Extended Calculus II (MATH158) Course Detail

Course Name	Course Code	Season	Lecture Hours	Application Hours	Lab Hours	Credit	ECTS
Extended Calculus II	MATH158	2. Semester	4	2	0	5	7.5

Pre-requisite Course(s)
Math 157 Extended Calculus I

Course Language	English
Course Type	Service Courses Taken From Other Departments
Course Level	Bachelor’s Degree (First Cycle)
Mode of Delivery	Face To Face
Learning and Teaching Strategies	Lecture, Question and Answer, Problem Solving.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives	The course is designed as a continuation of Math 157 Extended Calculus I and aims to give the students the computational skills in series, analytic geometry and multi-variable differential and integral calculus and line integrals to handle engineering problems.
Course Learning Outcomes	The students who succeeded in this course; understand and use sequences, infinite series, power series of functions, Taylor and Maclaurin series use analytic geometry through vectors and interpret lines, planes and surfaces in 3-dimensional space understand and use the functions of several variables, partial derivatives, chain rule, directional derivatives, gradient vectors and tangent planes, find local and absolute extrema of multivariable functions and use the Lagrange Multipliers understand and use double and triple integrals in different coordinate systems, understand line integral understand and apply the Green’s Theorem in plane
Course Content	Infinite series, vectors in the plane and polar coordinates, vectors and motions in space, multivariable functions and their derivatives, multiple integrals: double Integrals, areas, double integrals in polar coordinates, triple integrals in rectangular, cylindrical and spherical coordinates, line integrals, independence of path, Green?s Theorem.

Weekly Subjects and Releated Preparation Studies

Week	Subjects	Preparation
1	9.2 Infinite Series, 9.3 Convergence Tests for Positive Series (The Integral Test,Comparison Tests, The Ratio and Root Tests)	pp:503-519
2	9.4 Absolute and Conditional Convergence, 9.5 Power Series	pp:520-536
3	9.6 Taylor and Maclaurin Series (Convergence of Taylor Series; Error Estimates) 9.7 Applications of Taylor and Maclaurin Series,	pp:536-549
4	10.1 Analytic Geometry in Three Dimensions, 10.2 Vectors, 10.3 The Cross Product in 3-Space,	pp:562-585
5	10.4 Planes and Lines, 10.5 Quadric Surfaces,	pp:585-596
6	12.1 Functions of Several Variables, 12.2 Limits and Continuity	pp:669-681
7	Midterm
8	12.3 Partial Derivatives, 12.4 Higher Order Derivatives,	pp:681-693
9	12.5 The Chain Rule, 12.6 Linear Approximations, Differentiability, and Differentials,	pp:693-705 pp:706-707
10	12.7 Gradient and Directional Derivatives, 12.8 Implicit Functions,	pp:714-726
11	13.1 Extreme Values, 13.2 Extreme Values of Functions Defined on Restricted Domains, 13.3 Lagrange Multipliers,	pp:743-754 pp:756-760
12	14.1 Double Integrals, 14.2 Iteration of Double Integrals in Cartesian Coordinates,	pp:790-802
13	14.4 Double Integrals in Polar Coordinates, 14.5 Triple Integrals	pp:808-812 pp:818-824
14	14.6 Change of Variables in Triple Integrals (Cylindrical and Spherical Coordinates) 15.1 Vector and Scalar Fields, 15.2 Conservative Fields	pp:824-830 pp:842-857
15	15.3 Line Integrals, 15.4 Line Integrals of Vector Fields, 16.3 Green’s Theorem in the Plane,	pp:858-869 pp:903-906
16	Final Exam

Sources

Course Book	1. Calculus: A complete Course, R. A. Adams, C. Essex, 7th Edition; Pearson Addison Wesley
Other Sources	2. Thomas’ Calculus Early Transcendentals, 11th Edition.( Revised by M. D. Weir, J.Hass and F. R. Giardano; Pearson , Addison Wesley)
	3. Calculus: A new horizon, Anton Howard, 6th Edition; John Wiley & Sons
	4. Calculus with Analytic Geometry, C. H. Edwards; Prentice Hall
	5. Calculus with Analytic Geometry, R. A. Silverman; Prentice Hall

Evaluation System

Requirements	Number	Percentage of Grade
Attendance/Participation	-	-
Laboratory	-	-
Application	-	-
Field Work	-	-
Special Course Internship	-	-
Quizzes/Studio Critics	-	-
Homework Assignments	-	-
Presentation	-	-
Project	-	-
Report	-	-
Seminar	-	-
Midterms Exams/Midterms Jury	2	60
Final Exam/Final Jury	1	40
Toplam	3	100

Percentage of Semester Work	60
Percentage of Final Work	40
Total	100

Course Category

Core Courses
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

#	Program Qualifications / Competencies	Level of Contribution
#	Program Qualifications / Competencies	1	2	3	4	5

ECTS/Workload Table

Activities	Number	Duration (Hours)	Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)	16	4	64
Laboratory
Application	16	2	32
Special Course Internship
Field Work
Study Hours Out of Class	14	4	56
Presentation/Seminar Prepration
Project
Report
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury
Prepration of Final Exams/Final Jury	1	16	16
Total Workload			168