COURSE INFORMATION Course Title: CALCULUS II

Code	Course Type	Regular Semester	Theory	Practice	Lab	Credits	ECTS
MTH 102	A	2	3	2	0	4	7

Academic staff member responsible for the design of the course syllabus (name, surname, academic title/scientific degree, email address and signature)	NA
Lecturer (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	Doğan Önder
Second Lecturer(s) (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	NA
Teaching Assistant(s) and Office Hours:	NA
Language:	English
Compulsory/Elective:	Compulsory
Classroom and Meeting Time:
Course Description:	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, Lagrange multipliers. Double and triple integrals with applications. The line integral.
Course Objectives:	the objective of the course is to enable students to operate with infinite series and multivariable calculus. To understand the infinity sumand how the most important concepts of calculus apply to multivariable functions.

COURSE OUTLINE

Week	Topics
1	Rieman sum, definite integral, mean value theorem for integrals, fundamental theorem of calculus
2	Areas under the curve, area between curves
3	Application of integrals: volumes of solids by disc, washer and cylindrical shell methods, arc length of curves and surfaces of revolution.
4	Integration by Substitution, Integration by Parts, Trogonometric Integration, Improper integrals, their types.
5	Divergence and convergence. Evaluation.
6	Parametric Equation, Polar coordinates. Tangents, Area, arc length.
7	Infinite sequences. Divergence and convergence. Monotone sequences. Upper and lower bounds. Divergence test.
8	Integral test, comparison test, limit comparison test, ratio test, root test, alternating series test.
9	Absolute convergence. Strategy for series, estimations. Power series and functions. Taylor series. Applications of series.
10	Functions of several variables. Limits.
11	Partial derivatives, directional derivatives.
12	Elements from vector calculus: line integrals, Green's Theorem, Stokes' Theorem and the Divergence Theorem.
13	Double integrals, triple integrals, their applications.
14	Double integrals, triple integrals, their applications.

Prerequisite(s):	Good knowledge on limits, continuity , differentiation and integration.
Textbook:	James Stewart Calculus eighth edition
Other References:
Laboratory Work:
Computer Usage:
Others:	No

COURSE LEARNING OUTCOMES

1	How to find the nature of the series
2	How to determine the test useful to find the convergence of the series
3	the student should understand and expand a function into a power series
4	to be able to find the domain range and sketch a graph of a two variable function
5	to solve problems involving the change of rate of a function
6	to find the maximum and minimum and to identify if they are local or absolute extremum
7	to know to find the volume of solids using double integral in general domain
8	to use properly polar coordinates to evaluate the integral of two variable functions
9	to find volumes of solids using triple integrals
10	to enforce their previous knowledge in Calculus I

COURSE CONTRIBUTION TO... PROGRAM COMPETENCIES (Blank : no contribution, 1: least contribution ... 5: highest contribution)

No	Program Competencies	Cont.
Bachelor in Civil Engineering (3 years) Program

COURSE EVALUATION METHOD

Method	Quantity	Percentage
Homework	1	10
Midterm Exam(s)	1	30
Quiz	2	10
Final Exam	1	40
	Total Percent:	100%

ECTS (ALLOCATED BASED ON STUDENT WORKLOAD)

Activities	Quantity	Duration(Hours)	Total Workload(Hours)
Course Duration (Including the exam week: 16x Total course hours)	16	5	80
Hours for off-the-classroom study (Pre-study, practice)	14	3	42
Mid-terms	1	16	16
Assignments	1	5	5
Final examination	1	20	20
Other	3	4	12
Total Work Load:			175
Total Work Load/25(h):			7
ECTS Credit of the Course:			7