Calculus III Honors (Vector Calculus and Differential Forms)
Here are links of PowerPoint Presentations, PDF documents and Word documents.
Exam 1: Newtons Method, Jacobian Matrix, Lipschtiz Condition, Derivative definition of a Matrix, Newman Series, Norm, Length, Determinant, Kantorovitch's Theorem, Inverse Function Theorem, Cauchy Swartz, Global Inverse, Implicit Function Theorem, Criteria for Differentiability.
Exam 2: Smooth Curve, Tangent Space, Tangent Plane, Smooth Manifold, Parameterization, Unit Circle, Unit Sphere, Little Oh, Taylor Polynomial of Standard Functions, Properties, sin(x), cos(x), e^x, log(1+x), Binomial (1+x)^m, Geometric Series, Chain Rule, Quadratic Forms, Lagrange Multiplier, Positive/Negative Definite, Max/Min/Saddle Point, Extrema, Best Coordinate System, Curvature of a Curve/Plane, Mean Curvature of a Surface, Gaussian Curvature, Arc Length, and Osculating Plane.
Exam 3: Integration, Indicator Function, Dyatic Pavings, Volume of a Cube, Integrable Function, Pavable Set, Center of Gravity/Mass, Variance, Probability density conditions, Random Variable, Fubini's Theorem, Determinants and Volumes, Change of Variables, Polar Coordinates, Spherical Coordinates Map, Cylindrical Coordinates Map, General Change of Variables, Parallelogram and Volume, Parameterization, Arc Length, Surface Area, Torus, and Volume of Manifolds.
Final Exam: Forms and Fields, Elementary Forms, Dimention, Wedge Product, Integrate Parametric Domain, 1 Form Field Work, 2 Form Field Flux, 3 Form Field Density, 0 Form Field Function, Orientation of a Point/Curve/Surface, Orientation Preserving, Orienting Boundary, Exterior Derivatives, Fundamental Theorem of Calculus in Higher Dimentions, Strokes Theorem, Grad, Curl, Div, Greems Theorem, and Line Integral.
MATH 2411 course taken at the Georgia Institute of Technology.
Lesson Learned: The more ways you learn the material, the better you master it. I recommend using KhanAcademy and MIT OpenCourseWare.