| Course Description |
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| Course Name |
: |
Partial Differential Equations |
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| Course Code |
: |
MT 331 |
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| Course Type |
: |
Compulsory |
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| Level of Course |
: |
First Cycle |
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| Year of Study |
: |
3 |
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| Course Semester |
: |
Fall (16 Weeks) |
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| ECTS |
: |
5 |
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| Name of Lecturer(s) |
: |
Assoc.Prof.Dr. ZERRİN GÜL ESMERLİGİL
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| Learning Outcomes of the Course |
: |
Defines and classifies partial differential equations.
Knows the similarities and the differences between Ordinary differential equations and partial differential equations.
Is able to form a partial differential equation from given relations.
Finds integral surface of a fist degree semi-linear equation.
Finds an exponential form of solution for second order equations with constant coefficient.
Is able to reduce second order equation to canonical form.
Is able to find complete integral of second order equations using Lagrange Charpit Method.
Is able to use Lagrange Methods by using ratio.
Is able to solve second order partial differential equations.
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| Mode of Delivery |
: |
Face-to-Face |
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| Prerequisites and Co-Prerequisites |
: |
None |
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| Recommended Optional Programme Components |
: |
None |
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| Aim(s) of Course |
: |
The objectives of this course is to introduce the fundamental ideas of the partial differential equations of order one and two. |
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| Course Contents |
: |
Introduction to partial differential equations. First-order linear equations. Quasilinear first-order equations. Method of Lagrange. Cauchy problem for quasilinear first-order equations. Second order equations. Canonical forms. Hyperbolic, parabolic, elliptic equations. Method of Lagrange-Charpit. The wave equations.
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| Language of Instruction |
: |
Turkish |
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| Work Place |
: |
Classrooms of Faculty of Science Annex Building |
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Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
|
1 |
Classification and obtaining of Partial Differential Equations |
Read the relevant parts of the text and solve problems |
Lecture and Discussion |
|
2 |
Tangent planes, intersecting surfaces, the angle between two surfaces |
Read the relevant parts of the text and solve problems |
Lecture and Discussion |
|
3 |
Linear Equations of First Degree |
Read the relevant parts of the text and solve problems |
Lecture and Discussion |
|
4 |
Semi Linear Equations of First Degree and Lagrange Methods |
Read the relevant parts of the text and solve problems |
Lecture and Discussion |
|
5 |
The surface of the integral of a curve, Non-Linear Equations of First Degree |
Read the relevant parts of the text and solve problems |
Lecture and Discussion |
|
6 |
Compatible systems, Lagrange Charpit Methods |
Read the relevant parts of the text and solve problems |
Lecture and Discussion |
|
7 |
Compatible systems, Lagrange Charpit Methods |
Read the relevant parts of the text and solve problems |
Lecture and Discussion |
|
8 |
Midterm Exam |
Review the topics discussed in the lecture notes and sources |
Written Exam |
|
9 |
Second order equations with constant coefficients, Factorization of operators |
Read the relevant parts of the text and solve problems |
Lecture and Discussion |
|
10 |
Irreducible equations and Euler Equations |
Read the relevant parts of the text and solve problems |
Lecture and Discussion |
|
11 |
Find particular solutions and Classification and Quasi Linear Equations |
Read the relevant parts of the text and solve problems |
Lecture and Discussion |
|
12 |
Canonical Forms |
Read the relevant parts of the text and solve problems |
Lecture and Discussion |
|
13 |
Second order equations with variable coefficients |
Read the relevant parts of the text and solve problems |
Lecture and Discussion |
|
14 |
Reduction in Second order Equations |
Read the relevant parts of the text and solve problems |
Lecture and Discussion |
|
15 |
Solving Problems |
Solving problems |
Lecture and Discussion |
|
16/17 |
Final exam |
Review the topics discussed in the lecture notes and sources |
Written Exam |
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| Contribution of the Course to Key Learning Outcomes |
| # | Key Learning Outcome | Contribution* |
|
1 |
Is able to prove Mathematical facts encountered in secondary school. |
5 |
|
2 |
Recognizes the importance of basic notions in Algebra, Analysis and Topology |
5 |
|
3 |
Develops maturity of mathematical reasoning and writes and develops mathematical proofs. |
2 |
|
4 |
Is able to express basic theories of mathematics properly and correctly both written and verbally |
2 |
|
5 |
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. |
3 |
|
6 |
Expresses clearly the relationship between objects while constructing a model |
5 |
|
7 |
Draws mathematical models such as formulas, graphs and tables and explains them |
4 |
|
8 |
Is able to mathematically reorganize, analyze and model problems encountered. |
4 |
|
9 |
Knows at least one computer programming language |
4 |
|
10 |
Uses effective scientific methods and appropriate technologies to solve problems |
0 |
|
11 |
Knows programming techniques and is able to write a computer program |
1 |
|
12 |
Is able to do mathematics both individually and in a group. |
0 |
|
13 |
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians |
0 |
|
14 |
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields |
0 |
| * Contribution levels are between 0 (not) and 5 (maximum). |
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