MATHEMATICS | |||||
Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT2001 | Analysis III | Fall | 3 | 2 | 4 | 10 |
The course opens with the approval of the Department at the beginning of each semester |
Language of instruction: | En |
Type of course: | Must Course |
Course Level: | Bachelor |
Mode of Delivery: | Face to face |
Course Coordinator : | Instructor SOHEIL SALAHSHOUR |
Course Lecturer(s): |
Prof. Dr. NAFİZ ARICA |
Course Objectives: | This advanced calculus course will rigorously develop multivariable calculus and vector analysis. The topics covered in this course include Integrals of Rational Functions, Improper Integrals, Infinite Series, VectorValued Functions, Curves and Parametrizations, Functions of Several Variables. This course is a good preparation for students thinking of studying engineering, administration and economics. |
The students who have succeeded in this course; Will be able to calculate improper integrals. Will be able to test series for convergence and, if convergence is established, find approximations to their magnitudes. Will be able to apply Taylor's and McLaurin's series. Will be able to use algebraic operations on power series. Will be able to calculate limits of functions of several variables. Will be able to solve problems dealing with partial derivatives. Will be able to sketch the graphs of functions. Will be able to find local and absolute maxima and minima. |
In this course basic concepts and classification of improper integralswill be discussed. Sequences and series; power series; cartesian and polar coordinates; functions of several variables; partial derivatives; increments and differentials; chain rules. |
Week | Subject | Related Preparation | |
1) | Improper Integrals of type I and Improper Integral of type II. | ||
2) | Sequences and Convergence. Infinite Series. Convergent or Divergent Series. | ||
3) | PositiveTerm Series. The Ratio and Root Tests. | ||
4) | Alternating Series. | ||
5) | Absolute and Conditional Convergence. | ||
6) | Power Series. Algebraic Operations on Power Series. | ||
7) | Differentiation and Integration of Power Series. Abel’s Theorem. | ||
8) | Power Series Representations of Functions. Maclaurin and Taylor Series. | ||
9) | Applications of Taylor and Maclaurin Series. Taylor’s Formula Revisited. The Binomial Theorem and Binomial Series. | ||
10) | VectorValued Functions. Limits, Derivatives and Integrals of VectorValued Functions | ||
11) | Curves and Parametrizations. Arc Length. Piecewise Smooth Curves. | ||
12) | Functions of Several Variables. Limits and Continuity. | ||
13) | Partial Derivatives. Tangent Planes and Normal Lines. HigherOrder Derivatives. | ||
14) | Increments and differentials. Chain rule. Directional Derivatives and Gradients. Implicit Functions. |
Course Notes: | “Calculus. A Complete Course (fifth edition)”, by Robert A. Adams. Addison Wesley Longman. |
References: | . |
Semester Requirements | Number of Activities | Level of Contribution |
Attendance | % 0 | |
Laboratory | % 0 | |
Application | % 0 | |
Field Work | % 0 | |
Special Course Internship (Work Placement) | % 0 | |
Quizzes | 25 | % 15 |
Homework Assignments | % 0 | |
Presentation | % 0 | |
Project | % 0 | |
Seminar | % 0 | |
Midterms | 2 | % 45 |
Preliminary Jury | % 0 | |
Final | 1 | % 40 |
Paper Submission | % 0 | |
Jury | % 0 | |
Bütünleme | % 0 | |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 60 | |
PERCENTAGE OF FINAL WORK | % 40 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Laboratory | 0 | 0 | 0 |
Application | 10 | 2 | 20 |
Special Course Internship (Work Placement) | 0 | 0 | 0 |
Field Work | 0 | 0 | 0 |
Study Hours Out of Class | 10 | 2 | 20 |
Presentations / Seminar | 0 | 0 | 0 |
Project | 0 | 0 | 0 |
Homework Assignments | 16 | 5 | 80 |
Quizzes | 5 | 5 | 25 |
Preliminary Jury | 0 | 0 | 0 |
Midterms | 2 | 15 | 30 |
Paper Submission | 0 | 0 | 0 |
Jury | 0 | 0 | 0 |
Final | 1 | 40 | 40 |
Total Workload | 257 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |