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• Notes on graphing, rewriting and finding parametric equations
• Notes on trochoids, derivatives for paramteric curves, tangent lines and arc length
• Notes on polar coordinates
• Notes from last semester on polar coordinates
• Notes on tangent lines, areas and arc length in polar coordinates
• Notes on conic sections in Cartesian and polar coordinates
• Notes on conic sections in polar coordinates
• Notes on lines, planes and spheres in 3D
• Notes on vectors and their applications
• Notes on the dot product of vectors
• Notes on the cross product of vectors
• Notes on the cross product of vectors, parallelpipeds and lines and planes in 3D
• Notes on sketching surfaces in 3D
• Notes on sketching quadric surfaces in 3D
• Notes on limits in two dimensions
• Introductory example on existence of limits in 2D
• More on limits in two dimensions and introduction to vector functions
• Notes on partial derivatives and tangent planes
• Maple worksheet on intersection of surfaces
• Maple worksheet on tangent planes
• Notes on tangent planes, linear approximations and differentials
• Notes on the chain rule for partial derivatives and finding critical points
• Notes on classifying critical points and the directional derivative
• Notes on the directional derivative and locating extrema (global maximums and global minimums)
• Conclusion of example on global maximums and global minimums
• Notes on Lagrange multipliers
• Further notes on Lagrange multipliers
• Notes on approximating volumes and double integrals
• Notes on double integrals over general regions and changing the order of integration
• Notes on double integrals in polar coordinates
• Notes on the concept of a triple integral
• Notes on setting up triple integrals
• Notes on triple integrals in cylindrical coordinates
• Notes on triple integrals in spherical coordinates
• An additional example on triple integrals in spherical coordinates and introduction to vector fields
• Notes on path integrals of functions and vector fields
• Notes on the Fundamental Theorem for path integrals of functions and Green's Theorem
• Notes on divergence and curl vector fields and parametric equations for surfaces
• Notes on surface integrals, Stoke's Theorem and the Divergence Theorem