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Week
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Topics
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Study Metarials
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1
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Concavity and inflection points, second derivative test, asymptotes, curve sketching, Introduction to antiderivatives,
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R1- Section 2.10
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2
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indefinite integral and basic integral formulas, Rules for changing variables in
integrals
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R1- Section 6.1
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3
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Integration by writing in simple
fractions and integration by parts
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R1- Section 6.2
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4
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Recursion formulas for
integration and ceratin
examples
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R1- Section 6.3
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5
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Riemannian sums and Riemann
(definite) integral
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R1- Section 5.2, Section 5.3
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6
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Definite integral, its properties,
Mean-value theorem and
certain examples
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R1- Section 5.4
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7
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Fundamental theorem of
differential and integral
computation
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R1- Section 5.5
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8
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Calculation of area, arc length as application of the definite integral
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R1- Section 5.7
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9
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Evaluation of volume and surface of revolution.
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R1- Section 7.1
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10
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Improper integrals and their
types
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R1- Section 6.5
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11
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Tests for convergence relating
to improper integrals
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R1- Section 6.5
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12
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Sequences, subsequences, convergent sequences, limit superior, limit inferior, Cauchy sequences, introduction to real series
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R1- Section 9.1, Section 9.2
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13
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Convergence and divergence of
series
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R1- Section 9.3
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14
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Tests for convergence and
divergence of series
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R1- Section 9.4
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Prerequisites
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-
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Language of Instruction
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English
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Responsible
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Assoc. Prof. Dr. Mustafa ASLANTAŞ
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Instructors
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-
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Assistants
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Asst. Prof. Dr. Şerifenur CEBESOY ERDAL , Dr. Emel BOLAT YEŞİLOVA
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Resources
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R1. Adams, R. A. (1999). Calculus: A complete course. Don Mills, Ont: Addison-Wesley Longman.
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Supplementary Book
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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.
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Goals
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The goal of this course is to find indefinite and definite integral of functions, to evaluate area, arc length, surface area and volume, to examine tests for convergence relating to improper integrals and real valued series.
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Content
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Indefinite and definite integral, evaluation of area, arc length, surface area and volume, tests for convergence relating to improper integrals and real valued series
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Program Learning Outcomes |
Level of Contribution |
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1
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Having advanced theoretical and applied knowledge in the basic areas of mathematics
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3
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2
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Ability of abstract thinking
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-
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3
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To be able to use the acquired mathematical knowledge in the process of defining, analyzing and separating the problem encountered into solution stages.
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3
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4
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Associating mathematical achievements with different disciplines and applying them in real life
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-
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5
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Ability to work independently in a problem or project that requires knowledge of mathematics
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3
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6
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Ability to work harmoniously and effectively in national or international teams and take responsibility
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-
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7
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Having the skills to critically evaluate and advance the knowledge gained from different areas of mathematics
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-
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8
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To be able to determine what kind of knowledge learning the problem faced and to direct this knowledge learning process.
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-
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9
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To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time
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-
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10
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Ability to verbally and in writing convey thoughts on mathematical issues, and solution proposals to problems, to experts or non-experts.
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-
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11
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Being able to produce projects and organize events with social responsibility awareness
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-
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12
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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
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-
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13
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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
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-
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14
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Being conscious of acting in accordance with social, scientific, cultural and ethical values
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-
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