ÇAĞ UNIVERSITY
FACULTY OF ARTS AND SCIENCES
Code
Course
Title
Credit
ECTS
MAT 131
Calculus and Analytic Geometry I
5 (4

2
)
7
Prerequisites
None
Language of Instruction
English
Mode of Delivery
Face to face
Type and Level of Course
Compulsory/1
.Year/
Fall Semester EQF

Level 6
Lecturers
Name(s)
Lecture Hours
Office Hours
Contacts
Course Coordinator
Instructor Efsun Kürüm
Mn. 13

16 &
Tu
.
9

12
Wed.
9

12&Tu.16

17
efsunkurum@cag.edu.tr
Others

Course
Objective
The aims of the course are to familiarize the students with functions represented in a variety
of ways: graphical, numerical, analytical. They should understand the connections among
these representations. Additionally, the students should unde
rstand the meaning of the
derivative and should be able to use derivative to solve a variety of problems.
Learning Outcomes of the
Course
Students who have completed the course successfully should
be able to
Relationship
Prog. Output
Net Effect
1
identify
real valued functions and their properties
1, 5
5, 3
2
compute inverse of a function, limits of functions and their
applications
1, 3, 5
3, 4, 3
3
prove
theorems introduced in the course
3, 12
4, 3
4
apply
the theorems introduced i
n the course to solve problems
3, 1
5, 4
5
compute
the derivative of Real Valued Functions(RVF)
1,3, 5
3, 5, 5
6
analyze
and
construct
the graph of RVF
1, 6
3, 5
7
demonstrate an understanding of basic concepts of analytic
geometry in the plane and
space
1, 6, 3
3, 5, 3
8
demonstrate an understanding of later courses in advanced
calculus and
linear algebra.
1, 3
4, 4
Course Description
:
The course concentrates on (1) Functions, (2)Limit and Derivative of a Function of a Single
Variable, (3) A Tho
rough Discussion of the Basic Theorems of Differential Calculus: Intermediate Value, Extreme
Value, and the Mean Value Theorems, (4) Applications: Graph Sketching and Problems of Extrema.
Course Contents:( Weekly Lecture Plan )
Weeks
Topics
Preparation
Teaching Methods
1
Introduction to domain, range and various
representations of functions.
Textbook preliminaries
Lectures and presentations
2
Introduction to domain, range and various
representations of functions.
Textbook preliminaries
Lectures and
presentations
3
The Limit Concept: ε
–
δ definition,
Properties
Textbook Ch.1
Lectures
4
One

sided limits, limits at infinity
Textbook Ch.1
Lectures & illustrations
5
Continuity, Properties of continuous
Functions
Textbook Ch. 2
Lectures
6
Intermediate

V
alue and Extreme

Value
Theorems
Textbook Ch.2
Lectures
7
The Derivative Concept: Definition of the
Derivative. Properties of the Derivative
Textbook Ch.3
Lectures
8
Implicit Differentiation. Rolle's and the
Mean Value Theorems. Monotonicity
Theorem.
Text
book Ch.3
Lectures
9
The First and Second Derivative Tests
Textbook Ch.3
Lectures
10
The Inverse Function Theorem in one variable
Textbook Ch. 3
Problem solutions
11
Inverse trigonometric functions, L'Hospital's
Theorem.
Textbook Ch.4
Lectures
12
Asym
ptotes and Graph Sketching.
Textbook Ch.4
Lectures & illustrations
13
Problems of Maxima and Minima
Textbook Ch.4
Problem solutions
14
Problems of Maxima and Minima
Textbook Ch.4
Review
REFERENCES
Textbook
G.B. Thomas, F.R.Giordano, J.Hass, Calculus a
nd Analytic Geometry, Addison Wesley
Publishing, 2004.
Related links
www.calculus.org
http://www.sosmath.com/calculus/calculus.html
Recommended Rea
ding
E.Dubinsky, K.E. Schwingerdorf, and D.M.Mathews; Calculus, Concepts, and
Computers, Mc Graw Hill, 1995 2nd Edition.
ASSESSMENT METHODS
Activities
Number
Effect
Notes
Midterm Exam
2
4
0%
Quizzes
6
5%
Homework
5
5%
Effect of The Activities
5
0
%
Effect of The Final Exam
5
0%
ECTS TABLE
Contents
Number
Hours
Total
Hours in Classroom
14
6
84
Hours out Classroom
14
5
70
Homeworks
5
2
10
Quizzes
6
1
6
Midterm Exam
2
12
24
Final Exam
1
16
16
Total
Total / 30
ECTS Credit
210
=210/30=
7,0
7
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