MATH& 264 Calculus IV

5 credits

The fourth quarter of the calculus sequence continues the study of multivariable calculus, with emphasis on the calculus of vector-valued functions and space curves. Topics include partial derivatives, double and triple integrals, directional derivatives, gradient vectors, vector fields, Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem. Real world applications are emphasized.

Prerequisites: MATH& 163

Global Outcomes:
This course teaches to the global outcome of Critical Thinking.

Student Outcomes/Competencies:
Upon successful completion of this course students will be able to:

Identify key features of multivariable functions (local and absolute maximums and minimums, as well as saddle points)
Find the domain and range of a multivariable function, and sketch its typical level curve or level surface
Find both first-order and second-order partial derivatives of a multivariable function
Compute the gradient and apply it to finding equations of tangent lines and planes, as well as to computing directional derivatives of multivariable functions
Evaluate double and triple integrals, and apply these multiple integration principles to solving area, volume and average-value applications
Compute line and surface integrals, and use them to solve relevant applications
Use alternative coordinate systems (including polar, cylindrical, and spherical) to simplify multiple integration problems
Compute gradient, curl, and divergence, using vector and scalar fields appropriately
Apply Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem
Introduce first-order differential equations, including initial value problems
Use mathematical critical thinking skills, problem solving, pattern recognition, and substitution, following structural rules and quantitative modeling to solve problems requiring reasoning, critical thinking, and computation

Total Hours: 50 Lecture Hours: 50