INTERNATIONAL BURCH UNIVERSITY
Faculty of Engineering and Natural Sciences
Department of Information Technologies
20152016
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 
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 wellrounded 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 
 Introduction to Calculus 2; Improper Integrals
 Complex numbers.
 Application of Integration
 Sequences
 Series
 Parametric Equations and Polar Coordinates
 Midterm Review
 MIDTERM EXAM
 Postmidterm Review
 Functions of several variables
 Partial Derivatives
 Multiple Integrals
 Multiple Integrals: Double Integrals
 Multiple Integrals: Triple Integrals
 Final Exam Review

Description 
 Interactive Lectures
 Presentation
 Discussions and group work
 Problem solving
 Assignments

Description (%) 
Quiz  10  10  Midterm Exam(s)  1  30  Term Paper  1  15  Attendance  1  5  Final Exam  1  40 

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 
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 
