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Multivariable Calculus
Math 2110Q § 003
Fall 2017

Schedule

 Week Sec. Topic Materials Resources 1 12.1 Three dimensional coordinate systems Calculus I and II Review A robust 3D grapher 12.2 Vectors Lengths of vectors Seeing a vector in 3D 12.3 The dot product The dot and cross products The dot product in 3D 12.4 The cross product Practice with vectors (optional) Visualizing the cross product 2 12.5 Equations of lines and planes Intersections of lines and planes Parameterizing a line in 3D 12.6 Cylinders and quadric surfaces Understanding surfaces Visualzing quadric surfaces 3 14.1 Functions of several variables Contour plots and multi-variable domains Bivariate functions in Desmos A robust 3D grapher 14.3 Partial derivatives Higher-order partials Visualizing the partial derivative at a point 14.4 Tangent planes and linear approximation Tangent planes and linearization Seeing an infinite collection of tangent lines. A "good" linear approximation. Examples used in class: #1 (.png) #2 (.png) #3 (.png) 14.5 The chain rule The chain rule 4 14.6 Directional derivatives and the gradient vector The gradient and directional derivatives Visualizing directional derivatives 14.7 Local extrema of multi-variate functions Classifying extrema Visualizing absolute and local extrema A function with one local max, two local mins and three saddle points. A hard function to graph with a local minimum 15.1 Double integrals over rectangles Double integrals over rectangles Visualizing a single and a double Riemann sum 5 15.2 Double integrals over general regions Double integrals over general regions 15.3 Double integrals in polar coordinates Double integrals in polar coordinates 6 Review Exam 1: 7:30 - 8:30pm on 10/2 Covers sections 12.1 - 12.6, 14.1, 14.2, 14.3 - 14.7, 15.1 - 15.3 Practice Exam 1 (Solutions) Review Exercises Review of exam 1 15.3 Double integrals in polar coordinates 15.6 Triple integrals Triple integrals 7 15.6 Triple integrals 15.7 Triple integrals in cylindrical coordinates Triple integrals in cylindrical coordinates Visualizing cylindrical coordinates 8 15.7 Triple integrals in cylindrical coordinates 15.8 Triple integrals in spherical coordinates Triple integrals in spherical coordinates Visualizing spherical coordinates Basic surfaces in spherical coordinates Triple integrals "cheatsheet" 13.1 Vector functions and space curves Interactive examples Space curves #1 and #2 A line segment A gallery of space curves 9 13.2 Calculus of vector-valued functions Vector functions part 1 13.3 Arc length Vector functions part 2 Visualizing approximations of arc length A few practice problems 16.2 Line integrals of scalar functions Line integrals of scalar functions The area calculated in a line integral and in one projection 10 16.2 (and 16.1) Line integrals of vector fields Line integrals of vector fields Vector field examples #1 #2 and #3 16.3 The fundamental theorem for line integrals Fundamental theorem for line integrals 11 16.4 Green's theorem Green's theorem Review Exam 2: 7:30 - 8:30pm on 11/8 Covers sections 15.4, 15.6 - 15.8, 13.1 - 13.3, 16.1 - 16.3 Practice Exam 2 (Solutions) Review Exercises 12 16.5 Curl and divergence Curl and Divergence Curl examples #1 #2 #3 #4 #5 Divergence examples 16.6 Parametric surfaces and their areas Parametric surfaces 13 Fall Break No class 14 16.7 Surface integrals of scalar functions 16.7 Surface integrals of vector fields 16.7 Surface integrals Motivating examples 15 16.9 The divergence theorem Quiz 9 Quiz 9 Key 16.8 Stokes' theorem 16.9 The divergence theorem and Stokes' theorem 16 Final Exam 6 - 8pm on Wednesday 12/13/17 in Monteith 111 Cumulative Review questions Cheat sheet