MATH2400, Introduction to Differential Equations
Class Notes, Spring 2004
We're grateful to Kristian Montenegro for providing us with these
excellent notes. Thanks Kristian!
Chapter 2
Section 2.2, separation of variables for first-order equations
Section 2.3, circuits
Section 2.3, mixing
Section 2.3, compound interest, radioactive decay, cooling, gravitation
Section 2.3, review
Section 2.5, population growth and graphical methods for autonomous equations
Section 2.7, Euler's method
Chapter 3
Section 3.1, second-order equations (case of different real roots of characteristic equation)
Section 3.2, superposition principle and solving initial value problem
Section 3.3, linear independence and vector space interpretation
Section 3.3, linear independence and vector space interpretation,
continued
Section 3.4, case of complex roots of characteristic equation
Section 3.5, case of double roots of characteristic equation
Section 3.6, inhomogeneous equations
Section 3.6, more on inhomogeneous equations
Section 3.8, mechanical vibrations, undamped free case
Section 3.8, mechanical vibrations, damped free case, and LRC circuits
Section 3.9, forced mechanical vibrations
Chapter 7
Sections 7.1, 7.2, 7.3: Introduction to systems, review of matrices,
introduction to eigenvalues
Section 7.3, more on eigenvalues and eigenvectors
Section 7.5, solving systems of linear, constant-coefficient ODEs
Chapter 10
Section 10.1, Two-point boundary value problems
more on Section 10.1, Two-point boundary value problems
Section 10.2, Fourier series
Section 10.3, more on Fourier series
Section 10.4, Fourier series for even and odd functions
Outline of the separation of variables method for solving the heat equation
Section 10.5, the heat equation with homogeneous boundary conditions
Section 10.6, the heat equation with non-homogeneous boundary
conditions
Section 10.6, an example of the heat equation with non-homogeneous boundary
conditions
Section 10.7, a modified wave equation equation with free ends
Section 10.8, Laplace's equation