Calculus III

Catalog description

Topics from vector analysis and multivariate calculus will include vector calculus, directional and partial differentiation, gradients, differential calculus of vector valued functions, multiple, iterated, line and surface integrals and applications of these concepts. Upon completion of this course a student will be able to: (1) interpret and use precise mathematical language and be able to construct and follow mathematical proofs involving the calculus of vector-valued functions and functions of several variables; (2) analyze functions of several independent variables using differential calculus, algebraically and geometrically in Cartesian or other coordinate systems: (3) use multivariate calculus to solve optimization problems involving functions of several variables, including constrained problems, and be able to identify and interpret critical points of such functions; (4) use integral calculus of multivariable functions to solve physical and geometrical problems in Cartesian cylindrical, and spherical coordinate systems; (5) use a complete catalog of the tool of multivariable differential and integral calculus (e.g., limits multivariable functions, vector fields, derivatives and integrals of vector fields); (6) demonstrate mathematical creativity and critical thinking by applying problem-solving strategies to solve multiple-step problems involving the differential and integral calculus of vector fields and multivariable functions; (7) Use appropriate technology in the evaluation, analysis, and synthesis of information in problem-solving situations involving the calculus of vector fields and multivariable functions.