ORDINARY DIFFERENTIAL EQUATIONS (MA 4204 / MATH 252)
Fall 2024
Instructor
Mike O'Neil (oneil@cims.nyu.edu)
Office hours
Mon 3:00pm-4:00pm, 2 MTC 854
Thu 2:00pm-3:00pm, WWH 1119
(or by appointment)
Description
A first course in ordinary differential equations. This course covers methods for solving first-order linear and nonlinear equations, existence and uniqueness of solutions, and analytical methods for finding solutions. We will also study second-order linear equations, general theory and Wronskians, constant coefficient theory and mechanical vibrations, variation of parameters, and series solutions. More advanced topics toward the end of the semester will include systems of linear equations, eigenvector methods, qualitative analysis of nonlinear systems of equations, boundary-value problems, and an introduction to Fourier Series and Sturm-Liouville theory. Time permitting, we will also discuss the Laplace Transform and how it can be used to solve ODEs, as well as Green’s function methods for solving differential equations. View the syllabus for more detailed information.
Lecture
Monday & Wednesday 9:30am - 10:50am, RGSH 202
Recitation
Tianrun Gou (tg2674@nyu.edu)
Friday 9:30am - 10:50am, JAB 473
Office hours: TBA
Mike O'Neil (oneil@cims.nyu.edu)
Office hours
Mon 3:00pm-4:00pm, 2 MTC 854
Thu 2:00pm-3:00pm, WWH 1119
(or by appointment)
Description
A first course in ordinary differential equations. This course covers methods for solving first-order linear and nonlinear equations, existence and uniqueness of solutions, and analytical methods for finding solutions. We will also study second-order linear equations, general theory and Wronskians, constant coefficient theory and mechanical vibrations, variation of parameters, and series solutions. More advanced topics toward the end of the semester will include systems of linear equations, eigenvector methods, qualitative analysis of nonlinear systems of equations, boundary-value problems, and an introduction to Fourier Series and Sturm-Liouville theory. Time permitting, we will also discuss the Laplace Transform and how it can be used to solve ODEs, as well as Green’s function methods for solving differential equations. View the syllabus for more detailed information.
Lecture
Monday & Wednesday 9:30am - 10:50am, RGSH 202
Recitation
Tianrun Gou (tg2674@nyu.edu)
Friday 9:30am - 10:50am, JAB 473
Office hours: TBA
Materials
The following textbook will be used for the course:
- Martin Braun, Differential Equations and Their Applications, 4th ed., Springer, 1993
The following books might be useful as additional references:
- Boyce, DiPrima, and Meade, Elementary Differential Equations and Boundary Value Problems, 11th ed., Wiley, 2017
- Coddington, An Introduction to Ordinary Differential Equations, Dover, 1989
Grading
The overall course grade will be determined from a final numerical weighted average. The following breakdown will be used to compute an overall numerical grade:
- 10% Homework (weekly, lowest grade dropped)
- 25% Preliminary Exam 1
- 25% Preliminary Exam 2
- 40% Final exam (cumulative)
Announcements
- Grades and a link to Gradescope for homework submissions has been setup on Brightspace here.
The following textbook will be used for the course:
- Martin Braun, Differential Equations and Their Applications, 4th ed., Springer, 1993
The following books might be useful as additional references:
- Boyce, DiPrima, and Meade, Elementary Differential Equations and Boundary Value Problems, 11th ed., Wiley, 2017
- Coddington, An Introduction to Ordinary Differential Equations, Dover, 1989
Grading
The overall course grade will be determined from a final numerical weighted average. The following breakdown will be used to compute an overall numerical grade:
- 10% Homework (weekly, lowest grade dropped)
- 25% Preliminary Exam 1
- 25% Preliminary Exam 2
- 40% Final exam (cumulative)
Announcements
- Grades and a link to Gradescope for homework submissions has been setup on Brightspace here.
Schedule
Below is an updated list of discussion topics along with any documents that were distributed, homework assigned, etc.| Date | Topics | Materials |
|---|---|---|
| Sep 4 | Overview, 1st order equations | Braun 1.1-1.2 |
| Sep 9 | Integrating factors, separable equations | Braun 1.2-1.3 |
| Sep 11 | Separable equations, intervals of existence, orthogonal trajectories | Braun 1.4, 1.8(c) |
| Sep 16 | Exact equations | Braun 1.9 |
| Sep 16 | Existence and uniquness, Picard iterations | Braun 1.10 |
| Sep 23 | 2nd-order linear differential equations | Braun 2.1 |
| Sep 25 | Constant coefficient equations | Braun 2.2 |
| Sep 30 | Inhomogeneous equations, variation of parameters | Braun 2.3-2.4 |
| Oct 2 | Prelim Exam 1 | |
| Oct 7 | Series solutions | Braun 2.8 |
| Oct 9 | Regular singular points, Frobenius method | Braun 2.8.1, 2.8.2 |
| Oct 15 (TUE) | Frobenius method, Laplace transforms | Braun 2.8.3, 2.9 |
| Oct 16 | Laplace transforms | Braun 2.10, 2.11 |
| Oct 21 | The Delta function | Braun 2.12 |
| Oct 23 | Convolutions, Green's functions |
Braun 2.13 Bender and Orszag, 1.5 |
| Oct 28 | Systems of differential equations | Braun 3.1-3.4 |
| Oct 30 | Eigenvector solutions, complex roots |
Braun 3.8-3.9 (Braun 3.5-3.7, for review) |
| Nov 4 | Matrix exponential solutions | Braun 3.10 |
| Nov 6 | Prelim Exam 2 | |
| Nov 11 | Qualitative theory of systems of differential equations | Braun 4.1-4.3 |
| Nov 13 | Equilibria, stability of systems of DE | Braun 4.1-4.3 |
| Nov 18 | Phase portraits | Braun 4.4, 4.7 |
| Nov 20 | 2-point boundary value problems, separation of variables | Braun 5.1-5.3 |
| Nov 25 | Fourier series | Braun 5.4-5.5 |
| Nov 27 | ||
| Dec 2 | ||
| Dec 4 | ||
| Dec 9 | ||
| Dec 11 | NO CLASS -- FRIDAY SCHEDULE | |
| Dec 16 | Final exam |