Calculus notes (1st edition)

Component form of vectors Engineering vector notation Position vectors Magnitude of vectors Unit vectors Scalar multiples Parallel vectors

Parametric equations general form Parameters Parametric descriptions Parametric equations of a circle Proof of parametric circle

Cross products of 2 component vectors <x,y> and 3 component vectors <x,y,z> Engineering notation of cross products Order of cross products Properties of cross products Geometric property of cross product

Position vector function Vector Equations Parametric Equations Non-simple planes Normal vector Orthogonal vector

Extrusions along x,y,z axes Generating curves Traces in x,y,z Quadric surfaces classification Ellipsoid, Elliptic paraboloid, Hyperbolic paraboloid, Hyperboloid of one sheet, Hyperboloid of two sheets, Hyperbolic cones, Elliptic cones

Dot products Properties of dot products Angle of separation Geometric formula of dot product Projections Orthogonals

Intersections of cone(s) with a plane Parabola Ellipse Circle Hyperbola Semi-major axis Semi-minor axis Standard form of conics Asymptotes

Extrusions along x,y,z axes Generating curves Traces in x,y,z Quadric surfaces classification Ellipsoid, Elliptic paraboloid, Hyperbolic paraboloid, Hyperboloid of one sheet, Hyperboloid of two sheets, Hyperbolic cones, Elliptic cones

Component form of vectors Engineering vector notation Position vectors Magnitude of vectors Unit vectors Scalar multiples Parallel vectors

Parametric equations general form Parameters Parametric descriptions Parametric equations of a circle Proof of parametric circle

Position vector function Vector Equations Parametric Equations Non-simple planes Normal vector Orthogonal vector

Cross products of 2 component vectors <x,y> and 3 component vectors <x,y,z> Engineering notation of cross products Order of cross products Properties of cross products Geometric property of cross product

Intersections of cone(s) with a plane Parabola Ellipse Circle Hyperbola Semi-major axis Semi-minor axis Standard form of conics Asymptotes

Dot products Properties of dot products Angle of separation Geometric formula of dot product Projections Orthogonals

This file has all lecture notes from the semester with detailed theory definitions, examples, and uses. The file also includes written out and solved homework problems and an in depth final review which helped me get a 93% on the final exam.