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 
Use of calculus is widespread in science, engineering, medicine, business, industry, and many other fields. Calculus also provides important tools in understanding functions and has led to the development of new areas of mathematics including real and complex analysis, topology, and nonEuclidean geometry. 
COURSE OBJECTIVE 
1To expand understanding of mathematical topics that may have been previously studied.
2To introduce and explore topics that possibly have not been part of the student’s mathematical experience.
3To develop an appreciation for the development of mathematical thought.
4To learn the application of mathematics in real life problems and analyzing the results. 
COURSE CONTENT 
 01Vectors; Dot Products, Cross Products
 02Lines and Planes, Polar Coordinates
 03Surfaces and Coordinate Systems, Parameterized Curves
 04Arc Length and Curvature, Velocity and Acceleration
 05Functions of Several Variables, Limits, Continuity, Partial Derivatives
 06Tangent Planes and Linear Approximation, Chain Rule
 07Gradient, Directional Derivatives, 2nd Order Derivatives, Local Extrema
 08Local Extrema, Lagrange Multipliers
 09MIDTERM
 10Double Integrals, Iterated Integrals, Applications of Double Integrals
 11Triple Integrals, Transformation of Coordinates
 12Line Integrals In R2, Line Integrals in R3
 13Surface Integrals
 14Green's Theorem, Stokes' Theorem
 15Divergence Theorem

LABORATORY/PRACTICE PLAN 
 01Vectors; Dot Products, Cross Products
 02Lines and Planes, Polar Coordinates
 03Surfaces and Coordinate Systems, Parameterized Curves
 04Arc Length and Curvature, Velocity and Acceleration
 05Functions of Several Variables, Limits, Continuity, Partial Derivatives
 06Tangent Planes and Linear Approximation, Chain Rule
 07Gradient, Directional Derivatives, 2nd Order Derivatives, Local Extrema
 08Local Extrema, Lagrange Multipliers

 09MIDTERM
 10Double Integrals, Iterated Integrals, Applications of Double Integrals
 11Triple Integrals, Transformation of Coordinates
 12Line Integrals In R2, Line Integrals in R3
 13Surface Integrals
 14Green's Theorem, Stokes' Theorem
 15Divergence Theorem

Description 
 Interactive Lectures
 Practical Sessions
 Excersises
 Presentation
 Problem solving
 Assignments

Description (%) 
Quiz   25  Midterm Exam(s)   25  Final Exam  1  50 

Learning outcomes 
 01understand and apply two and three dimensional cartesian coordinate system 02recognize and classify the equations and shapes of quadratic surfaces
 03use the properties of vectors and operations with vectors 04recognize and construct the equations of lines and planes
 05operate with vector functions, find their derivatives and integrals, find the arc length 06understand and use the concept of a function of several variables, find its domain
 07calculate the limits of multivariable functions and prove the nonexistence of a limit 08find partial derivatives using the properties of differentiable multivariable functions and basic rules
 09apply partial derivatives for finding equations of tangent planes, normal lines, and for extreme values 10evaluate double and triple integrals in cartesian, polar, and cylindrical coordinates
 11apply multiple integrals for computing areas and volumes 12understand and use integration in vector fields

TEXTBOOK(S) 
 Thomas's Calculus, Eleventh Edition, George B. Thomas, Pearson International Edition, 2005
 Calculus a Complete Course, Sixth Edition, Robert A. Adams, Pearson Addison Wesley, 2006

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 

