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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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