WWW links for Mathematics 138A notes
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1 WWW links for Mathematics 138A notes General statements about the use of Internet resources appear in the document listed below. We shall give separate lists of links for each of the relevant files in the course directory. We shall give lists of clickable links for each file in the course directory which contains Internet references without clickable links. Since this list is fairly long, links to specific files in the course directory will not be included. 0. These are clickable links for the file containing general information about the course; namely, These are clickable links for (the course notes). I. Classical Differential Geometry of Curves I. 1. Cross products
2 I. 2. Parametrized curves I. 3. Arc length and reparametrization I. 4. Curvature and torsion I. 5. Frenet Serret Formulas I I. Topics from Geometry and Multivariable Calculus II. 1. Differential forms II. 2. Smooth mappings
3 II. 3. Inverse and Implicit Function Theorems _illstrtn2.gif II. 4. Inverse and Implicit Function Theorems I I I. Surfaces in 3-dimensional space III. 1. Mathematical descriptions of surfaces III. 2. Parametrizations of surfaces III. 3. Tangent planes III. 4. The First Fundamental Form III. 5. Surface area
4 III. 6. Curves as surface intersections I V. Oriented surfaces IV. 1. Normal directions and Gauss maps IV. 2. The Second Fundamental Form
5 IV. 3. Quadratic forms and adjoint transformations IV. 4. Normal, Gaussian and mean curvature IV. 5. Special classes of surfaces IV. 5. Special classes of surfaces IV. 6. Map projections V. Further Topics V. 1. Compatibility equations, Theorema Egregium V. 2. Fundamental Theorem of Local Surface Theory
6
7 V. 3. Riemannian metrics and hyperbolic geometry
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