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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT331 |
| Name | Partial Differential Equations |
| Term | 2019-2020 Academic Year |
| Semester | 5. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ZERRİN GÜL ESMERLİGİL |
| Course Instructor |
Prof. Dr. ZERRİN GÜL ESMERLİGİL
(Güz)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The objectives of this course is to introduce the fundamental ideas of the partial differential equations of order one and two.
Course Content
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.
Course Precondition
Resources
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Defines and classifies partial differential equations. |
| LO02 | Knows the similarities and the differences between Ordinary differential equations and partial differential equations. |
| LO03 | Is able to form a partial differential equation from given relations. |
| LO04 | Finds integral surface of a first degree semi-linear equation. |
| LO05 | Finds an exponential form of solution for second order equations with constant coefficient. |
| LO06 | Reduce second order equation to canonical form. |
| LO07 | Find complete integral of second order equations using Lagrange Charpit Method |
| LO08 | Applicates Lagrange Methods by using ratio. |
| LO09 | Solve second order partial differential equations. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | - | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 5 |
| PLO02 | - | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 5 |
| PLO03 | - | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 2 |
| PLO04 | - | Demonstrate the ability to express the basic theories of mathematics both correctly. | 2 |
| PLO05 | - | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 3 |
| PLO06 | - | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 5 |
| PLO07 | - | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 4 |
| PLO08 | - | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 4 |
| PLO09 | - | Comprehends at least one of the computer programming languages. | 4 |
| PLO10 | - | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 0 |
| PLO11 | - | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | 1 |
| PLO12 | - | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | 0 |
| PLO13 | - | Understands the programming techniques and shows the ability to do programming. | 0 |
| PLO14 | - | Demonstrates the ability to study mathematics both independently and as a group. | 0 |
| PLO15 | - | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | |
| PLO16 | - | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | |
| PLO17 | - | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | |
| PLO18 | - | Gains the ability to use information technologies effectively for contemporary mathematical applications. | |
| PLO19 | - | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | |
| PLO20 | - | Gains the consciousness of prefesional ethics and responsibility. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Classification and obtaining of Partial Differential Equations | Read the relevant parts of the text and solve problems | |
| 2 | Tangent planes, intersecting surfaces, the angle between two surfaces | Read the relevant parts of the text and solve problems | |
| 3 | Linear Equations of First Degree | Read the relevant parts of the text and solve problems | |
| 4 | Semi Linear Equations of First Degree and Lagrange Methods | Read the relevant parts of the text and solve problems | |
| 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 | |
| 6 | Compatible systems, Lagrange Charpit Methods | Read the relevant parts of the text and solve problems | |
| 7 | Compatible systems, Lagrange Charpit Methods | Read the relevant parts of the text and solve problems | |
| 8 | Mid-Term Exam | Review the topics discussed in the lecture notes and sources | |
| 9 | Second order equations with constant coefficients, Factorization of operators | Read the relevant parts of the text and solve problems | |
| 10 | Irreducible equations and Euler Equations | Read the relevant parts of the text and solve problems | |
| 11 | Find particular solutions and Classification and Quasi Linear Equations | Read the relevant parts of the text and solve problems | |
| 12 | Canonical Forms | Read the relevant parts of the text and solve problems | |
| 13 | Second order equations with variable coefficients | Read the relevant parts of the text and solve problems | |
| 14 | Reduction in Second order Equations | Read the relevant parts of the text and solve problems | |
| 15 | Solving problems | Solving Problems | |
| 16 | Term Exams | Review the topics discussed in the lecture notes and sources | |
| 17 | Term Exams | Review the topics discussed in the lecture notes and sources |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||