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. Recep ZIHNI Ali GÖKSU, Assoc. Prof. Dr. [email protected] [email protected] no email

 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 non-Euclidean geometry.

COURSE OBJECTIVE
1-To expand understanding of mathematical topics that may have been previously studied.
2-To introduce and explore topics that possibly have not been part of the student’s mathematical experience.
3-To develop an appreciation for the development of mathematical thought.
4-To learn the application of mathematics in real life problems and analyzing the results.

COURSE CONTENT
Week
Topic
1. 01-Vectors; Dot Products, Cross Products
2. 02-Lines and Planes, Polar Coordinates
3. 03-Surfaces and Coordinate Systems, Parameterized Curves
4. 04-Arc Length and Curvature, Velocity and Acceleration
5. 05-Functions of Several Variables, Limits, Continuity, Partial Derivatives
6. 06-Tangent Planes and Linear Approximation, Chain Rule
7. 07-Gradient, Directional Derivatives, 2nd Order Derivatives, Local Extrema
8. 08-Local Extrema, Lagrange Multipliers
9. 09-MIDTERM
10. 10-Double Integrals, Iterated Integrals, Applications of Double Integrals
11. 11-Triple Integrals, Transformation of Coordinates
12. 12-Line Integrals In R2, Line Integrals in R3
13. 13-Surface Integrals
14. 14-Green's Theorem, Stokes' Theorem
15. 15-Divergence Theorem

LABORATORY/PRACTICE PLAN
Week
Topic
1. 01-Vectors; Dot Products, Cross Products
2. 02-Lines and Planes, Polar Coordinates
3. 03-Surfaces and Coordinate Systems, Parameterized Curves
4. 04-Arc Length and Curvature, Velocity and Acceleration
5. 05-Functions of Several Variables, Limits, Continuity, Partial Derivatives
6. 06-Tangent Planes and Linear Approximation, Chain Rule
7. 07-Gradient, Directional Derivatives, 2nd Order Derivatives, Local Extrema
8. 08-Local Extrema, Lagrange Multipliers

 09-MIDTERM10-Double Integrals, Iterated Integrals, Applications of Double Integrals11-Triple Integrals, Transformation of Coordinates12-Line Integrals In R2, Line Integrals in R313-Surface Integrals14-Green's Theorem, Stokes' Theorem15-Divergence Theorem

TEACHING/ASSESSMENT
Description
• Interactive Lectures
• Practical Sessions
• Excersises
• Presentation
• Problem solving
• Assignments
Description (%)
Method Quantity Percentage (%)
Quiz25
Midterm Exam(s)25
Final Exam150
Total: 100
Learning outcomes
• 01-understand and apply two and three dimensional cartesian coordinate system 02-recognize and classify the equations and shapes of quadratic surfaces
• 03-use the properties of vectors and operations with vectors 04-recognize and construct the equations of lines and planes
• 05-operate with vector functions, find their derivatives and integrals, find the arc length 06-understand and use the concept of a function of several variables, find its domain
• 07-calculate the limits of multivariable functions and prove the nonexistence of a limit 08-find partial derivatives using the properties of differentiable multivariable functions and basic rules
• 09-apply partial derivatives for finding equations of tangent planes, normal lines, and for extreme values 10-evaluate double and triple integrals in cartesian, polar, and cylindrical coordinates
• 11-apply multiple integrals for computing areas and volumes 12-understand 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
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