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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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Derivative, Differentials, Rules for derivative, Chain rule
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R1: Section 2.2-2.4
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2
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Increasing and decreasing functions, Mean Value Theorem
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R1: Section 2.6
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3
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Implicit differentiation, Higher order derivatives, Anti derivative
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R1: Section 2.9-2.10
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4
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Inverse functions, Exponential and logarithmic functions, Natural logarithm
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R1: Section 3.1-3.3
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5
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Inverse trigonometric functions, Hyperbolic functions
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R1: Section 3.5-3.6
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6
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Linear differential equations with constant coefficients
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R1: Section 3.7
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7
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Related rates, Concavity and inflection points
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R1: Section 4.1, 4.3
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8
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Linear approximations, Error analysis, Indeterminate forms
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R1: Section 4.7, 4.9
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9
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Sum and product symbols, Some sum and product formulas, Series and sequences
Definite integral, Fundamental Theorem of Calculus
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R1: Section 5.1-5.3, 5.5
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10
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Techniques of integration
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R1: Section 6.1-6.3
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11
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Improper integrals
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R1: Section 6.5
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12
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Volumes of solids of revolution, Multiple integrals
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R1: Section 7.1, 14.1
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13
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Line integrals, Surface integrals, Greens Theorem
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R1: Section 15.3, 15.5, 16.3
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14
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Divergence Theorem, Stokes Theorem
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R1: Section 16.4-16.5
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Prerequisites
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-
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Language of Instruction
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Turkish / English
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Responsible
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Prof. Dr. Ahmet Yaşar ÖZBAN
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Instructors
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-
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Assistants
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-
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Resources
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R1. Adams, R.A. Essex, C., Calculus, A Complete Course, Seventh Edition. Pearson Canada, 2009.
R2. Zafran, L., Math Made a Bit Easier: Basic Math Explained in Plain English, CreateSpace, 2009.
R3. Lecture Notes
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Supplementary Book
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SR1. Natanson, I. P., Theory of Functions of a Real Variable, Chap. 1,, 14, Ungar, 1955.
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Goals
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The aim of this course is, in general, to teach basic terms related to mathematics included in scientific publications in English, and in particular to comprehend terms parallel to seen in basic mathematics courses and to provide students the ability to make translations from English to Turkish or vice versa.
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Content
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Differentials, Inverse functions, Linear differential equations, Related rates, Linear approximations, Series, Integration, Volumes of solids, Line and Surface integrals
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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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3
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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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2
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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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-
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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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3
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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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3
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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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