Honors Calculus III

Analysis of real- and vector-valued functions of one or more variables using tools from linear and multilinear algebra; stress is on theoretical aspects of the subject, including proofs of basic results. Topics include: geometry and algebra of vectors in 3-space, parametrized curves and arc length, linear transformations and matrices; Jacobian and gradient of a real-valued function, Implicit Function Theorem, extrema, Taylor's Theorem and Lagrange multipliers; multiple integrals, differential forms and vector fields, line integrals, parametrized surfaces and surface integrals, exact and closed forms, vector calculus. Recommendations: MATH 39 or permission of instructor. Students who receive credit for MATH 44 cannot receive credit for MATH 42.