MATH 102 DIFFERENTIAL AND INTEGRAL CALCULUS II

Vectors. Equations of surfaces and solids. Polar, cylindrical and spherical coordinates. Parametric representation. Dot and cross vector products. Multivariable functions. Limits and Continuity. Partial derivatives of multivariate functions, Directional Derivative, Gradient, Divergence, Curl. Fundamental theory of vector fields. Lagrange multipliers and multivariate function extrema. Line integrals, multiple integrals (double and triple) and applications to physics and geometry: volume calculation, mass, torque, surface area. Surface integrals and applications in fluid flow. Green’s theorem. Parametric representation of surfaces and applications. Stokes’ theorem. The divergence theorem.