Latest revision as of 16:19, 27 April 2017

Course Information

MATH235: Classical techniques for first and higher order equations and systems of equations. Laplace transforms. Phase plane and stability analysis of non-linear equations and systems. Applications to physics, mechanics, electrical engineering, and environmental sciences.

Class Time : 2:00 - 2:50 PM MWF

Class Location : BBW280

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

TA Information

TA: Danielle Barna

email: dbarna@mymail.mines.edu

Office Hours: Tuesday 4:00 - 5:00 PM

TA : Kate Bubar

email : kbubar@mymail.mines.edu

Office Hours : Tuesday 4:00 - 5:00 PM

TA : Jon Helland

email : jhelland@mines.edu

Office Hours : Thursday 8:00 - 9:00 AM

TA : Liam Pocher

email : lpocher@mymail.mines.edu

Office Hours : Wednesday 5:00 - 6:00 PM

Syllabi

• MATH235S17 Syllabus: Contents include, course policies, important dates, learning objectives, office hours, course content management, grade breakdown

Course Calendar

Here you will find a calendar for our course.

Course Content

The narrative of the course will be managed through lecture and the course evernote, MATH235-S17 Evernote. On this site you will not only find posts about course content but also the following:

• Course Text: Through the school's SpringerLink have access to the following text, David Logan, A First Course in Differential Equations. I have started annotating this book to include my thoughts, extra derivations if needed and suggested problems from the associated sections. Here is the link to the library holding, those on campus should be able to go straight to the pdf, while those off campus will have to VPN in. Here you will find my annotations to the text.

Evernote

Evernote gives a nice way to have a shareable/searchable system with simple text markup that can be made available across different platforms. Without demanding all users implement their own evernote profile at the premium level, a shared notebook can get a little cluttered. So, the following is a listing of the major features of the structure:

The course notes(abbreviated)

• 01. First-Order Solution Techniques
• 02. Taxonomy and Expectations
• 03. Mathematical Modeling With Scalar ODE
• 04. The Geometry of Differential Equations (first-order)
• 05. Bifurcations, Critical Slowing Down and Hysteresis

• 06. Second Order Linear Theory

• 07. Power-Series Solution Techniques - Part I

• 08. Power Series Solution Techniques - Part II (Frobenius Technique) --- To be created later.

• 09. Laplace Transforms

• 10. Linear Systems of ODE --- Comming Soon

• 11. Nonlinear Systems of Autonomous ODE

The course deliverables

• D0. Trigonometric Functions
• D1. Population Modeling
• D2. Dynamical Systems (Strogatz Reading)
• D3. Mathematical modeling and critical slowing down (soft-science application)
• D4. First-Order Recap
• D5. Second-Order Theory
• D6. Second Order Models
• D7. Linear Algebra
• D8. Systems of Autonomous ODE

The quizzes

• Q1. Solution techniques for first-order ODE (Part 1)
• Q2. Separation of variables, autonomous equations and phase lines
• Q3. Phase lines and bifurcations
• Q4. First-order solution techniques (Part 2)
• Q5. Solution techniques (Part 1)
• Q6. Solution techniques (Part 2)
• Q7. Solution techniques (Part 3)
• Q8. Review of the old quizzes

The examinations

• Midterm
• Final Exam

The projects

• P1. First-Order Modeling (Bead on a Rotating Hoop in a Viscous Fluid)

Lecture Pictures

It's pretty simple to record, and keep somewhat concurrent, a record of the lecture pictures. It would be great if video capture was so simple. Until those things get worked out, the following link will give you access to a dropbox folder where the pictures are shared.

50 Problems

• Here you will find a list of 50 problems that you will be expected to solve by the end of the semester. Here is a link to the youtube playlist of the solutions to a majority of these problems. Here is a solution file worked up by a Petroleum Engineer who graduated in 2017. I've not checked all of the problems, but her organization and thought process is crystal clear and was responsible for us redoing a couple of videos. So, they should be pretty solid.

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)

External materials

• Method of Undetermined Coefficients - 1st Order: Two examples
• Method of Undetermined Coefficients - 1st Order: Three examples
• Method of Undetermined Coefficients - 1st Order: Three examples