Math 001D Objectives and Student Learning Outcomes.
Course Objectives
| A. | Examine functions of several variables, define and compute limits of functions at points and define and determine continuity |
| B. | Define and compute partial derivatives, directional derivatives and differentials of multivariable functions and examine conditions of differentiability; find the equation of the tangent plane to a surface at a point |
| C. | Find local extreme values of functions of several variables, test for saddle points, examine the conditions for the existence of absolute extreme values, solve constraint problems using Lagrange multipliers, and solve related application problems |
| D. | Use rectangular, cylindrical and spherical coordinates systems to define space curves and surfaces in Cartesian and parametric forms |
| E. | Integrate functions of several variables |
| F. | Examine vector fields and define and evaluate line integrals using the Fundamental Theorem of Line Integrals and Green’s Theorem; compute arc length |
| G. | Define and compute the curl and divergence of vector fields and apply Green’s Theorem, Stokes’s Theorem and the Divergence Theorem to evaluate line integrals, surface integrals and flux integrals |
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Student Learning Outcome Statements (SLO) |
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• Student Learning Outcome: Graphically and analytically synthesize and apply multivariable and vector-valued functions and their derivatives, using correct notation and mathematical precision. |
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• Student Learning Outcome: Use double, triple and line integrals in applications, including Green's Theorem, Stokes' Theorem and Divergence Theorem. |
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• Student Learning Outcome: Synthesize the key concepts of differential, integral and multivariate calculus. |
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