Math 20D: Differential Equations

Contact information

Instructor:

Finn McGlade; fmcglade@ucsd.edu

TAs:

Yuan Hui; yuhui@ucsd.edu

Shihao Zhang; ushz051@ucsd.edu

Qihao Ye; q8ye@ucsd.edu

Office hours

McGlade: Tuesdays 9:00-11:00am, HSS 4085
Hui: Tuesdays, 2:00-4:00pm, HSS 5012
Zhang: Mondays, 9:00-11:00am, remote (see Canvas for zoom links)
Ye: Mondays, 1:00-3:00pm, APM 5720

Syllabus

Lecture Topics and Slides

Recorded lectures can be found on Canvas. Below NSS refers to the text Fundamentals of Differential Equations (9th edition) by Nagle, Saff, Snider

Lecture 1: Introduction to the harmonic oscillator Suggested reading NSS 4.1
Lecture 2: Vocabulary of differential equations and linear initial value problems Suggested reading NSS 1.1 & 6.1 (page 319 only)
Lecture 3: The complex exponential and non-linear 1st order initial value problems Suggest reading Paul's online math notes and NSS 1.2
Lecture 4: Implicit solutions and separable equations Suggested reading NSS 1.2 & 2.2
Lecture 5: First order linear ODEs and integrating factors Suggested reading NSS 2.3
Lecture 6: Applications of first order ODEs Suggested reading NSS 3.2 (up to the end of example 2)
Lecture 7: Homogeneous Linear Equation: The General Solution Suggested reading NSS 4.2
Lecture 8: Auxiliary Equations with Complex Roots Suggested reading NSS 4.3
Lecture 9: A closer look at free mechanical vibrations Suggested reading NSS 4.9
Lecture 10: An even closer look at free mechanical vibrations Suggested reading NSS 4.9
Lecture 11: Inhomogeneous Equations and Variation of Parameters I Suggested reading NSS 4.6
Lecture 12: A closer look at homogeneous equations and the Wronskian Suggested reading NSS 4.2 & 4.7
Lecture 13: Variation of Parameters II Suggested reading NSS 4.7
Lecture 14: Reduction of Order Suggested reading NSS 4.7
Lecture 15: Definition of Laplace Transform Suggested reading NSS 7.2
Lecture 16: Properties of Laplace Transform Suggested reading NSS 7.3
Lecture 17: Inverse Laplace Transform Suggested reading NSS 7.4
Lecture 18: More Inverse Laplace Transforms Suggested reading NSS 7.4
Lecture 19: Transforms of Discontinuous Functions I Suggested reading NSS 7.6
Lecture 20: Transforms of Discontinuous Functions II Suggested reading NSS 7.6
Lecture 21: Transforms of Discontinuous Functions III and the Dirac Delta Function I Suggested reading NSS 7.6 & 7.9
Lecture 22: The Dirac Delta Function II Suggested reading NSS 7.9
Lecture 23: Introduction to Systems of Linear Differential Equations Suggested reading NSS 9.1
Lecture 24: Normal Forms, Eigenvalues, and Eigenvectors Suggested reading NSS 9.4 & 9.5
Lecture 25: Solving System of Equations using Eigenvectors I Suggested reading NSS 9.5
Lecture 26: Solving System of Equations using Eigenvectors II Suggested reading NSS 9.5
Lecture 27: Solving System of Equations using Eigenvectors III Suggested reading NSS 9.6

Homework Assignments

Homework is due by 10:00pm Pacific time on Gradescope on the days listed below

Tuesday April 11 Homework 1
Tuesday April 18 Homework 2
Tuesday April 25 Homework 3
Tuesday May 9 Homework 4
Wednesday May 17 Homework 5
Tuesday May 23 Homework 6
Thursday June 1 Homework 7
Saturday June 10 Homework 8
Wednesday June 14 Extra Credit Final Exam Review Problem Set (Answers to Selected Exercises Available in NSS)

Exams

Midterm 1 Wednesday April 26th
Midterm 1 practice problems (Answers to Selected Exercises Available in NSS)
Midterm 2 Wednesday May 25th
Midterm 2 practice problems (Answers to Selected Exercises Available in NSS)
Practice Final Exam