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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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Basic definitions and theorems related to multiple integrals
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R1- Section 14.1
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2
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Reducing multiple integrals to consecutive integrals, changing variables in multiple integrals
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R1- Section 14.2, Section 14.4
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3
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Improper multiple integrals and comparison test for convergence , changing variables in improper multiple integrals
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R1- Section 14.3
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4
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Double integrals, converting regions in double integrals, double integrals in polar coordinates
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R1- Section 14.4
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5
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Applications of double integrals: finding area and volume, center of mass, moment of inertia
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R1- Section 14.7
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6
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Triple integrals, spherical and cylindirical coordinates, triple improper integrals
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R1- Section 14.5, Section 14.6
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7
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Application of triple integrals: volume, center of mass, moment of inertia
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R1- Section 14.7
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8
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Curves in n-dimensional space, parametrization of curves, basic definitions related to line integrals, line integrals of scalar and vector fields
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R1- Section 15.1, Section 15.2, Section 15.3
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9
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Line integrals in 3 dimensional space, path of independence, exact differentials, line integrals in plane
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R1- Section 15.4, Section 15.5
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10
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Green`s theorem, multiple connected regions
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R1- Section 16.3
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11
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Surfaces in nth-dimensional space, parametrization of surfaces, smooth surfaces, directions in surfaces
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R1- Section 15.5, Section 15.6
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12
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Surface integrals of scalar and vector fields
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R1- Section 15.5
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13
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Divergence and Stoke`s Theorem
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R1- Section 16.4, Section 16.5
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14
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Applications of line and surface integrals
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R1- Section 15.4, Section 15.5
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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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Prof. Dr. Faruk POLAT
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Instructors
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-
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Assistants
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Dr. Emel Bolat Yeşilova
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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. Stewart, J. (2015). Calculus (8th Ed.). Cengage Learning, Boston.
SR2. Hass, J.R., Heil, C.E., Weir, M.D. (2017). Thomas` Calculus (14 Ed.). Pearson, London.
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Goals
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To teach the basic properties of multiple integrals, double and triple integrals, applications of line integrals and surface integrals.
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Content
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Double integrals, triple integrals, line integrals, surface integrals, Green`s and Stokes` Theorems.
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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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4
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2
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Ability of abstract thinking
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2
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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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4
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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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2
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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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-
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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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