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Apr 20, 2024
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Catalog 2015-2016 [ARCHIVED CATALOG]
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MATH& 254 Calculus IV5 credits
Fourth quarter of the calculus sequence. Calculus IV introduces the study of multivariable calculus, with a focus on functions of two or three variables. Topics include: first-order differential equations, partial derivatives, directional derivatives, gradient vectors, multiple integration, vector fields, line and surface integrals, Green’s Theorem, Stokes’s Theorem, and the Divergence Theorem.
Prerequisites: MATH& 153 .
Student Outcomes/Competencies:
Upon successful completion of this course students will be able to:
- Solve first-order differential equations, including initial value problems
- Construct the phase line for an autonomous differential equation
- 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 find equations of tangent lines and planes and to compute directional derivatives for multivariable functions
- Find local maxima and minima and saddle points of multivariable functions
- Identify absolute maximum and minimum values of a multivariable function on a given region
- Evaluate double and triple integrals
- Solve area, volume, and average-value problems using multiple integration
- Use alternate coordinate systems (polar, cylindrical, spherical) to simplify multiple integration problems
- Use vector and scalar fields appropriately, particularly when computing a gradient, curl, or divergence
- Use and compute line and surface integrals
- Apply Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem
- Use the mathematical critical thinking skills of problem solving, pattern recognition, substitution, following structural rules, and quantitative modeling to solve problems requiring reasoning, critical thinking, and computation
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