ANALYSIS II

Course Code:

MATH 156

Semester:

Spring

Course Type:

Core

P:

3

Lab:

2

Laboratuvar Saati:

0

Credits:

4

ECTS:

8

Prerequisite Courses:

ANALYSIS I

Calculus I

Course Language:

English

Course Objectives:

To teach integration techniques and some applications of integrals such as calculating areas and volumes. To teach sequences and series and their convergence divergence,

Course Content:

General review. Integrals; fundamental theorem of calculus, integration by parts, approximate integration, improper integrals. Applications of integration: Areas, volumes, arc length, average value of a function, other applications. Infinite sequences and series; sequences, series, convergence tests, representations of functions as power series Taylor series and Maclaurin series.

Course Methodology:

1: Lecture, 2: Problem Solving

Course Evaluation Methods:

A: Written Examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Program Learning Outcomes	Teaching Methods	Assessment Methods
1) Evaluates the integral of functions of single variable.	1,2,4,7	1,2	A
2) Uses integrals to evaluate areas and volumes.	1,2,7	1,2	A
3) Learns the notion of convergence of a series.	2,4,7	1,2	A
4) Represents some functions with power series.	1,2,4,7	1,2	A
5) Calculates partial derivatives of multi variable functions.	1,4,7	1,2	A
6) Calculates local and global minimum and maximum values.	1,2,4,7	1,2	A

Course Flow

DERS AKIŞI
Hafta	Konular	Ön Hazırlık
1	Definite Integral and Indefinite Integral
2	Fundamental Theorem of Calculus, Substitution, Integration by Parts
3	Trigonometric Substitutions, Integrals of Rational Functions
4	Areas of Plane Regions, Improper Integral
5	Volume, Arclength and Surface Area
6	The algebraic and order properties of real numbers
7	The completeness property, applications of the supremum property
8	Sequences and their limits
9	Monotone sequences, subsequences and the Bolzano-Weierstrass theorem
10	Cauchy sequences, Cauchy criterion
11	Infinite Series
12	Convergence Tests
13	Absolute and Conditional Convergence
14	Power Series, Taylor Series and Applications

Recommended Sources

RECOMMENDED SOURCES
Textbook	James Stewart, Calculus: Concepts and Contexts, 2nd Edition
Additional Resources

Material Sharing

MATERIAL SHARING
Documents
Assignments
Exams

Assessment

IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	2	100
Quizzes
Assignments
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		60
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		40
Total		100

COURSE CATEGORY

Core Courses

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 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
7	Ability of self-development in fields of interest			x
8	Ability to learn, choose and use necessary information technologies
9	Lifelong education			x

ECTS

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
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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