Course Name: | ADVANCED CALCULUS II |
Code | Course type | Regular Semester | Theoretical | Practical | Credits | ECTS |
MATH 206 | 2 | 4 | 4 | 2 | 5 | 5 |
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Name of Lecturer(s)-Academic Title: | Jamal Gaderov - |
Teaching Assistant: | - |
Course Language: | English |
Course Type: | Main |
Office Hours | 8:45- 17:00 |
Contact Email: | [email protected]
Tel:07507285243 |
Teacher's academic profile: | MSc
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Course Objectives: | The aim of this course it to establish modern mathematical ideas and calculations on the basic subjects of calculus. The main purpose is to make clear and more understandable to the previous calculus contents. Moreover, this course aims to contribute an understanding on advanced application of derivative and integration in math and in the other sciences. |
Course Description (Course overview): | Functions of several variables, their limits, derivatives and integrals, directional derivatives, gradient, vector-valued functions, divergence and curl, Taylor's theorem, Lagrange multipliers, multiple integrals, change of variables, line integrals, Green's theorem |
COURSE CONTENTWeek | Hour | Date | Topic | 1 |
4 |
3-7/2/2019 |
Tangents and slopes. Differentiable functions. | 2 |
4 |
10-14/2/2019 |
Tangents and slopes. Differentiable functions. |
| 3 |
4 |
17-21/2/2019 |
Derivative of elementary functions. Derivative rules. | 4 |
4 |
24-28/2/2019 |
Derivative of elementary functions. Derivative rules. |
| 5 |
4 |
3-7/3/2019 |
Extreme of functions. Monotonicity of functions. First derivative test | 6 |
4 |
26-28/3/2019 |
Extreme of functions. Monotonicity of functions. First derivative test |
| 7 |
4 |
31/3-4/4/2019 |
Mean Value Theorem, Rolle’s theorem. Generalized Mean Value Theorem | 8 |
4 |
7-11/4/2019 |
Mean Value Theorem, Rolle’s theorem. Generalized Mean Value Theorem |
| 9 |
4 |
14-18/4/2019 |
Midterm Exam | 10 |
4 |
21-25/4/2019 |
Indefinite integral. Calculations of indefinite integral |
| 11 |
4 |
28/4-2/5/2019 |
Indefinite integral. Calculations of indefinite integral | 12 |
4 |
5-9/5/2019 |
Finite sums. Summation notation and properties. |
| 13 |
4 |
12-16/5/2019 |
The Definite integral. Fundamental Theorem of Calculus | 14 |
4 |
19-23/5/2019 |
The Definite integral. Fundamental Theorem of Calculus |
| 15 |
4 |
26-30/5/2019 |
Application of definite integral. Areas and Volumes | 16 |
4 |
9-13/6/2019 |
Final Exam |
| 17 |
4 |
16-20/6/2019 |
Final Exam |
|
COURSE/STUDENT LEARNING OUTCOMES | | 1 | Differential Calculus | 2 | Integral Calculus | 3 | Analogue of these conceptions in real life |
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COURSE'S CONTRIBUTION TO PROGRAM OUTCOMES (Blank : no contribution, I: Introduction, P: Profecient, A: Advanced ) | Program Learning Outcomes |
Cont. | 1 | Demonstrate an understanding of the common body of knowledge in mathematics. | P | 2 | Demonstrates an understanding of pedagogical content knowledge, technology and perfectible assessment. | A | 3 | Demonstrate the ability to think critically, research scientifically, and become modern and up-to-date. | | 4 | Understands the interrelationship of human development, cognition, and culture and their impact on learning. | | 5 | Demonstrate the ability to apply analytical and theoretical skills to model and solve mathematical problems. | A | 6 | Demonstrate the ability to effectively use a variety of teaching technologies and techniques and classroom strategies to positively influence student learning. | A | 7 | Understands how to form connections among educators, families, and the larger community to promote equity and access to education for his/her students. | | 8 | Understands assessment and evaluation of student performance and learning and program effectiveness. | P | 9 | Communicates effectively and works collaboratively within the context of a global society. | |
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Prerequisites (Course Reading List and References): | Analysis books |
Student's obligation (Special Requirements): | Do homework and exercises |
Weekly Laboratory/Practice Plan: | Week | Hour | Date | Topics | 1 |
2 |
3-7/2/2019 |
Examples and Exercises on differentiable functions. | 2 |
2 |
10-14/2/2019 |
Examples and Exercises on differentiable functions. |
| 3 |
2 |
17-21/2/2019 |
Examples and Exercises on Derivative rules. | 4 |
2 |
24-28/2/2019 |
Examples and Exercises on Derivative rules. |
| 5 |
2 |
3-7/3/2019 |
Examples and Exercises on extreme of functions | 6 |
2 |
26-28/3/2019 |
Examples and Exercises on extreme of functions |
| 7 |
2 |
31/3-4/4/2019 |
Examples and Exercises in Mean Value, Rolle’s Theorem | 8 |
2 |
7-11/4/2019 |
Examples and Exercises in Mean Value, Rolle’s Theorem |
| 9 |
2 |
14-18/4/2019 |
Examples and Exercises on Indefinite integrals. Integration by parts, substitutions | 10 |
2 |
21-25/4/2019 |
Examples and Exercises on Indefinite integrals. Integration by parts, substitutions |
| 11 |
2 |
28/4-2/5/2019 |
Examples and Exercises on limit of finite sums. | 12 |
2 |
5-9/5/2019 |
Examples and Exercises on limit of finite sums. |
| 13 |
2 |
12-16/5/2019 |
Examples and Exercises on definite integral | 14 |
2 |
19-23/5/2019 |
Examples and Exercises on definite integral |
| 15 |
2 |
26-30/5/2019 |
Examples and Exercises on calculation of areas and volumes | 16 |
2 |
9-13/6/2019 |
Examples and Exercises on calculation of areas and volumes |
| 17 |
2 |
16-20/6/2019 |
Examples and Exercises on calculation of areas and volumes |
|
Course Book/Textbook: | Thomas Calculus,
Robert Adams Complete Calculus Course |
Other Course Materials/References: | Boards, MArkers |
Teaching Methods (Forms of Teaching): | Lectures, Excersises, Self Evaluation, Project |
COURSE EVALUATION CRITERIA
Method | Quantity |
Percentage (%) | Participation | 1 | 10 | Quiz | 1 | 10 | Homework | 1 | 10 | Midterm Exam(s) | 1 | 30 | Final Exam | 1 | 40 |
Total | 100 |
Examinations: Essay Questions, Short Answers, Matching |
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Extra Notes:
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ECTS (ALLOCATED BASED ON STUDENT) WORKLOADActivities | Quantity | Duration (Hour) | Total Work Load | Contact Hours (Theoretical hours + Practical hours/2) x Weeks | | | 0 | Hours for off-the-classroom study | | | 0 | Study hours for the Midterm Exam | | | 0 | Study hours for the Final Exam | | | 0 | Other | | | 0 | ECTS | | | 0 | | | | 0 | | | | 0 | Total Workload | 0 | ECTS Credit (Total workload/25) | 0 |
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