Math 292 - Honors Calculus IV
Description
Math 292 is the second course in the honors calculus sequence, after Math 291. This course covers the elementary theory of ordinary differential equations, along with an introduction to partial differential equations (time permitting).
Topics covered
Topics covered in Math 292 usually include:
- Standard prototypes of ordinary differential equations, methods of solving
- First-order linear ODE
- Bernoulli and Riccati equations
- Reduction of order
- Flows on the real line
- Existence and uniqueness for first-order autonomous equations
- Matrix exponentials and generalized eigenvectors
- Applications to solving systems of ordinary differential equations, Duhamel’s formula
- Picard’s theorem and Picard iteration
Note that the exact list of topics may vary by instructor and semester. Additional topics may include oscillations, Green’s functions and Sturm–Liouville theory, an introduction to partial differential equations, and the calculus of variations; usually, at least some of these are covered.
Comments on prerequisites
Completing 250 and 251 with a grade of A is usually sufficient for receiving permission to take 292 without having previously taken 291.
Miscellaneous information
It is not necessary to take Math 292 after Math 291, but many people do. Someone who takes 292 but not 291 might be at a slight disadvantage due to having less practice with real analysis, but 291 is not necessary to succeed in 292.
Resources
Textbook
The usual textbook for the class is a set of course notes produced by Eric Carlen, available online at http://sites.math.rutgers.edu/~carlen/292S18/ODE2018.pdf. This text is known to have many typos.
Additional materials
Lecture notes from when the course was taught by Zheng-Chao Han in Spring 2021, which complement the Carlen notes, may be found online at https://math292-pretext-textbook.netlify.app/math292-textbook.html.
Previous course webpages from when the course was taught by Eric Carlen may be found online: Spring 2018, Spring 2016, Spring 2015, Spring 2014, Spring 2013, Spring 2012, and Spring 2011.