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[MAS102] Topic 8. Approximations and Differentiation미적분학II '20 2020. 8. 30. 00:00
◎ 관련 단원 및 교과목(Thomas' Calculus 14.6) Tangent Planes and Differentials(Thomas' Calculus 14.9) Taylor's Formula for Two Variables(Vector Calculus 4.1) Differentials and Taylor's Theorem(MAS242) 해석학II ◎ 주요 제재- Differential- Taylor's Theorem; Taylor Polynomial- Lagrange's Remainder Form for Taylor Approximation ※ Comment 두 함수의 곱의 Taylor series를 구할 때, 각각의 Taylor series들을 단순히 곱해서 구해도 되기는 됩니다. 원하는 차수 뒤..
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[MAS102] Topic 7. Vector Fields미적분학II '20 2020. 8. 29. 23:39
◎ 관련 단원 및 교과목(Thomas' Calculus 16.2) Vector Fields and Line Integrals; Work, Circulation, and Flux(Thomas' Calculus 16.3) Path Independence, Conservative Fields, and Potential Functions(Vector Calculus 3.3) Vector Fields: An Introduction(Vector Calculus 3.4) Gradient, Divergence, Curl, and the Del Operator(Vector Calculus 6.3) Conservative Vector Fields ◎ 주요 제재- Definition of Vector Field- Diver..
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[MAS102] Topic 6. Differential Geometry on Curves미적분학II '20 2020. 8. 25. 23:59
◎ 관련 단원 및 교과목(Thomas' Calculus 13.1) Curves in Space and Their Tangents(Thomas' Calculus 13.3) Arc Length in Space(Thomas' Calculus 13.4) Curvature and Normal Vectors of a Curve(Thomas' Calculus 13.5) Tangential and Normal Components of Acceleration(Vector Calculus 3.1) Parametrized Curves and Kepler's Laws(Vector Calculus 3.2) Arclength and Differential Geometry(MAS321) 미분기하학개론 ◎ 주요 제재- Definit..
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[MAS102] Topic 5. The Chain Rule미적분학II '20 2020. 8. 25. 23:56
◎ 관련 단원 및 교과목(Thomas' Calculus 14.4) The Chain Rule(Thomas' Calculus 14.5) Directional Derivatives and Gradient Vectors(Vector Calculus 2.5) The Chain Rule(Vector Calculus 2.6) Directional Derivatives and the Gradient(MAS241) 해석학I(MAS242) 해석학II(MAS321) 미분기하학개론 ◎ 주요 제재- The Chain Rule- Partial Derivatives on Polar/Cylindrical/Spherical Coordinates- Tangent Planes for Level Surfaces- Implicit Func..
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[MAS102] Topic 4. Geometrical Interpretation of Derivatives미적분학II '20 2020. 8. 25. 23:53
◎ 관련 단원 및 교과목(Thomas' Calculus 14.3) Partial Derivatives(Thomas' Calculus 14.5) Directional Derivatives and Gradient Vectors(Thomas' Calculus 14.6) Tangent Planes and Differentials(Vector Calculus 2.3) The Derivative(Vector Calculus 2.6) Directional Derivatives and the Gradient ◎ 주요 제재- Geometrical Meaning of Directional/Partial Derivatives- Tangent Lines/Planes
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[MAS102] Topic 3. The Derivative미적분학II '20 2020. 8. 25. 23:50
◎ 관련 단원 및 교과목(Thomas' Calculus 14.3) Partial Derivatives(Thomas' Calculus 14.5) Directional Derivatives and Gradient Vectors(Vector Calculus 2.3) The Derivative(Vector Calculus 2.4) Properties; Higher-order Partial Derivatives(Vector Calculus 2.6) Directional Derivatives and the Gradient(MAS241) 해석학I(MAS242) 해석학II ◎ 주요 제재- Directional Derivative- Partial Derivative- Differentiability
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[MAS102] Topic 1. Basic Topology미적분학II '20 2020. 8. 24. 01:42
◎ 관련 단원 및 교과목(Thomas' Calculus 14.1) Functions of Several Variables(Vector Calculus 2.1) Functions of Several Variables; Graphing Surfaces(Vector Calculus 2.2) Limits(MAS241) 해석학I ◎ 주요 제재- Open and Closed Sets- Connected and Simply-connected Sets- Basic Notions of Functions- Graphs- Level Sets and Contour Sets- Quadratic Surfaces