Mathematics (English) | |||||
Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 |
Course Code: | MATH152 | ||||
Course Name: | Calculus for Mathematics Students 2 | ||||
Semester: | Spring | ||||
Course Credits: |
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Language of instruction: | English | ||||
Course Condition: | |||||
Does the Course Require Work Experience?: | No | ||||
Type of course: | Compulsory Courses | ||||
Course Level: |
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Mode of Delivery: | Face to face | ||||
Course Coordinator: | Prof. Dr. SELÇUK DEMİR | ||||
Course Lecturer(s): | Assist. Prof. Dr. Doğa Can Sertbaş | ||||
Course Assistants: |
Course Objectives: | The course aims to teach the improper integrals, sequences and series, differentiation, optimization and integration of functions of several variables, various coordinate systems and to gain the ability to use these concepts in solving mathematical problems. |
Course Content: | The content of the course consists of improper integrals, sequences and series, approximation of functions by series, functions of several variables, differentiation of functions of several variables, optimizing functions of several variables, integrating functions of several variables, integrals in Cartesian and polar coordinates. |
The students who have succeeded in this course;
1) Compute the integrals over unbounded regions. 2) Learn the notion of convergence of series and use various tests to determine series convergence; find Taylor representations of functions and approximate functions via Taylor polynomial. 3) Comprehend and use the concept of a function of several variables, draw graphs in 3 dimensional spaces. 4) Compute partial derivatives, directional derivatives and write equations of tangent planes to surface; apply partial derivatives to find and test local extrema. 5) Evaluate double integrals in Cartesian and polar coordinates and triple integrals in Cartesian coordinates. |
Week | Subject | Related Preparation |
1) | Improper integrals | |
2) | Sequences, infinite series | |
3) | The divergence and integral tests | |
4) | The ratio and alternating series tests | |
5) | Power series, Taylor series | |
6) | Vectors, dot product | |
7) | Cross product, planes and surfaces | |
8) | Midterm Exam | |
9) | Functions of several variables, limits and continuity | |
10) | Partial derivatives, chain rule, directional derivatives, gradient, tangent planes | |
11) | Maximum/minimum problems | |
12) | Double integrals over rectangular regions | |
13) | Double integrals over general regions or in polar coordinates | |
14) | Triple integrals |
Course Notes / Textbooks: | Giordano, Frank R., Hass, Joel, Weir, Maurice D., Thomas, George B., Thomas' Calculus, 11th Edition, ISBN 9780321185587, 2004, Addison-Wesley. |
References: | Calculus: A Complete Course, Richard A. Adams, Prentice Hall, 6th ed, 2006. |
Course Learning Outcomes | 1 |
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Program Outcomes | |||||||||||
1) Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline. | |||||||||||
2) Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems. | |||||||||||
3) Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques. | |||||||||||
4) Have the ability to think analytically and use the time effectively in the process of deduction. | |||||||||||
5) Have the ability to search the literature, understand and interpret scientific articles. | |||||||||||
6) Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License. | |||||||||||
7) Have the ability to work efficiently in interdisciplinary teams. | |||||||||||
8) Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations. | |||||||||||
9) Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards. | |||||||||||
10) Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria. | |||||||||||
11) Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves. |
No Effect | 1 Lowest | 2 Average | 3 Highest |
Program Outcomes | Level of Contribution | |
1) | Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline. | 2 |
2) | Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems. | 3 |
3) | Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques. | 2 |
4) | Have the ability to think analytically and use the time effectively in the process of deduction. | 3 |
5) | Have the ability to search the literature, understand and interpret scientific articles. | |
6) | Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License. | |
7) | Have the ability to work efficiently in interdisciplinary teams. | |
8) | Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations. | |
9) | Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards. | |
10) | Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria. | |
11) | Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves. |
Semester Requirements | Number of Activities | Level of Contribution |
Midterms | 1 | % 40 |
Final | 1 | % 60 |
total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 40 | |
PERCENTAGE OF FINAL WORK | % 60 | |
total | % 100 |
Activities | Number of Activities | Preparation for the Activity | Spent for the Activity Itself | Completing the Activity Requirements | Workload | ||
Course Hours | 13 | 0 | 4 | 52 | |||
Application | 13 | 0 | 2 | 26 | |||
Study Hours Out of Class | 13 | 0 | 6 | 78 | |||
Midterms | 1 | 0 | 15 | 15 | |||
Final | 1 | 0 | 25 | 25 | |||
Total Workload | 196 |