INTERNATIONAL BURCH UNIVERSITY
Faculty of Engineering and Natural Sciences
Department of Information Technologies
2015-2016

SYLLABUS
Code Name Level Year Semester
MTH 102 Calculus II Undergraduate 1 Spring
Status Number of ECTS Credits Class Hours Per Week Total Hours Per Semester Language
Compulsory 6 3 + 2 150 English

 Instructor Assistant Coordinator Ahmed El Sayed, Assist. Prof. Dr. Jasmin Kevric Ali GÖKSU, Assoc. Prof. Dr. [email protected] [email protected] no email

 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.

COURSE OBJECTIVE
•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.

COURSE CONTENT
Week
Topic
1. Introduction to Calculus 2; Improper Integrals
2. Complex numbers.
3. Application of Integration
4. Sequences
5. Series
6. Parametric Equations and Polar Coordinates
7. Midterm Review
8. MIDTERM EXAM
9. Post-midterm Review
10. Functions of several variables
11. Partial Derivatives
12. Multiple Integrals
13. Multiple Integrals: Double Integrals
14. Multiple Integrals: Triple Integrals
15. Final Exam Review

LABORATORY/PRACTICE PLAN
Week
Topic

TEACHING/ASSESSMENT
Description
• Interactive Lectures
• Presentation
• Discussions and group work
• Problem solving
• Assignments
Description (%)
Method Quantity Percentage (%)
Quiz1010
Midterm Exam(s)130
Term Paper115
Attendance15
Final Exam140
Total: 100
Learning outcomes
• 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
TEXTBOOK(S)
• Stewart, Calculus: Early Transcendentals, 7th edition, Thomson Brooks/Cole

ECTS (Allocated based on student) WORKLOAD
Activities Quantity Duration (Hour) Total Work Load
Lecture (14 weeks x Lecture hours per week)14342
Laboratory / Practice (14 weeks x Laboratory/Practice hours per week)14228
Midterm Examination (1 week)122
Final Examination(1 week)122
Preparation for Midterm Examination11515
Preparation for Final Examination12525
Assignment / Homework/ Project11818
Seminar / Presentation11818