Lesson 15: Applications of Optimization

Preview

Here's the on-ramp for this lesson.


What Will We Learn?

  • In this lesson we'll run through various examples of optimizing functions of real-world interest. The applications we'll discuss span physiology, engineering, economics, game theory, and more. Throughout we'll also practice our mathematical modeling skills. Because this lesson blends both the theory of optimization and mathematical modeling, it tends to be the most difficult lesson in a calculus course. But that's okay. With enough practice, diligence, and communication with me and your peers, you will succeed. I am 100% confident of that.


Why Do We Need to Learn This?

  • While we've discussed plenty of applications in the first 14 lessons in this course, this particular lesson illustrates the true power of calculus. Optimization is a topic that shows up not only in mathematics but also all across the sciences and social sciences -- both living and non-living things and processes are almost constantly acting to optimize their results. In addition, this lesson solidifies our mathematical modeling skills. That itself is valuable, separate from the optimization context, because mathematical modeling is a skill that comes in handy in daily life, careers, and yes, in follow-up math and science/social science courses.

Review

Learn

The lesson notes below contain a learning plan with three stages -- Learn, Reflect, and Practice -- and guidance for what to do within each stage. Some tips for you as you work through this resource, and those that it points to:

  • I recommend using Cornell Notes (or a modification of it; see this video starting at the 1:05 mark) to take notes on the lesson and the videos. This note-taking method balances detail with big-picture thinking to help you summarize and retain what you are learning. See this other video for additional note-taking techniques you might want to experiment with.

Lesson Notes

Lesson 15.pdf

Video 1 (Example 4.23)

Video 2 (Example 4.24)

Reflect

If you are currently enrolled in this course with me, submit the written reflections Google Form I have emailed you after working through the lesson notes and videos. Some tips:

  • Submit substantive, but concise, answers to each question; you will be doing the future you a big favor by taking time now to accurately and succinctly summarize what you have learned from the lesson.

  • Send yourself a copy of your reflections; they will come in handy later when you start preparing for quizzes and other assessments.

If you are not currently enrolled in this course with me, those written reflections ask three reflective questions designed to help you retain what you've learned and pinpoint any remaining areas of confusion. Those questions are:

  • Please summarize the main mathematical takeaways from the lesson notes.

  • What was the most interesting part of what you learned, and why?

  • What, if anything, do you still find confusing?

Practice

Work through the practice problems suggested below to see how much of this lesson you've understood.

Lesson 15 PP.pdf