|
Week
|
Topics
|
Study Metarials
|
|
1
|
Pointwise and uniform convergence of sequences of functions
|
R1-Section 1
|
|
2
|
Relationship between uniform convergence, integral and derivative
|
R1-Section 1
|
|
3
|
Uniform convergence of series of functions and its relationship between integral and derivative
|
R1-Section 2
|
|
4
|
Introduction to power series
|
R1-Section 3
|
|
5
|
Derivative and integral of the power series
|
R1-Section 3
|
|
6
|
Taylor and Maclaurin series, their
applications
|
R1-Section 4
|
|
7
|
Vector valued functions, Limit and continuity of vector valued functions
|
R1-Section 5
|
|
8
|
Derivative of vector valued functions
|
R1-Section 5
|
|
9
|
Funtions of Several Variables
|
R1-Section 6
|
|
10
|
Funtions of Several Variables,Limits and Continuity for functions of several variables
|
R1-Section 6
|
|
11
|
Partial derivatives, the chain rule and total differentials
|
R1-Section 6
|
|
12
|
Directional derivatives and derivatives of the implicit functions
|
R1-Section 6
|
|
13
|
Taylor expansion of functions of two variables, Maxima and minima, Regional transforms, Functional Dependence
|
R1-Section 6
|
|
14
|
Vector fields, differentiation under the integral sign
|
R1-Section 6
|
|
Prerequisites
|
-
|
|
Language of Instruction
|
English
|
|
Responsible
|
Assoc. Prof. Dr. Faruk POLAT
|
|
Instructors
|
-
|
|
Assistants
|
Asst. Prof. Dr. Şerifenur CEBESOY ERDAL
|
|
Resources
|
R1- Lecture notes
|
|
Supplementary Book
|
SR1- Adams, R. A. (2007). Calculus. Addison-Wesley.
SR2-Bartle, R. G., Sherbert, D. R. (2010). Introductİon to Real Analysİs. John Wİley & Sons., Fourth Edition.
|
|
Goals
|
The aim of this course is to teach notions of convergence of sequences and series of functions, the radius and interval of convergence of power series, Taylor series, limits, continuity, derivatives and integrals of vector-valued functions, limits and continuity of functions of several variables, partial derivatives and the chain rule.
|
|
Content
|
Pointwise and uniform convergence of sequences of functions, relationship between uniform convergence, integral and derivative, uniform convergence of series of functions and its relationship between integral and derivative, derivative and the integral of the power series, taylor series, taylor`s expansion of funtions, limits, continuity, derivatives and integral of the vector-valued functions, limits and continuity of functions of several variables, partial derivatives, the chain rule, and total diferentials, directional derivatives and derivatives of the implicit functions
|
|
Program Learning Outcomes |
Level of Contribution |
|
1
|
Having advanced theoretical and applied knowledge in the basic areas of mathematics
|
4
|
|
2
|
Ability of abstract thinking
|
3
|
|
3
|
To be able to use the acquired mathematical knowledge in the process of defining, analyzing and separating the problem encountered into solution stages.
|
4
|
|
4
|
Associating mathematical achievements with different disciplines and applying them in real life
|
-
|
|
5
|
Ability to work independently in a problem or project that requires knowledge of mathematics
|
-
|
|
6
|
Ability to work harmoniously and effectively in national or international teams and take responsibility
|
-
|
|
7
|
Having the skills to critically evaluate and advance the knowledge gained from different areas of mathematics
|
-
|
|
8
|
To be able to determine what kind of knowledge learning the problem faced and to direct this knowledge learning process.
|
-
|
|
9
|
To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time
|
-
|
|
10
|
Ability to verbally and in writing convey thoughts on mathematical issues, and solution proposals to problems, to experts or non-experts.
|
-
|
|
11
|
Being able to produce projects and organize events with social responsibility awareness
|
-
|
|
12
|
Being able to follow publications in the field of mathematics and exchange information with colleagues by using a foreign language at least at the European Language Portfolio B1 General Level
|
-
|
|
13
|
Ability to use computer software (at least at the Advanced Level of European Computer Use License), information and communication technologies for solving mathematical problems, transferring ideas and results
|
-
|
|
14
|
Being conscious of acting in accordance with social, scientific, cultural and ethical values
|
-
|