Weeks | Topics |
1 |
The theory of curves, change of parameters
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2 |
Serret-Frenet vectors and vector fields
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3 |
Curvature, curvature axes, centers of curvature, curvature spheres
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4 |
Osculating spheres, involute-evolute
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5 |
Riemann manifold, the covariant derivative
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6 |
Normal vector field, orientation, geodesics
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7 |
Parallelism, Figure operator
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8 |
Midterm Exam
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9 |
Gauss transformation, matrix calculation of Weingarten transformation
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10 |
Basic forms, algebraic invariants of Figure operator
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11 |
Principal curvatures, principal directions, mean curvature, curvature lines
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12 |
Euler's theorem and mean curvatures
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13 |
Olin Rodriges formulas, Dupin indicatrix
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14 |
Final Exam
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