MATH224 Calculus III w/ Honors

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Contents

Course Information

Course Description

Early introduction of vectors, linear algebra, multivariable calculus. Vector fields, line and surface integrals. Prerequisites: C or better in MATH112 or MATH122.

Student Learning Outcomes

At the conclusion of the class students will be able to:

  1. identify the differences between single and multivariate differential/integral calculus and when applicable explain the consequences.
  2. interpret the operators of multivariate differential/integral calculus and use them to solve problems associated with summation, extreme values, constrained optimization and instantaneous rates of change.
  3. list the operators of vector analysis, apply them to solve problems related to the fundamental theorem of calculus for vector--valued multivariate function and justify their combination with physical interpretations.

Italicized words correspond to verbs associated with the cognitive domain (knowledge-based) portion of Bloom's Taxonomy.

Instructor Information

Instructor : Scott Strong

Office : Stratton Hall 205

Office Phone : 303.384.2446

email : sstrong@mines.edu

Office Hours: MWF @ 4:00pm in SH205, R @ 3:00pm in SH205 and R @ 4:00pm by appointment (Online Booking)

Digital Resources: Blog, Evernote Notebook



Instructor : Gus Greivel

Office : Stratton Hall 202

Office Phone : 303.273.3840

email : ggreivel@mines.edu

Office Hours: MWF @ 9:00-10:50am, R @ 8:00-9:50am

TA Information

TA : Jon Helland

email : jhelland@mines.edu

Office Hours : R @ 4:00-5:00pm, SH201


TA : Clay Kramp

email : ckramp@mines.edu

Office Hours : R @ 4:00-5:00pm, SH201


TA : Kate Bubar

email : kbubar@mines.edu

Office Hours : by appointment


TA : Liam Pocher

email : lpocher@mines.edu

Office Hours : MW @ 4:00-6:00pm, SH201

Syllabi

Textbook Information

  • Calculus Early Transcendentals, 6th edition, Steward Amazon Link(buy used for cheap)

Mathematica

Course Content

100 problems from multivariate calculus

The following link will take you to a pdf that contains between 80 and 100 problems associated with calculus in several variables.

  If you are doing additional problems from other textbooks and would 
  like to give other students access to your work, then feel free 
  to upload them to us [ here](jotform to be created).

Studio Materials

Challenge Problem Submission Area

This link will take you to the jotform used to submit your challange problem attempts.

Studio #0

  * Wolfram's Handson Mathematica Tutorial 
    (Level: Novice, Goal: Up through "Basic Graphics)"
  * MATH224 Specific Tutorial: Function instantiation, plot and manipulate commands 
    (Level: Novice to Intermediate, Goal: Up through 10:08) 
     * Here is the associated Mathematica notebook, for you to follow along.
     * Do not worry about the second part yet, i.e. contour plot, solve command and graphics options. 
       You can take a look if you want. The degree of difficulty increases and if it feels stressful 
       then stop. We will fold those commands in over time.   
     * Liam, the maker of the video was told to speak slowly enough 
       so that the video could be played at double-speed. Feel free to do this. 
     * Please take notes as you go through the video. We will ask you about insights 
       you had along the way and compile these for use in future experiences.

Studio #1

This week we will be visualizing conics and quadric surface via Mathematica. We will also form our working groups. There are also three deliverables, Mathematica notebook and hand calculations associated with the Studio assignment, an individual submission asking about Mathematica and Mindset and an individual team assignment.


Studio #2

This week we will be leveraging Mathematica to help us understand the behavior of surfaces with respect to the apparatus of limits. Groups have been formed and each has been associated with an Undergraduate TA mentor who will introduce themselves to your group today. There will be two deliverables, hand calculations associated with the Studio assignment with Mathematica corroboration, an individual submission asking about Mathematica and Learning Preferences.

Studio #3

This week will be less about Mathematica and more about concepts/calculations related to linear approximation and propagation of error.

The challenge problem is about the multivariate Taylor series and asks students to work with the Mathematica to plot surfaces, points, tangent planes and quadric surface approximations. In total, there are five challenge attempts. It is recommended that all groups attempt CP #1 and CP#4. Those interested in mathematical notation and linear algebra should also attempt CP #3. Mathematica junkies should do CP#2 and CP#5.

The individual submission asks you to look at the Tuckman's stages of group development, Belbin roles and, with these topics in mind, reflect on how your team is functioning.

Returned Materials

  • Studio #1 grades are up. The feedback can be found here. The average grade was 90%, which is derived from three separate assessments, organization(worth 25%), communication(25%) and correctness(50%).
  • The data from HW#0, which asked you for music and movie suggestions, can be found here(xls). We made a wordcloud for movies and [ music].

Studio #4

Returned Materials

  • Studio #2 grades are up. The feedback can be found here. The average grade was 95%, which is derived from three separate assessments, organization(worth 25%), communication(25%) and correctness(50%).
  • The data from studio #1 has been compiled. Here you will find responses to the questions, "What might you like to see in future studios?", "What do you know about Mathematica that you think other students might not know but would want to know?" The statistics associated with student attitudes/perceptions of Mathematica are also included.


Studio #5


Returned Materials

  • Studio #3 grades are up. The feedback can be found here. The average grade was 94%, which is derived from three separate assessments, organization(worth 25%), communication(25%) and correctness(50%).
  • The data from studio #2 has been compiled. Here you will find responses to the question, What, if any, topics are causing you difficulty at this time? What do you think is the root of the difficulty?" The statistics associated with student attitudes/perceptions of Mathematica are also included.Learning preferences data was, in some sense, corrupted. We ask that you re-submit these data this week.

Studio #6

This is a free studio where you can ask questions about previous studios, challenge problems, the 100 questions and....

Studio #7

This was the midterm exam.

Studio #8

This week we begin our work on multiple integration. We have a Mathematica notebook that can be used to help visualize the domain of integration as well as the integral calculation.



Returned Materials

The midterm exam will be returned in Studio.

 Midterm results
  Average = 87.9%
  Median = 90.0%
  A's=29(55%)
  B's=18(34%)
  C's=3 (5.6%)
  D's=2 (3.8%)
  F's=1 (1.89%)
  • Studio #4 grades are up. The feedback can be found here. The average grade was 93.5%, which is derived from three separate assessments, organization(worth 25%), communication(25%) and correctness(50%).
  • Studio #5 grades are up. The feedback can be found here. The average grade was 91.0%, which is derived from three separate assessments, organization(worth 25%), communication(25%) and correctness(50%).


Studio #9 Materials

Returned Materials

None this week. Upon submission studio #8 will be returned next week.

Studio #10 Materials

Returned Materials

  • Studio #8 grades are up. The feedback can be found here. The average grade was 95.6%, which is derived from three separate assessments, organization(worth 25%), communication(25%) and correctness(50%).

Studio #11 Materials

Studio #12 Materials

This week we consider conservative vector fields and surface integrals over scalar fields.


Returned Materials

  • Studio #9 and #10 grades are up. The feedback can be found here. The average grade was 94% and 96.7%, which is derived from three separate assessments, organization(worth 25%), communication(25%) and correctness(50%).

Studio #13 Materials

Supplemental Materials

MATH224 - Fall 2014 Materials

Linear Algebra

* Linear Algebra Notes
* Linear Algebra Problems
* Linear Algebra Slides
* Essence of Linear Algebra (youtube playlist)
* Linear Algebra for Planar Linear Systems of ODE (Used for MATH235 but applicable here)


Quadric Surfaces

Examples of Student Work

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