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MATHEMATICAL ANALYSIS IV
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| Course Name |
Code |
Regular Semester |
ECTS Credits |
Credits |
Lecture |
4
|
| Application |
2
|
|
Mathematical Analysis IV
|
0252012
|
3
|
7.5
|
5
|
Laboratory (Hour/Week) |
-
|
|
| Course Language |
Turkish
|
| Compulsory or Elective |
Compulsory
|
| Equipment |
Board, Overhead Projector, Projector, Notebook, CD
|
| Instructor |
Department of Mathematics
|
| Course Contents |
Double and triple integrals/ Change of variables for double and triple integral/ Cylindrical and Spherical coordinates/ Application of double and triple integrals/ Improper integrals/ Gamma and Beta functions/ Integrals, which depend on parameter/ Leibnitz Rule/ Line integral and existence theorem/ Green's theorem/ Line integral in three-dimensional spaces/ Surface integrals/ Diverjans and Stokes Theorem
|
| Course Objectives |
-
To give fundamentals of mathematics knowledge
-
To be able to analyse the problem which are met in the fields of mathematics and to gain the ability of problem solving
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To gain analytical thinking, discussion and evaluation
|
Course Outcomes
(The knowledge and the skills that the student will gain at the end of the course) |
-
To have the fundamentals of mathematical knowledge and culture
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To have analytical thinking and evaluation
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The skill of evaluation and studying the problems which occur in other disciplines
|
| Textbook |
Lecture notes
|
| Additional References |
-
“Advanced Calculus” Wilfred Kaplan Wesley-Publishing Company, 1984
-
Advanced Calculus” David V. Widder , Prentice-Hall,1968
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“Calculus” Thomas- Finney Addison-Wesley , 1998
|
|
| Prerequisite Courses |
-
|
| Prerequisite Subjects |
0251011 Analysis 1 - 0251012 Analysis 2 subjects
|
| Homework/Project |
-
|
| Laboratory |
-
|
| Computer Applications |
-
|
| Additional Practices |
-
|
|
| Course Evaluation Criteria |
|
Number |
Effective Proportion % |
| Midterm Exams |
2
|
60
|
| Quiz |
-
|
-
|
| Homework |
-
|
-
|
| Term Projects |
-
|
-
|
| Term Papers |
-
|
-
|
| Laboratory |
-
|
-
|
| Other |
-
|
-
|
| Final Exam |
1
|
40
|
|
| Division of Course Credit (%) |
Basic Sciences |
-
% |
| Basic Engineering and Departmental Core Courses |
-
% |
| Departmental Core Courses |
100
% |
| Social Sciences |
-
% |
|
|
| WEEKLY COURSE PLAN |
| Week |
Subject |
| 1 |
Double integrals and existence theorem
|
| 2 |
Application of double integrals. Change of variables
|
| 3 |
Application of triple integrals
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| 4 |
Cylindrical and Spherical coordinates
|
| 5 |
Improper integrals
|
| 6 |
Gamma and Beta functions
|
| 7 |
Integrals, which depend on parameter. Leibnitz Rule
|
| 8 |
1st Midterm exam
|
| 9 |
Line integral and existence theorem
|
| 10 |
Green's theorem. Dependence of path
|
| 11 |
Line integral in three-dimensional spaces
|
| 12 |
Surface integrals
|
| 13 |
2nd Midterm exam
|
| 14 |
Diverjans Theorem
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| 15 |
Stokes Theorem
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|
|
| Prepared by |
Department of Mathematics
|
Date |
01.01.2007
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