COURSE INFORMATON
Course Title Code Semester L+P Hour Credits ECTS
Partial Differential Equations * MT   331 5 3 3 5

Prerequisites and co-requisites
Recommended Optional Programme Components None

Language of Instruction Turkish
Course Level First Cycle Programmes (Bachelor's Degree)
Course Type
Course Coordinator Prof.Dr. Zerrin Gül ESMERLİGİL
Instructors
Prof.Dr.ZERRİN GÜL ESMERLİGİL1. Öğretim Grup:A
Prof.Dr.ZERRİN GÜL ESMERLİGİL2. Öğretim Grup:A
 
Assistants
Goals
The objectives of this course is to introduce the fundamental ideas of the partial differential equations of order one and two.
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.

Learning Outcomes
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Course's Contribution To Program
NoProgram Learning OutcomesContribution
12345
1
Is able to prove Mathematical facts encountered in secondary school.
X
2
Recognizes the importance of basic notions in Algebra, Analysis and Topology
X
3
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
X
4
Is able to express basic theories of mathematics properly and correctly both written and verbally
X
5
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
X
6
Expresses clearly the relationship between objects while constructing a model
X
7
Draws mathematical models such as formulas, graphs and tables and explains them
X
8
Is able to mathematically reorganize, analyze and model problems encountered.
X
9
Knows at least one computer programming language
X
10
Uses effective scientific methods and appropriate technologies to solve problems
11
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
X
12
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
13
Knows programming techniques and is able to write a computer program
14
Is able to do mathematics both individually and in a group.

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
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 Midterm 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
16-17 Final exam Review the topics discussed in the lecture notes and sources

Recommended or Required Reading
Textbook
Additional Resources