MA 261 Multivariate Calculus, Section 555, Summer 2018

• Course webpage: MA 261 - Multivariate Calculus (includes course calendar, assignment sheet, ground rules, etc.)
• My email: price79@purdue.edu
• My office hours: Monday and Thursday, 11:00 am to noon, in MATH 645, or by appointment
• The grader for Section 555 is Dustin Enyeart. Any questions on how homework or quizzes are graded should be directed to him.
• Dustin's office hours: Monday, 3:20 pm - 4:20 pm, in MATH 711.
• You may attend any of the office hours listed here, even if you are not in that instructor's/grader's section.
• You may also go to the Math Help Room, MATH 205, Monday through Friday, 10:00 am to 4:00 pm

• The final exam will be Friday, August 3, 2018, 1-3 pm, in PHYS 112
• The final exam study guide is posted below.
• Feel free to ask questions about the final exam review problems on Piazza!

• Geogebra has an excellent 3D plotter, if you want to plot some surfaces.
• 2D Vector Field Plotter
• 3D Vector Field Plotter
• Parametric Surface Plotter
• I have a Line Integral or Surface Integral. What do I do?!
• Here are my responses to your comments when I asked for feedback on the class.

Note: While I strive to have good notes, I do make mistakes every so often. There is no guarantee that my notes are error free. That being said, the main ideas should be conveyed correctly.

• Lesson 1: Geometry of Space and Vectors (12.1, 12.2, 12.3, 12.4)
• Topics: Coordinate planes, spheres, vectors, dot product, cross product
• Lesson 2: Lines, Planes, Cylinders, and Quadric Surfaces (12.5, 12.6)
• Topics: Equations of lines, equations of planes, cylinders, traces, classification of quadric surfaces
• Lesson 3: Vector Functions and Space Curves (13.1, 13.2)
• Topics: vector functions, space curves, intersections of surfaces and/or space curves, derivatives of vector functions, the tangent vector to a space curve
• Lesson 4: Arc Length and Curvature (13.3)
• Topics: arc length, parameterization of a vector function in terms of arc length, smooth curves, the unit tangent vector, the unit normal vector, curvature
• Lesson 5: Motion in Space: Velocity and Acceleration (13.4)
• Topics: displacement, average velocity, velocity, speed, acceleration
• Lesson 6: Functions of Several Variables (14.1)
• Topics: functions of several variables, domains, level curves, contour plots
• Lesson 7: Limits, Continuity, and Partial Derivatives (14.2, 14.3)
• Topics: limits and continuity of multivariate functions, partial derivatives, higher order partial derivatives, Clairaut's Theorem
• Lesson 8: Linear Approximations and the Chain Rule (14.4, 14.5)
• Topics: tangent planes, linear approximations, differentials, the chain rule, implicit differentiation formula
• Lesson 9: Directional Derivatives and Local Extrema (14.6, 14.7)
• Topics: directional derivatives, the gradient vector, maximal increase in direction of gradient, local extrema and saddle points, the second derivatives test
• Lesson 10: Constrained Optimization (14.7, 14.8)
• Topics: absolute extrema, Extreme Value Theorem, finding absolute extrema on a boundary/constraint by parameterization or by Lagrange Multipliers
• Lesson 11: Double Integrals over Rectangles (15.1)
• Topics: volumes under a surface, double integrals over rectangles, partial integrals, iterated integrals
• Lesson 12: Double Integrals over Arbitrary Regions and by Polar Coordinates (15.2, 15.3)
• Topics: double integrals over arbitrary regions, setting up double integrals, switching order of integration, average value of a 2-variable function, polar coordinates, converting double integrals into polar coordinates, using double integrals to compute areas in the xy-plane.
• Lesson 13: Applications of Double Integrals (15.3, 15.4, 15.5)
• Topics: review of integration by polar coordinates, finding mass, moments, and centroids of a 2-dimensional lamina with variable density, finding the surface area of a surface z=f(x,y) using double integrals
• Lesson 14: Triple Integrals (15.6)
• Topics: triple integrals over arbitrary regions, setting up triple integrals, volumes using triple integrals
• Lesson 15: Triple Integrals using Cylindrical Coordinates (15.7)
• Topics: cylindrical coordinates, setting up and evaluating triple integrals using cylindrical coordinates
• Lesson 16: Triple Integrals using Spherical Coordinates (15.8)
• Topics: spherical coordinates, setting up and evaluating triple integrals using spherical coordinates
• Lesson 17: Vector Fields (16.1)
• Topics: vector fields, visualizing vector fields, gradient vector fields
• Lesson 18: Line Integrals (16.2)
• Topics: line integrals of multivariate functions over curves, line integrals of vector fields over curves, work done by a force field on an object moving along a curve
• Lesson 19: The Fundamental Theorem for Line Integrals (16.3)
• Topics: fundamental theorem for line integrals, path independence of line integrals over a conservative vector field, a condition for determining whether a vector field is conservative, finding a potential function for a conservative vector field, using the fundamental theorem to compute some line integrals, proof of the Law of Conservation of Energy
• Lesson 20: Green's Theorem (16.4)
• Topics: orientation of a curve, Green's Theorem, computing line integrals of vector fields along a closed curve using Green's Theorem
• Lesson 21: Curl and Divergence (16.5)
• Topics: the gradient operator, curl, using curl to check whether a vector field is conservative, divergence, how curl and divergence operate on vector fields
• A YouTube video by 3Blue1Brown on getting an intuitive understanding of divergence and curl
• Lesson 22: Parametric Surfaces (16.6)
• Topics: identifying a parametric surface by eliminating the parameter, grid lines of a parametric surface, finding parametric equations for a surface
• Lesson 23: Areas of Parametric Surfaces and Surface Integrals (16.6, 16.7)
• Topics: tangent plane of a parametric surface, finding surface area of a parametric surface, surface integrals of functions
• Lesson 24: More on Surface Integrals (16.7)
• Topics: surface integrals where the surface can be decomposed into several surfaces, oriented surfaces, flux integrals, surface integrals of vector fields
• Lesson 25: Stokes' Theorem (16.8)
• Topics: induced orientation on a boundary curve of a surface, Stokes' Theorem, using Stokes' Theorem to compute the surface integral of the curl of a vector field as a line integral, using Stokes' Theorem to replace a surface with a nicer surface, using Stokes' Theorem to compute the line integral of a vector field by finding a surface with the curve as its boundary
• Lesson 26: The Divergence Theorem (16.9)
• Topics: The Divergence Theorem, computing surface integrals of closed surfaces using the Divergence Theorem

• Quiz 1
• Quiz 2
• Quiz 3
• Quiz 4
• Quiz 5
• Quiz 6
• Quiz 7
• Quiz 8
• Quiz 9
• Quiz 10