Week 2
Getting Started: Modelling and Linear Models
Business
The start of the week email. No need to reread it if you received it. It's just linked here in case anyone accidentally deleted it (it's happened before 🥺). Definitely let me know if you didn't receive it though so we can figure out why not.
Mathematical Modelling
- Mathematical Modelling: The Process 📹 Pencast 3:09|📘 PDF
- Problem → Model → Manipulation → Solution → Interpretation
- Warm-up Problems 📹 Pencast 6:45|📘 PDF
- A couple of artificial puzzle problems.
- Pet Biscuits 📹 Pencast 11:17|📘 PDF
- Another puzzle problem, but that will turn out to be "just like" a real-world problem.
- Sony's Secret 📹 Pencast 8:11|📘 PDF
- The real-world problem that is "just like" the puzzle problem above. Model forms are powerful because they are reusable in many domains.
- Mathematics is the language of patterns 📹 Pencast 19:53|📘 PDF
- One definition of mathematics is "the language humans have created for describing patterns". Here we go looking for patterns in lists of numbers. And meet Carl Friedrich Gauss as a boy.
Linear Models
- Examples of linear models 📄 Slide Show
- You will probably encounter far more linear models than any other kind. They are everywhere! Here are some examples, with a bit of commentary.
- Four Forms of Linear Models 📹 Pencast 14:41|📘 PDF
- You will encounter linear relationships described using 1) the English language (watch for "for every"), 2) tables of number pairs, 3) graphs, and 4) equations. Here's a brief review of these four forms and how to translate between them.
- Review: Solving Systems of Equations 📹 Pencast 8:40|📘 PDF
- Two methods: Substitution and Elimination. Most students have more experience with substitution, but elimination will generalize to working with matrices next week...
- Existence and Uniqueness of Solutions (in 2D) 📹 Pencast 15:40|📘 PDF
- Two big questions: 1) Can a system have more than one solution? 2) Can a system have no solutions?
- Solving 3 equations in 3 unknowns 📹 Pencast 9:02|📘 PDF
- Most students have more experience with substitution, but elimination will generalize to working with
matrices next
week, so we solve this system using elimination.
Three equations in three unknowns is as many as one ever wants to do by hand. For this size, and definitely for larger systems, a computer is your friend. - Existence and Uniqueness of Solutions in 3D 📘 PDF
Exercise Sets
Exercise Set 2 Part 1: Problems and Solutions. Due by 4 pm next Monday (January 18).
Exercise Set 2 Part 2: Problems and Solutions Due by 4 pm next Monday (January 18).
Assignment
The first assignment is posted. Due by 4 pm next Friday (January 22).