INTERNATIONAL BURCH UNIVERSITY
Faculty of Engineering and Natural Sciences
Department of Information Technologies
||Number of ECTS Credits
||Class Hours Per Week
||Total Hours Per Semester
||3 + 2
|Infinite series, power series, Taylor series. Vectors, lines and planes in space. Functions of several variables: Limit, continuity, partial derivatives, The chain rule, directional derivatives, tangent plane approximation and differentials, extreme values, Double and triple integrals with applications. The line integral.
|•Obtain a well-rounded introduction to the area of integration techniques, applications of integrals, parametric curves and polar coordinates;
•Deepen students' knowledge of problem formulation, problem solving and modelling techniques required for successful application of mathematics obtained in previous calculus courses;
•Competently use the appropriate technology to model data, implement mathematical algorithms and solve mathematical problems.
•Cultivate the analytical skills required for the efficient use and understanding of mathematics.
- Introduction to Calculus 2; Improper Integrals
- Complex numbers.
- Application of Integration
- Parametric Equations and Polar Coordinates
- Midterm Review
- MIDTERM EXAM
- Post-midterm Review
- Functions of several variables
- Partial Derivatives
- Multiple Integrals
- Multiple Integrals: Double Integrals
- Multiple Integrals: Triple Integrals
- Final Exam Review
- Interactive Lectures
- Discussions and group work
- Problem solving
| Midterm Exam(s)||1||30|
| Term Paper||1||15|
| Final Exam||1||40|
- Use integral calculus to solve applied problems, such as computations of area, length, volume, surface area and work
- Recognize and evaluate improper integrals
- Explain clearly the definition of an infinite series as the limit of a sequence of partial sums. Recognize a geometric series and correctly apply the convergence theorem
- Be able to apply convergence tests (comparison, ratio, root, alternating series test) in order to decide convergence/divergence/conditional convergence
- Derive the leading terms in the Taylor Polynomial for a function of one variable.
- Be able to explain the concept of radius of convergence of a power series, and apply the convergence tests to compute it in concrete situations
- Recognize functions defined parametrically, and be able to translate between parametric equations and other ways of describing a function.
- Develop an understanding of the rectangular coordinate system in 3‐space and of the use of vectors
- Stewart, Calculus: Early Transcendentals, 7th edition, Thomson Brooks/Cole
|ECTS (Allocated based on student) WORKLOAD
|Lecture (14 weeks x Lecture hours per week)||14||3||42|
|Laboratory / Practice (14 weeks x Laboratory/Practice hours per week)||14||2||28|
|Midterm Examination (1 week)||1||2||2|
|Final Examination(1 week)||1||2||2|
|Preparation for Midterm Examination||1||15||15|
|Preparation for Final Examination||1||25||25|
|Assignment / Homework/ Project||1||18||18|
|Seminar / Presentation||1||18||18|