A First Course in Curves and Surfaces

• CURVESExamples, Arclength Parametrization
  Local Theory: Frenet Frame
  Some Global Results
  
• SURFACES: LOCAL THEORYParametrized 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 TOPICSHolonomy 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 CALCULUSLinear Algebra Review
  Calculus Review
  Differential Equations
  

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