ANALYSIS I

Course Code:

MATH 155

Semester:

Fall

Course Type:

Core

P:

3

Lab:

2

Laboratuvar Saati:

0

Credits:

4

ECTS:

8

Course Language:

English

Course Objectives:

To teach the students the concepts of limits, derivatives and integrals of functions of a single variable and have them maintain the ability to make calculations in these issues, which are the fundamental knowledge that is necessary for main research areas in mathematics

Course Content:

Introduction to calculus, sequences, series, convergence. Functions limits and derivatives. Differentiation rules, the chain rule, implicit differentiation, linear approximations. Applications of differentiation, minimum and maximum values, shapes of curves, optimization, applications to business and economics.

Course Methodology:

1: Anlatım, 2: Problem Çözme

Course Evaluation Methods:

A: Yazılı sınav, B: Ödev

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Teaching Methods	Assessment Methods
1) Learns the concept of limit, continuity	1,2	A
2) Learns the concept of convergence of sequences and series	1,2	A
3) Evaluates derivatives	1,2	A
4) Uses derivative to find extrema	1,2	A
5) Uses L’Hospital rule to evaluate limits	1,2	A

Course Flow

COURSE CONTENT
Week	Topics	Study Materials
1	Introduction to Calculus
2	Sequences, Series, Limit
3	Functions, Composition of Functions, Inverse Functions
4	Exponential Functions and Logarithms
5	Trigonometric Functions
6	The Limit of a Function, Calculating Limits using Limit Laws
7	Continuity, Limits Involving Infinity
8	Tangents, Velocities, and Other Rates of Change, Derivatives, The Derivative as a Function
9	What Does f’ say about f? Derivatives of Polynomials and Exponential Functions, The Product and Quotient Rules
10	Derivatives of Trigonometric Functions, The Chain Rule
11	Implicit Differentiation, Derivatives of Logarithmic Functions, Linear Approximations, Taylor Polynomial
12	Maximum and Minimum Values
13	Graphing with Calculus and Calculators
14	Intermediate Forms, and L’Hospital’s Rule, Optimization Problems, Applications to Business and Economics

Recommended Sources

RECOMMENDED SOURCES
Textbook	Calculus, Concepts & Contexts by James Steawart, 7^th edition.
Additional Resources

Material Sharing

MATERIAL SHARING
Documents
Assignments
Exams

Assessment

ASSESSMENT
IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	1	100
Quizzes	0	0
Assignments	0	0
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE	1	60
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		40
Total		100

Course’s Contribution to Program

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)					x
2	Acquiring fundamental knowledge on fundamental research fields in mathematics					x
3	Ability to form and interpret the relations between research topics in mathematics					X
4	Ability to define, formulate and solve mathematical problems					X
5	Consciousness of professional ethics and responsibilty			X
6	Ability to communicate actively			X
7	Ability of self-development in fields of interest					X
8	Ability to learn, choose and use necessary information technologies	X
9	Lifelong education			X

ECTS

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
Activities	SAYISI	Süresi (Saat)	Toplam İş Yükü (Saat)
Course Duration (14x Total course hours)	14	5	70
Hours for off-the-classroom study (Pre-study, practice)	14	6	84
Mid-terms (Including self study)	1	20	20
Quizzes
Assignments
Final examination (Including self study)	1	25	25
Total Work Load			199
Total Work Load / 25 (h)			7,99
ECTS Credit of the Course			8

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