Kelly MacArthur

Assistant Chair
Instructor Lecturer

Office: JWB 218
Email: macarthur@math.utah.edu

University of Utah
Department of Mathematics
155 S. 1400 E. JWB 233
Salt Lake City, UT
84112-0090 USA

Math2210 Calculus 3
Spring, 2015





Class Notes



Class Schedule/Information

  • Calculus 3 Lecture Videos (Note: All videos listed below by name refer to videos on this link.)

      Week 1 (January 12-16)

    • For Monday's class: watch 1 Parametric Equations lecture video (10.4)
    • For Wednesday's class: watch 2A & 2B Cartesian Coordinates in 3-space lecture videos (11.1)
    • For Friday's class: watch 3A & 3B Vectors lecture video (11.2)

      Week 2 (January 19-23)

    • For Monday's class: relax, Monday is a holiday!
    • For Wednesday's class: watch 4A & 4B Dot Product & 4C Planes lecture videos (11.3)
    • For Friday's class: watch 5A & 5B The Cross Product lecture videos (11.4)

      Week 3 (January 26-30)

    • For Monday's class: watch 6 Vector-valued Functions, Curvilinear Motion lecture video (11.5)
    • For Wednesday's class: make sure you understand sections 11.3-11.5 (we'll do more practice for these sections)
    • For Friday's class: watch 7 Lines and Tangent Lines in 3-Space lecture video (11.6)

      Week 4 (February 2-6)

    • For Monday's class: watch 8 Surfaces in 3-Space and 9A Spherical and Cylindrical Coordinates lecture videos (11.8, 11.9)
    • For Wednesday's class: be prepared to ask questions as review for first midterm.
    • For Friday's class: be prepared to take the Midterm 1.

      Week 5 (February 9-13)

    • For Monday's class: watch 9B Spherical and Cylindrical Coordinates and 10 Functions of Two or More Variables lecture video (11.9, 12.1)
    • For Wednesday's class: watch 11A & B Partial Derivatives lecture videos (12.2)
    • For Friday's class: watch 12A Limits and 12B Continuity lecture videos (12.3)

      Week 6 (February 16-20)

    • For Monday's class: relax, Monday is a holiday!
    • For Wednesday's class: watch 13 Differentiability & Gradients lecture video (12.4)
    • For Friday's class: watch 14 Directional Derivatives lecture videos (12.5)

      Week 7 (February 23-27)

    • For Monday's class:watch 15 Chain Rules lecture video (12.6)
    • For Wednesday's class: watch 16A & B Tangent PLanes and Approximations lecture videos (12.7)
    • For Friday's class: watch 17A & B Maxima and Minima lecture videos (12.8)

      Week 8 (March 2-6)

    • For Monday's class: we'll finish covering sections 12.7 & 12.8
    • For Wednesday's class: be prepared to ask questions as review for first midterm.
    • For Friday's class: be prepared to take the Midterm 2.

      Week 9 (March 9-13)

    • For Monday's class: watch 18A & B Lagrange Multipliers lecture videos (12.9)
    • For Wednesday's class: watch 19A Double Integrals over Rectangles & Iterated Integrals lecture video (13.1)
    • For Friday's class: watch 19B Double Integrals over Rectangles & Iterated Integrals lecture video (13.2)

      Week 10: March 16-20 is Spring Break--there is NO school!!


      Week 11 (March 23-27)

    • For Monday's class:watch 20 Double Integrals over Non-Rectangular Regions lecture video (13.3)
    • For Wednesday's class: watch 21 Double Integrals in Polar Coordinates lecture video (13.4)
    • For Friday's class: watch 22A & B Surface Area lecture videos (13.6)

      Week 12 (March 30-April 3)

    • For Monday's class: watch 23 Triple Integrals in Cartesian Coordinates lecture video (13.7)
    • For Wednesday's class: watch 24 Triple Integrals in Cylindrical and Spherical Coordinates lecture video (13.8)
    • For Friday's class: watch 25 The Jacobian lecture video (13.9)

      Week 13 (April 6-10)

    • For Monday's class: watch 26 Vector Fields lecture video (14.1)
    • For Wednesday's class: be prepared to ask questions as review for first midterm.
    • For Friday's class: be prepared to take the Midterm 3.

      Week 14 (April 13-17)

    • For Monday's class:watch 27A & B Line Integrals and Work lecture videos (14.2)
    • For Wednesday's class: watch 28 Independence of Path lecture video (14.3)
    • For Friday's class: watch 28 Independence of Path lecture video (14.3)

      Week 15 (April 20-24)

    • For Monday's class: watch 29 Green's Theorem in the Plane lecture video (14.4)
    • For Wednesday's class: watch 30 Surface Integrals lecture video (14.5)
    • For Friday's class: watch 31 Gauss's Divergence Theorem lecture video (14.6)

      Week 16 (April 27-May 1)

    • For Monday's class: watch 32 Stokes' Theorem lecture video (14.7)
    • Wednesday: Final Review, 9:30-11:00 a.m.
    • Thursday: Final Exam, 7:00 - 10:00 a.m. (starting an hour early to give you additional time)



    Extra Problems/Reference materials



    Exam Reviews

    • Midterm 1 Review: (covers sections 10.4, 11.1-11.6, 11.8)
      Note: For the exam, you may bring one 8.5x11 inch sheet of paper of notes (front and back). No electronics allowed during the exam.

    • Midterm 1 Review Book Assignment

    • Here is another Calc 3 exam (from a different instructor)
      On this exam, do problems #1abde, 2, 3, 4a, 5 for additional practice.

    • Yet another set of exams and suggested problems to do. Test 1 and Test 2 do problems #1-3, and 5 on each of them.


    • Midterm 2 Review: (covers sections 11.9, 12.1-12.8)
      Note: For the exam, you may bring one 8.5x11 inch sheet of paper of notes (front and back). No electronics allowed during the exam.

    • Midterm 2 Review Book Assignment

    • Here is another Calc 3 exam (from a different instructor)
      On this exam, do problems #1-4 for additional practice.

      And a set of quizzes from the same teacher that have some good practice questions:
      Quiz 4, Quiz 5, Quiz 6, Quiz 7

    • Yet another exam to do. Exam and Key


    • Midterm 3 Review: (covers sections 12.9, 13.1-13.4, and 13.6-13.9)
      Note: For the exam, you may bring one 8.5x11 inch sheet of paper of notes (front and back). No electronics allowed during the exam.

    • Midterm 1 Review Book Assignment

    • Here is another Calc 3 exam (from a different instructor)
      On this exam, do problems #1, 2 (parts 1 and 2), and 4ab for additional practice.
      Also do #3b on this exam.

    • And a set of quizzes from the same teacher that have some good practice questions:
      Quiz 7 (do number 1),Quiz 8, Quiz 9 (do problems 1 and 2)

    • Yet another set of exams and suggested problems to do. Test 2 (do problems 1, 2, 3ab, 4)


    • Final Review: (covers everything we've covered in class this semester)
      Note: For the exam, you may bring one 8.5x11 inch sheet of paper of notes (front and back). No electronics allowed during the exam.

    • Final Review Assignment

    • Extra Final Review Problems (read through the Final Review Assignment to make sense of this link)

    • Extra Final Review Answers (to Extra Final Review Problems that were assigned)

    • Here is another Calc 3 Final Exam (From a different instructor) and the Key