|
Week
|
Topics
|
Study Metarials
|
|
1
|
Real numbers, absolute value, equation and inequalities, properties of linear point sets, basic definitions related to functions
|
R1- Section P.1, Section P.2, Section P.3, Section P.4
|
|
2
|
Polynomials, rational functions, piecewise functions,
|
R1- Section P.5, Section P.6
|
|
3
|
Trigonometric functions, exponential and logarithmic functions
|
R1- Section P.7
|
|
4
|
Limits of functions, one sided limits, limit theorems
|
R1- Section 1.1, Section1.2
|
|
5
|
Limits at infinity and infinite limits, indeterminate forms, examples related to limits
|
R1-Section 1.3
|
|
6
|
Limits of trigonometric, exponential and logarithmic functions
|
R1- Section 1.3
|
|
7
|
Continuous functions and basic properties, properties of continuous functions defined on a closed and bounded interval
|
R1- Section 1.4
|
|
8
|
Uniform continuity
|
R1-Section 1.5
|
|
9
|
The concept of derivative and its geometric interpretation, differential concept,
rules of derivation,
derivative of trigonometric functions
|
R1- Section 2.1, Section 2.2, Section 2.3, Section2.5
|
|
10
|
Chain rule, higher order derivatives,
derivative of inverse functions
|
R1- Section 2.4, Section2.6, Section 3.1
|
|
11
|
Derivatives of exponential and
logarithmic functions, implicit
differentiation, derivatives of
parametric functions
|
R1- Section 3.2, Section 3.3, Section 2.9
|
|
12
|
Mean-value theorem, increasing
and decreasing functions,
maximum and minumum
values, first derivative test.
|
R1- Section 2.8, Section 4.4
|
|
13
|
Concavity and inflection points,
second derivative test,
asymptotes, curve sketching, polar coordinates
|
R1- Section 4.5, Section 4.6
|
|
14
|
Maximum, Minimum problems,
related rates, L`hospital rule
|
R1-Section 4.8, Section 4.3
|
|
Prerequisites
|
-
|
|
Language of Instruction
|
English
|
|
Responsible
|
Prof. Dr. Faruk POLAT
|
|
Instructors
|
-
|
|
Assistants
|
Assoc. Prof. Dr. Mustafa ASLANTAŞ, Asst. Prof. Dr. Şerifenur CEBESOY ERDAL , Dr. Emel BOLAT YEŞİLOVA
|
|
Resources
|
R1. Adams, R. A. (1999). Calculus: A complete course. Don Mills, Ont: Addison-Wesley Longman.
|
|
Supplementary Book
|
SR1. Bayraktar, M. (2020). Kalkülüs I. Matus Yayınları. SR2. Bartle, R. G. , Sherbert, D. R. (2010). Introduction to Real Analysis, John Wiley&Sons, Fourth edition.
|
|
Goals
|
The aim of this course is to examine the concepts of sequence, subsequence, convergent sequence, lower and upper limit, Cauchy sequence, limit and continuity of functions, trigonometric, exponential, logarithmic and hyperbolic functions, uniformly continuity, properties of continuous function, derivative, rules of differentiation, higher order derivative, geometric and physical meaning of derivative, extremes, theorems related to derivative, limits the uncertain situations and differentiation, sketching curve in cartesian and polar coordinates .
|
|
Content
|
Sequence, subsequence, convergent sequence, lower and upper limit, Cauchy sequence, limit and continuity of functions, trigonometric, exponential, logarithmic and hyperbolic functions, uniformly continuity, properties of continuous function, derivative, rules of differentiation, higher order derivative, geometric and physical meaning of derivative, extremes, theorems related to derivative, limits the uncertain situations and differentiation, sketching curve in cartesian and polar coordinates .
|
|
Program Learning Outcomes |
Level of Contribution |
|
1
|
Having advanced theoretical and applied knowledge in the basic areas of mathematics
|
3
|
|
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
|
Associating mathematical achievements with different disciplines and applying them in real life
|
3
|
|
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
|
-
|