 |
7) | To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement, | |
8) | To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense, | 4 |
9) | By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere, | 4 |
10) | To be able to continue lifelong learning by renewing the knowledge, the abilities and the competencies which have been developed during the program, and being conscious about lifelong learning, | 4 |
11) | To be able to adapt and transfer the knowledge gained in the areas of mathematics ; such as algebra, analysis, number theory, mathematical logic, geometry and topology to the level of secondary school, | 2 |
12) | To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. | 3 |