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Jan 16, 2019
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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

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