Dave's Web Corner

MTH-261 Resources

• Outline
• Assessments
• Handouts
• Video
• Technology

Outline

• Chapter 12 Vectors and the Geometry of Space
  • 12.1 Three-Dimensional Coordinate Systems
  • 12.2 Vectors
  • 12.3 The Dot Product
  • 12.4 The Cross Product
  • 12.5 Equations of Lines and Planes
  • 12.6 Cylinders and Quadric Surfaces
• Chapter 13 Vector Functions
  • 13.1 Vector Functions and Space Curves
  • 13.2 Derivatives and Integrals of Vector Functions
  • 13.3 Arc Length and Curvature
  • 13.4 Motion in Space: Velocity and Acceleration
• Chapter 14 Partial Derivatives
  • 14.1 Functions of Several Variables
  • 14.2 Limits and Continuity
  • 14.3 Partial Derivatives
  • 14.4 Tangent Planes and Linear Approximations
  • 14.5 The Chain Rule
  • 14.6 Directional Derivatives and the Gradient Vector
  • 14.7 Maximum and Minimum Values
  • 14.8 Lagrange Multipliers
• Chapter 15 Multiple Integration
  • 15.1 Double Integrals over Rectangles
  • 15.2 Iterated Integrals
  • 15.3 Double Integrals over General Regions
  • 15.4 Double Integrals in Polar Coordinates
  • 15.5 Applications of Double IntegralsTriple Integrals
  • 15.6 Surface Area
  • 15.7 Triple Integrals
  • 15.8 Triple Integrals in Cylindrical Coordinates
  • 15.9 Triple Integrals in Spherical Coordinates
  • 15.10 Change of Variables in Multiple Ingegrals
• Chapter 16 Vector Calculus
  • 16.1 Vector Fields
  • 16.2 Line Integrals
  • 16.3 The Fundamental Theorem for Line Integrals
  • 16.4 Green's Theorem
  • 16.5 Curl and Divergence
  • 16.6 Parametric Surfaces and Their Areas
  • 16.7 Surface Integrals
  • 16.8 Stokes' Theorem
  • 16.9 The Divergence Theorem
  • 16.10 Summary

Assessments

• Deadlines
  • All homework is due at the beginning of class on the date indicated.
  • All exams are given in class on the date indicated.
  • Late homework is not accepted and there are no make-ups for missed exams. Contact me before the deadline if you have a conflict with a deadline and we will find a mutually agreeable solution.
  • Solutions are posted under these links after the deadline.
• Homework
  • due Thursday, August 29:
    • (none)
  • due Thursday, September 5:
    • 1, 2, 3, 4, 5, 6, 7, 8
  • due Thursday, September 12:
    • 9, 10, 11
  • due Thursday, September 19:
    • 12, 13, 14, 15, 16
  • due Thursday, September 26:
    • 17, 18, 19, 20, 21
  • due Tuesday, October 1:
    • 22, 23
  • due Thursday, October 10:
    • 24, 25, 26
  • due Thursday, October 17:
    • 14.6 - , 14.7 - , 14.8 -
  • due Thursday, October 24:
    • 15.1 - , 15.2 - , 15.3 -
  • due Thursday, October 31:
    • 15.4 - , 15.5 - , 15.6 -
  • due Tuesday, November 5:
    • 15.7 - , 15.8 - , 15.9 -
  • due Thursday, November 14:
    • (none)
  • due Thursday, November 21:
    • 15.10 - , 16.1 - , 16.2 -
  • due Tuesday, November 26:
    • 16.3 - , 16.4 - , 16.5 -
  • due Tuesday, December 3:
    • 16.6 - , 16.7 -
  • due Tuesday, December 10:
    • 16.8 - , 16.9 - , 16.10 -
• Exams
  • Thursday, October 3: Exam 1
    • Exam 1 (solutions)
    • Exam 1 covers sections 12.1-12.6, 13.1-13.4, and 14.1-14.3
  • Thursday, November 7: Exam 2
    • Exam 2 (solutions)
    • Exam 2 covers sections 14.4-14.8 and 15.1-15.7
  • Thursday, December 12: Exam 3
    • Exam 3 (solutions)
    • Exam 3 covers sections 15.8-15.10 and 16.1-16.10

Handouts

• Announcements
  • Using Mathematica.pdf
  • Schmidt Award
  • Math Graduate Award
  • Honors Program introduction
  • Tutoring Center services
• Graph Paper
  • Graph Paper is a folder containing a variery of graph paper
  • Rectangular Grids 1 Large Coarse
  • Rectangular Grids 1 Large Medium
  • Rectangular Grids 3 Small
  • Rectangular Grids 6 Small
  • Isometric Grids 1 Large
  • Isometric Grids 3 Small
  • Isometric Grids 6 Small
• Excerpts of Text
  • chap12sec01.pdf
  • chap12sec02.pdf
  • chap12sec03.pdf
  • chap12sec04.pdf
• Formula Sheets
  • Formulas 1
  • Formulas 2
  • Formulas 3
  • Formulas 4
• Additional Exam Practice
  • Useful Vector and Curve Practice Problems.zip
  • Sample Exam Problems.zip
  • Other Exam Problems.zip
  • Multiple Integral Problems.zip
  • Green Gauss Stokes Problems.zip
• Lines, Planes, and Distance
  • Dot and Cross Product Properties and Uses
  • Dot Product Consequences (solution)
  • cross product consequences (solution)
  • Distance or Intersection (solution)
  • More Distance Problems
  • Line and Plane Equations
  • Parallelepiped Surgery
  • Parallelepiped Decomposed Into Six Tetrahedra
• Quadric Surfaces
  • The Quadric Surfaces
• Cylindrical and Spherical Coordinates
  • The Polar Cap
• Calculus Facts
  • How to Differentiate Stuff
  • The Hyperbolic Functions
  • Reduction Formulas
  • Wallis' Formula
  • Center of Mass
• The Frenet Frame
  • Frenet Frame - Theory and Practice
  • The Frenet Frame Derived
  • Frenet Frame Example
• Multivariable Functions
  • Surfing Article
  • Ice Cream Cone
  • Double Integral Boot Camp
• Green's, Gauss', Stokes' Theorems
  • Circle Parameterizations
  • Conservative Fields
  • Green's Theorem (Curl Form)
  • Green's Theorem (Divergence Form)
  • Surface Integral Example
  • Gauss' Theorem
  • Stokes' Theorem

Video

• Topics
  • The Cauchy-Schwarz Inequality
  • The Triangle Inequality
  • The Direction Cosines
  • The Intersection of Two Planes
  • Problem 07 Complicated Intersection
  • Problem 08 Plane Intersects Cylinder
  • Arc Length Parameterization
  • Frenet Frame Movie
  • An Interesting Curve in Space
  • Optimization Problem Comparison
  • all MTH-261 Topics
  • (miscellaneous)
    • 2-2-95, 2-2-119, 2-3-157, 2-3-181, 2-4-220, 2-6-349, 2-7-415

Technology

• Communication
  • Zoom
  • Joining a Zoom Webinar
• Desmos
  • Conic Sections as Degree 2 Polynomial Equations
  • Conic Sections as Traces of Surfaces
  • Quadric Surfaces
  • Projections of Intersecting Cylinders
• Excel
  • partial derivatives
• Mathematica
  • Basic Graphing.nb
  • Lines and Curves in Space.nb
  • Dot and Cross Products.nb
  • A Curve on a Sphere.nb
  • Packing Bowling Ball.nb
  • Intersecting Cylinders.nb
  • frenet_frame_demonstration.nb
  • Frenet Frame Example.nb
  • Frenet Frame Illustration.nb
  • Level Curve and Vertical Trace Demonstration.nb
  • Level Curve and Vertical Trace Demonstration II.nb
  • Level Curves and Surfaces.nb
  • Implicitly Defined Curves and Level Curves.nb
  • Level Surface Example.nb
  • Surfaces Regions Contours.nb
  • 261-21-Problem-FA-24.nb
  • Surfaces Limits and Continuity.nb
  • 261-exercise-04-01-43-alt.nb
  • Implicit Differentiation Tangent Plane.nb
  • Review Problem-13-01-18.nb
  • Review Problem-14-04-24.nb
  • Partial Derivatives and Symmetry.nb
  • Absolute Minimum and Maximum Images.nb
  • 261-exercise-04-07-344.nb
  • Lagrange Multiplier Problem.nb
  • Lagrange Multiplier Example.nb
  • Lagrange Multipliers and Level Curves.nb
  • Density of a Plate.nb
  • 261-exercise-05-03-148.nb
  • Center of Mass Moments of Inertia.nb
  • Integration over Arbitrary Regions.nb
  • 261-exercise-06-02-80-alt-demo
  • Flux through Cone