Comprehensive Mathematics II

SYLLABUS

• Power series, radius of convergence and interval of convergence.
• Limits and continuity of functions of several variables.
• Partial derivatives, the derivative, tangent planes, the gradient and directional derivatives.
• Taylor’s theorem, Lagrange multipliers.
• Polar, Cylindrical, and spherical coordinates.
• Integration in two and three variables, change of the order of integration, change of variables, the Jacobian.
• Vector fields, div and curl.
• Line integrals, surfaces and surface area, surface integrals of scalar functions.
• Simple functions of a complex variable.
• The complex derivative and analytic functions.
• Complex integration, Cauchy’s theorem (simple form), Cauchy’s integral formula.
• 2^nd order linear differential equations, particular and general solutions, the solution space.
• Simple systems of differential equations.
• The phase plane.
• Applications and models.