List of `Multivariable and Vector Calculus Examples' by section of Stewart, 7 edition Sec. 12.1 - Three dimensional coordinates systems Sec. 12.2 - Vectors Application of vectors to a tension problem Determine tangent vector at a point of a plane curve Sec. 12.3 - The dot product Determine the angle between two plane curves using dot product Cauchy-Schwarz inequality Triangle inequality for vectors Sec. 12.4 - The cross product Sec. 12.5 - Equations of lines and planes Distance from a point to a plane Distance from a point to a line Distance from a point to a line using scalar projection Find plane equidistant from two points Find plane given a line in the plane and orthogonal to a given plane Sec. 12.6 - Cylinders and quadric surfaces Using traces to determine quadric surfaces Determine quadric surface from quadratic equation Sec. 13.1 - Vector functions and space curves Matching problem for parametric equations Sec. 13.2 - Derivatives and integrals of vector functions Determine vector equations of a tangent line Determine the angle of intersection between two plane curves Sec. 13.3 - Arc length and curvature Determine curvature of plane curve Studying curvature of a family of plane curves Determine osculating circle to curve Sec. 14.1 - Functions of several variables Sec. 14.2 - Limits and continuity Limit proof for multivariate function Continuity of multivariate function Sec. 14.3 - Partial derivatives Sec. 14.4 - Tangent planes and linear approximations Applications of partial derivatives to determine tangent plane and normal line to surface Sec. 14.5 - The chain rule Application of partial derivatives Sec. 14.6 - Directional derivatives and the gradient vector The gradient and level curves Application of gradient to determine tangency of two surfaces Sec. 14.7 - Maximum and minimum values Absolute max min Optimize function of two variables Maximum/minimum example Extreme value theorem example Sec. 14.8 - Lagrange multipliers Lagrange multipliers Method of Lagrange multipliers Method of Lagrange multipliers with two constraints Sec. 15.1 - Double integral over rectangles Introduction to the double integral Sec. 15.2 - Iterated integrals Sec. 15.3 - Double integrals over general regions Integrating over a general region Sec. 15.4 - Double integrals in polar coordinates Double integral with polar coordinates Sec. 15.7 - Triple integrals Triple integrals - basic Sec. 15.8 - Triple integrals in cylindrical coordinates Cylindrical coordinates - level 1 Cylindrical Coordinates - level 2 Sec. 15.9 - Triple integrals in spherical coordinates Spherical coordinates - level 1 Spherical coordinates - level 2 Rectangular to spherical coordinates Sec. 15.10- Change of variables in multiple integrals Sec. 16.1 - Vector fields Sec. 16.2 - Line integrals Line integral example Work computed using line integral Sec. 16.3 - The Fundamental Theorem for line integrals Sec. 16.4 - Green's Theorem Green's Theorem Stewart 16.4.13 Sec. 16.5 - Curl and divergence Sec. 16.6 - Parametric surfaces and their areas Sec. 16.7 - Surface integrals Sec. 16.8 - Stokes' Theorem Stokes Theorem example Stokes Theorem to compute a vector surface Sec. 16.9 - The Divergence Theorem Divergence Theorem to compute a surface integral