# MATH224 Calculus III w/ Honors

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## Course Information## Course DescriptionEarly introduction of vectors, linear algebra, multivariable calculus. Vector fields, line and surface integrals. Prerequisites: C or better in MATH112 or MATH122. ## Student Learning OutcomesAt the conclusion of the class students will be able to: -
*identify*the differences between single and multivariate differential/integral calculus and when applicable*explain*the consequences. -
*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. -
*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 InformationInstructor : 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
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 InformationTA : Jon Helland email : jhelland@mines.edu Office Hours : R @ 4:00-5:00pm, SH201
email : ckramp@mines.edu Office Hours : R @ 4:00-5:00pm, SH201
email : kbubar@mines.edu Office Hours : by appointment
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 calculusThe 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 AreaThis 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 ## Studio #1This week we will be visualizing conics and quadric surface via Mathematica. We will also form our working groups. There are also
- 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 #2This 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 - 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 #3This 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 #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- Studio #4: Partial Derivatives, Directional Derivatives and the Mulivariate Chain Rule and the 2nd Derivatives Test)
- Mathematica notebook for plotting/testing critical points
- Mathematica notebook for finding/plotting/testing critical points
- Blog post with tutorials for Show, Solve and NDSolve commands
- Jotform submission (group)
- Jotform submission (individual)
## 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- Studio#5: Lagrange Multipliers
- Mathematica notebook for plotting surfaces with constraint curves and LM points
- More complicated Mathematica notebook that seeks to automate the process
- Jotform submission (group)
## 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 #6This is a free studio where you can ask questions about previous studios, challenge problems, the 100 questions and.... ## Studio #7This was the midterm exam. ## Studio #8This 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.
- Studio#8: Multiple Integration
- Mathematica notebook for plotting domains of integration
- Hand calculations associated with Mathematica notebook
- Jotform submission (group)
## Returned MaterialsThe 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 MaterialsNone 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#11: Line Integrals over vector and scalar fields
- 11a.LineIntegralOverScalarFields.nb
- 11b.LineIntegralOverVectorFields.nb
- Jotform submission (group)
## Studio #12 MaterialsThis week we consider conservative vector fields and surface integrals over scalar fields. - Studio#12: Conservative fields and surface integrals over scalar fields
- 12.SurfaceIntegralOverScalarFields.nb
- Jotform submission (group)
## 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- Studio#13: Surface integrals over vector fields and Stokes' theorem
- 13.SurfaceIntegralOverVectorFields.nb
- Jotform submission (group)
## Studio #14 Materials## Returned Materials- Studio #11 and #12 grades are up. The feedback can be found here. The average grade was 95.7% and 96.8%, which is derived from three separate assessments, organization(worth 25%), communication(25%) and correctness(50%).
- The projects are graded and can be found here. The average grade was 88.58% which is derived from three separate assessments, organization(worth 25%), communication(25%) and correctness(50%).
## Course information## 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
- Line Integration, notes and problems
- Surface integration, notes and problems
- Vector Calculus Formulae
## 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 |