MATH 307F: Introduction to Differential Equations

Instructor: David Clancy

Email address: djclancy@uw.edu

Office Hours: I’ll have two hours (Thursdays 9am-11am Seattle time) of in-person office hours each week, and I’ll record solutions to several homework questions each week. The solutions will be more-or-less step-by-step solutions.

Office Hours Location: There will be a zoom link posted on Canvas (class restricted link).

Useful External Resources (included roughly in the order they are used in class)

• Slope field plotter: https://homepages.bluffton.edu/~nesterd/apps/slopefields.html
• The Euler’s method notebook that I used in class. (I think mostly useful for the function called Euler in the code). here
• Paul’s math notes for autonomous differential equations. here
• Paul’s math notes for partial fractions: here
• Desmos graphing tool for damped harmonic oscillators: here
  • Can be used to visualize how changing various physical properties of the graph (e.g. damping constant, mass, forcing frequency) affects the behaviour of the solution.

    Calendar

This course is just during the Summer B term which lasts July 23, 2020 - August 21, 2020. It is just over 4 weeks.

Important Note: Some of the references to certain weeks in the lecture videos will probably not apply. The videos were recorded during Spring 2020 and include 22 lectures. Since there are only 13 lectures, most of the “class” days include two lectures.

Week	Pre-recorded Lecture Videos	Topics and Textbook Sections	Additional Material
Week 1 Friday July 24	Modelling Direction Fields. YouTube Panopto Euler’s Method and Separable ODEs (part 1) YouTube Panopto	Prerequisite Skills Basic Modelling and Solutions Euler’s Method Separable ODEs Sections 1.1, 1.2, 2.7	Some notes for the recorded videos: here
Week 2 Monday July 27	Euler’s Method and Separable ODEs (part 2) YouTube Panopto Newton’s Laws and Freefalling Objects YouTube Panopto	Euler’s Method Separable ODEs Linear First Order Sections: 2.7, 2.2, 2.1	Some notes for the recorded videos: video 1 video 2
Week 2 Wednesday July 29	Free Falling Objects and Separable ODEs YouTube Panopto Linear First Order Differential Equations YouTube Panopto	Linear First Order ODEs Section: 2.1	Some notes for the recorded videos: video 1 video 2
Week 2 Friday July 31	Linear First Order (cont.) YouTube Panopto Mixing YouTube Panopto	Modeling with First Order ODEs Sections: 2.3, 2.5	Some notes for the recorded videos: video 1 video 2
Week 3 Monday August 3	Logistic Growth Problems YouTube Panopto Second Order Differential Equations YouTube Panopto	Population Dynamics Second Order ODEs Sections: 2.5, 3.1	Some notes for the recorded videos: video 1 video 2 Notes on complex numbers
Week 3 Wednesday August 5	Second Order Differential Equations (cont.) YouTube Panopto Factoring Differential Operators YouTube Panopto	Roots and Second Order ODEs Sections: 3.1, 3.3, 3.4	Some notes for the recorded videos: here
Week 3 Friday August 7	Midterm Exam	Midterm Topics (TBA)
Week 4 Monday August 10	Method of Undetermined Coefficients YouTube Panopto Harmonic Oscillator YouTube Panopto	Method of Undetermined Coefficients Harmonic Oscillators Sections: 3.5, 3.7	Some notes for the recorded videos: video 1
Week 4 Wednesday August 12	Damped Harmonic Oscillator YouTube Panopto Harmonic Oscillators with Forced Vibrations YouTube Panopto	Harmonic Oscillators Forcing Sections: 3.7, 3.8	Some notes for the recorded videos: video 1 video 2 video 2
Week 4 Friday August 14	Forced Vibrations YouTube Panopto Correction YouTube Panopoto Forced Vibrations and Laplace Transforms YouTube Panopto	Forcing Laplace Transforms Sections: 3.8, 6.1	Some notes for the recorded videos: video 1 video 2
Week 5 Monday August 17	Partial Fractions Review YouTube Panopto Step/Heaviside Functions YouTube Panopto	Partial Fractions Laplace Transform Using a Table Inverse Laplace Transform Using a Table Initial Value Problems with Laplace Transforms Sections: 6.1, 6.2	Some notes for the recorded videos: video 2
Week 5 Wednesday August 19	Discontinuous Forcing YouTube Panopto Delta Functions YouTube Panopto	Step Functions Discontinuous Forcing Delta Functions Sections: 6.3, 6.4, 6.5	Some notes for the recorded videos: video 1
Week 5 Friday August 21	Final Exam	Final Exam Topics (TBA)