Differentlal Geometry (Local)
- Chapter 1: Theory of Curves, 1.1 Introduction on the theory of curves and the geometry of curves with Maple 1.2 Arc length Parametrization. 1.3 Frenet Formulas. 1.4 Some implications of torsion and curvature. 1.5 Intrinsic equation of a curve. 1.6 Interesting curves and application of the theory of curves and projectile motions.1.7 Fundamental theorem of the theory of curves. 1.8 The Geometry of curves on and geodesic circles.
- Chapter 2: Local and Global Theory of Surfaces, 2.1 Definition of ordinary and regular surfaces and interesting surfaces with Maple. 2.2 Differentiable surface and continuous and differentiable function on a surface. 2.3 Curves on surfaces, tangent vector and tangent spaces on surfaces. 2.3 Orientable surfaces. 2.4 Directional derivative and tangent vector field and 1-form fields on a surface. 2.5. Differentiable functions between surfaces. 2.6 First fundamental forms. 2.7 Second fundamental