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

Instructor 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

• Scott's Syllabus

• Gus's Syllabus

• Class Schedule

Textbook Information

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

Mathematica

• CSM Mathematica Site License and Installation Information
• Wolfram's Handson Mathematica Tutorial

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.

MATH224 Problem List

Chronological listing of hyperlinks

Studio Materials

Challenge Problem Submission Area

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

Studio #0

• Jotform Pre-Quiz Survey
• Mathematica Video Tutorials (Total Run Time: Approx. 60 minutes)

  * 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 #1: Conics and Quadrics
• Mathematica Notebook - Conics and Quadric Surfaces
• Jotform submission for Studio #1: Submit at the start of Studio on 9/8/2016
• Mindsets in MATH224 and Beyond (pdf) and Mindsets in MATH224 and Beyond (docx)
• Jotform submission for individuals: Submit any time
• Jotform submission for Initial Team Assignment (Due: 9/7/2016 by 11:59pm)

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 #2: Limits and Partial Derivatives
• Studio #2: Mathematica tutorial on differentiation
• Studio #2(challenge problem): Derivatives and differential equations notebook
• Studio #2: Jotform submission (group)
• Studio #2: Jotform submission (individual)

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.

• Studio #3: Linearizations and Propagation of Error
• Mathematica notebook for plotting linear approximations to surfaces (challenge work)
• Mathematica notebook for plotting curves on surfaces (challenge work)
• [ Jotform submission (group)]
• [ Jotform submission (individual)]

Returned Materials

• Studio #2 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].

Supplemental Materials

MATH224 - Fall 2014 Materials

• Summary of results from single-variable calculus
• Homework 1 - Conics and Quadric Surfaces
• Homework 2 - Limits and Partial Derivatives

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)

• Matrix Transformations - Draft

Quadric Surfaces

• Quadric Surface Applets

Examples of Student Work

• Example of great discussion and use of whitespace/organization
• Good example of leaving space for future note taking
• Good example of clear organization and code breakdown