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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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Geometries and same related notions, affine space and Euclidean space
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R1- Chapter 1.1, 1.2
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2
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Topological manifold, diffeomorphism, differentiable manifold
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R1- Chapter 1.3, 1.4, 1.5
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3
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Tangent vectors, tangent spaces and vector fields
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R1- Chapter 1.6, 1.7
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4
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Directional derivative, covariant derivative
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R1- Chapter 1.9
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5
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Integral curve
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R1- Chapter 1.10
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6
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Lie operator
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R1- Chapter 1.11
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7
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Gradient divergence rotational function and the differential of a transformation
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R1- Chapter 1.12, 1.13
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8
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Curves and change of parameter
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R1- Chapter 2.1
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9
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Serret-Frenet vectors
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R1- Chapter 2.2
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10
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The osculating planes of a curve, curvatures and its geometric meanings
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R1- Chapter 2.3, 2.4
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11
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Curvature centers, osculating spheres
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R1- Chapter 2.5
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12
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Some frame fields
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R1- Chapter 2.6
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13
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Parallel curve pairs and involute evolute curve pair
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R1- Chapter 2.7.1, 2.7.2
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14
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Bertrand curve pair and Mannheim curve pair
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R1- Chapter 2.7.3, 2.7.4
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