readme

This note is outcome of SP 2025 MATH 441. Differential Equations in UIUC, taught by professor Nikolaos Tzirakis.
The text book is Elementary Differential Equations and Boundary Value Problems, Ninth Edition.

Topic by chapter

CH1 Introduction: recap

CH2 First Order Differential Equations:

• 2.6 exact equations and integrating factor technique

CH3 Second Order Linear Equations:

• fundamental set
• 3.2/3.3 Wronskian determinant
• 3.4 reduction of Order technique, order reduce by substitution technique and repeated root
• 3.5 solution difference technique
• 3.6 variation of parameters technique

CH4 Higher Order Linear Equations:

• linear differential operator
• characteristic polynomial
• 4.4 Abel’s identity

CH5 Series Solutions of Second Order Linear Equations:

• radius of convergence
• series solutions technique

CH8 Numerical Methods: didn’t cover this chapter in class, but readme will cover some of it.

CH7 Systems of First Order Linear Equations:

• Eigenvalue and Eigenvector
• systems of first order ODEs

CH9 Nonlinear Differential Equations and Stability:

• Jacobian matrix
• stability