Math 2242 Course Outline

Check with your instructor for the class syllabus, exam schedules and textbook information.

Week 1: Matrices and Determinants(Review); Inner product ; the cross Product; Equations of planes; equations of lines in space.

Week 2: Curvilinear coordinates (Polar, Cylindrical, Spherical); Differentiable Functions; Differentiation of vector valued functions; Gradients and Directional derivatives.

Week 3: The Chain Rule of vector valued functions of several variables; Property of the derivative; paths and curves. Review of relevant portions of Taylor’s theorem for several variables; Tangent plane; Linear approximation.

Week 4: Review; First Exam.

Week 5: Arc length; Vector fields; Divergence and Curl.

Week 6: Multiple Integrations (Review); Change of Variables.

Week 7: Oriented curve; parameterizations of curves; Path integral; Line Integrals.

Week 8: Level Surface; Parameterized Surfaces; Area of Surface; Surfaces of Revolution, Surface Integral of Scalar functions.

Week 9: Break.

Week 10: Review; Second Test.

Week 11: Normal Vectors; Oriented surface; Surface Integrals of vector fields.

Week 12: Green’s Theorem; Applications; Stokes’ Theorem.

Week 13: Stokes’ Theorem; Conservative Fields.

Week 14: Divergence Theorem; Applications.

Week 15: Third Test; Review; Catch-up.

Week 16: Final exam

Optional topics, at instructor’s discretion: Lagrange multipliers; further applications.