An introduction to multivariable calculus through vectors in 3D, curves, functions of several variables, partial derivatives, min/max problems, multiple integration. Vector Calculus not covered.
|Vectors and geometry of space: dot and cross product, lines and planes, cylinders and quadric surfaces||12.1-12.6||3|
|Vector functions and curves: limits, continuity, tangent vector and motion, integrals, arc length, curvature||13.1-13.4||5|
|Functions of several variables: domain, graphs and level sets, limits and continuity, partial derivatives, chain rule, directional derivatives and gradients, tangent planes, extreme values and saddle points, Lagrange multipliers, Taylor's theorem||14.1-14.9||12|
|Multiple integrals: double and triple integrals over rectangles and general regions, area by double integration, integrals in polar, cylindrical and spherical coordinates, substitutions in multiple integrals.||15.1-15.8||10|