TYPE OF COURSE UNIT	Compulsory Course
LEVEL OF COURSE UNIT	Bachelor's Degree
YEAR OF STUDY	1
SEMESTER	Second Term (Spring)
NUMBER OF ECTS CREDITS ALLOCATED	8
NAME OF LECTURER(S)	Assistant Professor Özge Dalmanoğlu
LEARNING OUTCOMES OF THE COURSE UNIT	At the end of this course, the students; 1) Know the rules of limit in multivariable functions. 2) Solve problems related to the continuity of functions of several variables. 3) Interpret the concept of partial derivative geometrically and solve related questions. 4) Calculate area and volume with the help of double integrals.
MODE OF DELIVERY	Face to face
PRE-REQUISITES OF THE COURSE	No
RECOMMENDED OPTIONAL PROGRAMME COMPONENT	Calculus 1
COURSE DEFINITION	The concept of multivariable function, Domain, range and graphs of functions, limit and continuity of functions in two variable case, partial derivative of functions of two variables, chain rule, directional derivative, gradient. The concept of tangent plane. Local extremum values, absolute extremum values and applications. Lagrange multipliers, double integral concept, area and volume calculations with double integral (Cartesian and in polar coordinates).
COURSE CONTENTS	WEEK TOPICS 1st Week Functions of several variables, topology of R^n 2nd Week Domain and range of multivariable functions, graphs. Level curves 3rd Week Limit and Continuity 4th Week Continuity 5th Week Derivatives of functions of several variables, Partial derivatives, Chain Rule 6th Week Implicit derivative, higher order derivatives 7th Week Directional derivative, Gradient, Tangent plane and normal line 8th Week Midterm Exam 9th Week Extremums of multivariable functions and applications. 10th Week Lagrange Multipliers 11th Week The concept of double integral 12th Week Area and volume calculations with double integral 13th Week Double integrals in polar coordinates 14th Week General review
RECOMENDED OR REQUIRED READING	1. G.B.Thomas, Thomas-Calculus, 11th Edition, Addison Wesley, 2006. 2. R.A.Adams, Calculus, 4th edition, Addison Wesley, 1999. 3. Dennis G. Zii, Warren S. Wright, Calculus, Matematik Cilt II, Çeviri Editörü: Prof. Dr. İsmail Naci Cangül
PLANNED LEARNING ACTIVITIES AND TEACHING METHODS	Lecture,Questions/Answers,Problem Solving
ASSESSMENT METHODS AND CRITERIA	Quantity Percentage(%) Mid-term 1 40 Quiz 2 10 Total(%) 50 Contribution of In-term Studies to Overall Grade(%) 50 Contribution of Final Examination to Overall Grade(%) 50 Total(%) 100
ECTS WORKLOAD	Activities Number Hours Workload Midterm exam 1 2 2 Preparation for Quiz 5 4 20 Individual or group work 12 3 36 Preparation for Final exam 11 3 33 Course hours 13 6 78 Preparation for Midterm exam 7 4 28 Laboratory (including preparation) Final exam 1 2 2 Homework 11 3 33 Total Workload 232 Total Workload / 30 7,73 ECTS Credits of the Course 8
LANGUAGE OF INSTRUCTION	Turkish
WORK PLACEMENT(S)	No