A First Course in Curves and Surfaces download free tutorial in pdf

CURVES
- Examples, Arclength Parametrization
- Local Theory: Frenet Frame
- Some Global Results
SURFACES: LOCAL THEORY
- Parametrized Surfaces and the First Fundamental Form
- The Gauss Map and the Second Fundamental Form
- The Codazzi and Gauss Equations and the Fundamental Theorem of Surface Theory
- Covariant Differentiation, Parallel Translation, and Geodesics
SURFACES: FURTHER TOPICS
- Holonomy and the Gauss-Bonnet Theorem
- An Introduction to Hyperbolic Geometry
- Surface Theory with Differential Forms
- Calculus of Variations and Surfaces of Constant Mean Curvature
Appendix. REVIEW OF LINEAR ALGEBRA AND CALCULUS
- Linear Algebra Review
- Calculus Review
- Differential Equations

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A First Course in Curves and Surfaces in pdf