FACULTY OF ARTS AND SCIENCES

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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

RECENT PERFORMANCE