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Scope:
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This course extends calculus concepts to multivariable and vector settings, enabling students to model and
analyze real-world phenomena involving three-dimensional motion, surfaces, and fields. Emphasis is placed on vector operations,
multiple integration, and key theorems such as Green’s, Stokes’, and Divergence, which have broad applications in mathematics, physics,
and engineering.
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Course Learning Outcomes:
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1. Apply parametric equations and polar coordinates to analyze and calculate the area and arc length of curves
2. Apply vector operations (dot product and cross product) and coordinate systems (cartesian, cylindrical, and spherical) to solve problems involving lines, planes, and surfaces in both two and three-dimensional space
3. Analyze functions of several variables using limits, continuity, partial derivatives, and solve optimization problems with gradients, the Chain Rule, and Lagrange multipliers
4. Compute multiple integrals over various regions and apply them to find centers of mass, moments of inertia, and perform change of variables
5. Analyze vector fields and apply integral theorems, including Green's Theorem, Stokes' Theorem, and the Divergence Theorem, to compute line, surface, and volume integrals in various contexts.
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