I have been using Mathematica in my dynamical systems class for a few years. I don’t have a systematic curriculum related to it, though, and need to develop clearer computational learning goals, as well as a pathway for students to develop computational skills.<\/p>\n
Ideally, by the end of the semester, students would be able to do an analysis of a one-parameter dynamical system with the aid of computational tools. They would find fixed points, identify stability, create phase portraits and bifurcation diagrams, and perhaps create stability diagrams. I would expect them to be able to identify global bifurcations, as well. For limit cycles, I need to make a decision on my expectations. I suppose I would like for students to be able to create a curve of initial conditions, use “Events” in Mathematica of Matlab integration, and identify the stability \/ existence of a limit cycle in a 2d system.<\/p>\n
At the moment I’ve been relying on Mathematica and some students have chosen to use Matlab. I would like to move towards Python. Currently the dynamical systems course is the only place students work with Mathematica, while Python is an option across a range of courses.<\/p>\n
This means I need to learn how to set up Python for a class. At the moment I’m taking a look at Koehler and Kim, 2018 for some guidance on this. They go in the direction of Jupyter Notebooks so I will explore that for now.<\/p>\n
1) Install the Anaconda application on my Mac.
\n2) Open the Anaconda Navigator: it has seven options when I first open it (Jupyter lab, Jupyter notebook, Qt console, Spyder, Glueviz, Orange 3, RStudio). The first four are already installed and I have the option to Launch them. For the other three, I have the option to install them. I’ll launch Jupyter notebook.<\/p>\n
Koehler and Kim 2018: Interactive Classrooms with Jupyter and Python. The Mathematics Teacher. Vol. 111, No. 4 (January\/February 2018), pp. 304-308 (5 pages)<\/p>\n","protected":false},"excerpt":{"rendered":"
I have been using Mathematica in my dynamical systems class for a few years. I don’t have a systematic curriculum related to it, though, and need to develop clearer computational learning goals, as well as a pathway for students to develop computational skills. Ideally, by the end of the semester, students would be able to […]<\/p>\n","protected":false},"author":8032,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[157888,157887],"tags":[],"class_list":["post-222","post","type-post","status-publish","format-standard","hentry","category-dynamical-systems","category-learning-and-teaching"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7E5LF-3A","jetpack-related-posts":[{"id":118,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2019\/06\/10\/dynamical-systems-strogatz-chapter-2\/","url_meta":{"origin":222,"position":0},"title":"Dynamical Systems: Strogatz Chapter 2","author":"siams","date":"10 June 2019","format":false,"excerpt":"Following this text, students study 1d, then 2d, then 3d flows. \u00a0In 1d, we find stability, construct phase portraits, and in chapter 3, make bifurcation diagrams. \u00a0We loop back to these topics with more complexity in 2d. \u00a0This creates natural \"spacing\". A few notes on spacing: Spacing improves induction\/generalization from\u2026","rel":"","context":"In "Dynamical Systems"","block_context":{"text":"Dynamical Systems","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/dynamical-systems\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":126,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2019\/06\/11\/dynamical-systems-strogatz-chapter-3\/","url_meta":{"origin":222,"position":1},"title":"Dynamical Systems: Strogatz Chapter 3","author":"siams","date":"11 June 2019","format":false,"excerpt":"\u00a0 Section 3.0: Introduction I need to help students distinguish between parameters and variables. The beam bending example is ok, but the intuition isn't so clear. \u00a0If I back up on the load does the beam straighten (is this a supercritical pitchfork)? It would be nice to introduce an intuitive\u2026","rel":"","context":"In "Dynamical Systems"","block_context":{"text":"Dynamical Systems","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/dynamical-systems\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":112,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2019\/06\/10\/dynamical-systems-math-21b-differential-equations-background\/","url_meta":{"origin":222,"position":2},"title":"Dynamical Systems: Math 21b differential equations background","author":"siams","date":"10 June 2019","format":false,"excerpt":"For students who have taken Math 1b, AM\/Math 21a, Math 21b, there was 6-7 week of differential equations background (11 classes in Math 1b + 9 classes in 21b). \u00a0See my prior post for the Math 1b diff eq content that is relevant to Dynamical Systems. Student diff eq background\u2026","rel":"","context":"In "Dynamical Systems"","block_context":{"text":"Dynamical Systems","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/dynamical-systems\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":108,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2019\/06\/10\/dynamical-systems-math-1b-differential-equations-background\/","url_meta":{"origin":222,"position":3},"title":"Dynamical systems: Math 1b differential equations background.","author":"siams","date":"10 June 2019","format":false,"excerpt":"I have been using the Strogatz textbook for teaching dynamical systems. \u00a0The course has multivariable calculus and linear algebra prerequisites. \u00a0Students might take the prerequisite courses different places. \u00a0For students who have taken Math 1b, AM\/Math 21a, Math 21b, there was 6-7 week of differential equations background (11 classes in\u2026","rel":"","context":"In "Dynamical Systems"","block_context":{"text":"Dynamical Systems","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/dynamical-systems\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":132,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2019\/06\/12\/dynamical-systems-strogatz-chapter-5\/","url_meta":{"origin":222,"position":4},"title":"Dynamical Systems: Strogatz Chapter 5","author":"siams","date":"12 June 2019","format":false,"excerpt":"This chapter is mainly review of topics from prerequisite courses. \u00a0Steve does introduce the (Delta, tau)-plane for classifying fixed points of linear systems. \u00a0This chapter is a return to linear systems. There isn't a \"summary\" section in between Chapter 4 and Chapter 5. \u00a0That is probably a worthwhile spot to\u2026","rel":"","context":"In "Dynamical Systems"","block_context":{"text":"Dynamical Systems","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/dynamical-systems\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":130,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2019\/06\/12\/dynamical-systems-strogatz-chapter-4\/","url_meta":{"origin":222,"position":5},"title":"Dynamical Systems: Strogatz Chapter 4","author":"siams","date":"12 June 2019","format":false,"excerpt":"This chapter is not included in Steve's youtube videos. 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