Math 13: Multivariable Calculus

Spring 2019


  • The latest homework will always appear on top.

  • If you are interested in learning to typeset mathematics here is a list of resources compiled by Rebecca Weber on LaTex

    Homework assignments

  • Late Homework will not be accepted, for this reason we will allow you to drop a lowest score in a homework.
  • Make sure that in your homework you indicate everyone that helped you in the homework or anyone with whom you collaborated.

    WebWork problems: These problems are very important. We will discuss most of them in class. Please be sure that you understand these problems thoroughly as you will be asked to present some of these problems in class.

    Written assignments: These problems will graded in detail and are due once a week on Wednesdays.

    Week 10
    Saturday, June 1:
    • Final Exam 11:30 - 2:30 in Silsby 028
    • We hope you have a great summer!
    Wednesday, May 29:
    • Topic: Final Review
    • WebWork Sec. 17.3 (due tonight at 10PM)
    • Study for the final chapters 15, 16 and 17
    Monday, May 27:
    • Memorial Day! No class.

    Week 9
    Friday, May 24:
    • Topic: The Divergence Theorem
      This theorem relates surface integrals to triple integrals.
    • WebWork Sec. 17.3 (due Wednesday at 10PM)
    • Reading Homework: Read Sect. 17.3 (Due Monday at the beginning of class)
    • Written Homework: Homework Set #9 (not collected )
    Wednesday, May 22:
    • Topic: Stoke's Theorem and Surface Independence
      We discuss surface indepence for curl vector fields.
    • WebWork Sec. 17.2 (due Monday at 10PM)
    • Reading Homework: Read Section 17.3 (due Friday at the beginning of class)
    • Written Homework: Homework Set #9 (not collected)
    Monday, May 20:
    • Topic: Stoke's Theorem
      We generalize Green's Theorem to 3 dimensions
    • WebWork Sec. 17.2 (due Wednesday at 10PM)
    • Reading Homework: Read Section 17.2 (Due Wednesday at the beginning of class)

    Week 8
    Friday, May 17:
    • Topic: Green's Theorem over general regions
      A 2-dimensional special case of Stoke's Theorem.
    • WebWork Sec. 16.4 (due Monday at 10PM)
    • Reading Homework: Read Sect. 17.2 (Due Monday at the beginning of class)
    • Written Homework: Homework Set #8 (due Wed. May 22 at the beginning of class)
    Wednesday, May 15:
    • Topic: Green's Theorem
      Today we study the relationship between line integrals over a simple closed curve C and a double integral over the plane region D bounded by C.
    • WebWork Sec. 16.4 (due Monday at 10PM)
    • Reading Homework: Read Section 17.1 (due Friday at the beginning of class)
    • Written Homework: Homework Set #8 (due Wed. May 22 at the beginning of class)
    Monday, May 13:
    • Topic: Surface Integrals of vector fields
      We will learn about integrating vector fields over surfaces.
    • WebWork Sec. 16.5 (due Wednesday at 10PM)
    • Reading Homework: Read Section 17.1 (Due Wednesday at the beginning of class)

    Week 7
    Friday, May 10:
    • Topic: Surface Integrals of scalar valued functions
      We will learn about integrating over surfaces.
    • WebWork Sec. 16.4 (due Monday at 10PM)
    • Reading Homework: Read Sect. 16.5 (Due Monday at the beginning of class)
    • Written Homework: Homework Set #7 (due Wed. May 15 at the beginning of class)
    Wednesday, May 8:
    • Topic: Parametrized Surfaces
      Today we will learn about how to parametrize a surface
      • Reading Homework: Read Section 16.4 (due Friday at the beginning of class)
    • Written Homework: Homework Set #7 (due Wed. May 15 at the beginning of class)
    Monday, May 6:
    • Topic: Review for Midterm #2 on Wednesday
    • Reading Homework: Review Sections 15.6, 16.1, 16.2 and 16.3

    Week 6
    Friday, May 3:
    • Topic: Line Integrals and Conservative Vector Fields
      The fundamental theorem for conservative vector fields.
    • WebWork Sec. 16.3 (due Monday at 10PM)
    • Reading Homework: Read Sect. 16.4 (Due Monday at the beginning of class)
    • Written Homework: Homework Set #6 (due Wed. May 8 at the beginning of class)
    Wednesday, May 1:
    • Topic: Vector Line Integrals
      These are integrals over curves - Today we will do line integrals of vector fields
    • WebWork Sec. 16.2 (due Friday at 10PM)
      • Reading Homework: Read Section 16.3 (due Friday at the beginning of class)
    • Written Homework: Homework Set #6 (due Wed. May 8 at the beginning of class)
    Monday, April 29:
    • Topic: Scalar Line Integrals
      These are integrals over curves - Today we will do line integrals of scalar valued functions.
    • WebWork Sec. 16.2 (due Wednesday at 10PM)
    • Reading Homework: Read Section 16.2 (due Wednesday at the beginning of class)

    Week 5
    Friday, April 26:
    • Topic: Vector Fields
      Conservative vector fields and the potential function
    • WebWork Sec. 16.1 (due Monday at 10PM)
    • Reading Homework: Read Sect. 16.2 (Due Monday at the beginning of class)
    • Written Homework: Homework Set #5 (due Wed. May 1 at the beginning of class)
    Wednesday, April 24:
    • Topic: Vector Fields and operations on vector fields
      Introduction to vector fields
    • WebWork Sec. 16.1 (due Friday at 10PM)
      • Reading Homework: Read Section 16.1 (due Friday at the beginning of class)
    • Written Homework: Homework Set #5 (due Wed. May 1 at the beginning of class)
    Monday, April 22:
    • Topic: Change of variables for functions of three variables
      We will generalize the change of variables formula for functions of three variables.
    • WebWork Sec. 15.6 (due Wednesday at 10PM)
    • Reading Homework: Read Section 16.1 (due Wednesday at the beginning of class)

    Week 4
    Friday, April 19:
    • Topic: Change of variables
      Today we will continue with change of variables.
    • WebWork Sec. 15.6 (due Monday at 10PM)
    • Reading Homework: Read Sect. 15.6
    • Written Homework: Homework Set #4 (due Wed. April 24 at the beginning of class)
    Wednesday, April 17:
    • Topic: Review for Midterm #1 - Midterm tonight
      We will solve problems in class to prepare for the midterm.
      • Reading Homework: Read Section 15.6 (due Friday at the beginning of class)
    • Written Homework: Homework Set #4 (due Wed. April 24 at the beginning of class)
    Monday, April 15:
    • Topic: Intro Change of variables
      Polar, cylindrical and spherical are special cases of change of variables, in Sec. 15.6 we learn how it is done in general.
    • There won't be WebWork due on Wednesday.
    • Reading Homework: Read Section 15.6 (due Friday at the beginning of class)

    Week 3
    Friday, April 12:
    • Topic: Applications of triple integrals
      Today we will finish applications of double and triple integrals.
    • WebWork Sec. 15.4 (due Monday at 10PM)
    • Reading Homework: Begin reviewing for the exam on Section 15.1-15.5
    • Written Homework: Homework Set #3 (due Wed. April 17 at the beginning of class)
    Wednesday, April 10:
    • Topic: Applications of double and triple integrals
      Today we will discuss physical applications of double and triple integrals.
    • WebWork Sec. 15.4 (due Friday at 10PM)
      • Reading Homework: Read Section 15.5 (due Friday at the beginning of class)
    • Written Homework: Homework Set #3 (due Wed. April 17 at the beginning of class)
    Monday, April 8:
    • Topic: Triple integrals using cylindrical and spherical coordinates
      Today we will learn to use cylindrical and spherical coordinates for evaluating triple integrals.
    • WebWork Sec. 15.4 (due Wednesday at 10PM)
    • Reading Homework: Read Section 15.5 (due Wednesday at the beginning of class)

    Week 2
    Friday, April 5:
    • Topic: Double integrals using polar coordinates
      Today we will learn how to use polar coordinates when evaluating double integrals.
    • WebWork Sec. 15.4 (due Monday at 10PM)
    • Reading Homework: Read Sect. 15.4 (due Mon. April 8 at the beginning of class)
    • Written Homework: Homework Set #2 (due Wed. April 10 at the beginning of class)
    Wednesday, April 3:
    • Topic: Triple integrals over more general regions
      Today we do triple integrals over regions that are more general.
    • WebWork Sec. 15.3 (due Friday at 10PM)
      • Reading Homework: Read Section 15.4 (due Friday at the beginning of class)
    • Written Homework: Homework Set #2 (due Wed. April 10 at the beginning of class)
    Monday, April 1:
    • Topic: Introduction to triple integrals over boxes
      Today we will learn to integrate functions of three variables.
    • WebWork Sec. 15.3 (due Wednesday at 10PM)
    • Reading Homework: Read Section 15.3 (due Wednesday at the beginning of class)

    Week 1
    Friday, March 29:
    • Topic: Integration over more general regions
      Today we will learn how to integrate a multivariable function over regions that are not rectangles.
    • WebWork Sec. 15.2 (due Monday at 10PM)
    • Reading Homework: Read Sect. 15.3 (due Mon. April 1 at the beginning of class)
    • Written Homework: Homework Set #1 (due Wed. April 3 at the beginning of class)
    Wednesday, March 27:
    • Topic: Iterated Integrals
      Today we introduce the idea of integrating a multivariable function over rectangles.
    • WebWork Sec. 15.1 (due Friday at 10PM)
      • Reading Homework: Read Section 15.2 (due Friday at the beginning of class)
    • Written Homework: Homework Set #1 (due Wed. April 3 at the beginning of class)
    Monday, March 25:
    • Topic: Introduction and Review
      Today we will review and discuss the objectives of the course.
    • WebWork Tutorial (due Wednesday at 10PM)
    • Reading Homework: Read Section 15.1 (due Wednesday at the beginning of class)



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