Ebook: Understanding Multivariable Calculus: Problems, Solutions, and Tips (The Great Courses)

36 Lectures 1 A Visual Introduction to 3-D Calculus 2 Functions of Several Variables 3 Limits, Continuity, and Partial Derivatives 4 Partial Derivatives-One Variable at a Time 5 Total Differentials and Chain Rules 6 Extrema of Functions of Two Variables 7 Applications to Optimization Problems 8 Linear Models and Least Squares Regression 9 Vectors and the Dot Product in Space 10 The Cross Product of Two Vectors in Space 11 Lines and Planes in Space 12 Curved Surfaces in Space 13 Vector-Valued Functions in Space 14 Kepler's Laws-The Calculus of Orbits 15 Directional Derivatives and Gradients 16 Tangent Planes and Normal Vectors to a Surface 17 Lagrange Multipliers-Constrained Optimization 18 Applications of Lagrange Multipliers 19 Iterated integrals and Area in the Plane 20 Double Integrals and Volume 21 Double Integrals in Polar Coordinates 22 Centers of Mass for Variable Density 23 Surface Area of a Solid 24 Double Integrals in Polar Coordinates 25 Triple Integrals in Cylindrical Coordinates 26 Triple Integrals in Spherical Coordinates 27 Vector Fields-Velocity, Gravity, Electricity 28 Curl, Divergence, Line Integrals 29 More Line Integrals and Work by a Force Field 30 Fundamental Theorem of Line Integrals 31 Green's Theorem-Boundaries and Regions 32 Applications of Green's Theorem 33 Parametric Surfaces in Space 34 Surface Integrals and Flux Integrals 35 Divergence Theorem-Boundaries and Solids 36 Stokes's Theorem and Maxwell's Equations