"A Second Course in Differential Equations Class Notes" Webpage

A Second Course in Differential Equations Class Notes
Elementary Differential Equations and Boundary Value Problems, 5th Edition
by Richard Diprima and William Boyce, John Wiley & Sons (1991).

Diprima and Boyce's Elementary Differential Equations and Boundary Value Problems book, 5th edition

Copies of the classnotes are on the internet in PDF format as given below. These notes and supplements have not been classroom tested (and so may have some typographical errors). They are based on a senior-level differential equations class I taught at Louisiana State University in Shreveport (MATH 455) in fall 1992.

Announcement for the Class. Class Announcement Syllabus for the LSUS Class. Class Syllabus

Review of Introductory Differential Equations. Review notes

Chapter 6. The Laplace Transform.

Section 6.1. Definition of the Laplace Transform. Section 6.1 notes
Section 6.2. Solution of Initial Value Problems. Section 6.2 notes
Section 6.3. Step Functions.
Section 6.4. Differential Equations with Discontinuous Forcing Functions.
Section 6.5. Impulse Functions.
Section 6.6. The Convolution Integral.

Chapter 7. Systems of First Order Linear Equations.

Section 7.1. Introduction. Section 7.1 notes
Section 7.2. Review of Matrices. Section 7.2 notes
Section 7.3. Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors. Section 7.3 notes
Section 7.4. Basic Theory of Systems of First Order Linear Equations. Section 7.4 notes
Section 7.5. Homogeneous Linear Systems with Constant Coefficients. Section 7.5 notes
Section 7.6. Complex Eigenvalues. Section 7.6 notes
Section 7.7. Repeated Eigenvalues. Section 7.7 notes
Section 7.8. Fundamental Matrices. Section 7.8 notes
Section 7.9. Nonhomogeneous Linear Systems. Section 7.9 notes

Test 1 (7.1-7.9). Test 1

The Derivation of Kepler's Laws of Planetary Motion From Newton's Law of Gravity. Derivation of Kepler's Laws

Chapter 9. Nonlinear Differential Equations and Stability.

Section 9.1. The Phase Plane; Linear Systems. Section 9.1 notes This section includes a solution for underdamped, overdamped, and critically damped harmonic motion.
Section 9.2. Autonomous Systems and Stability. Section 9.2 notes This section includes an analysis of the nonlinear pendulum equation.
Section 9.3. Almost Linear Systems. Section 9.3 notes This section includes an analysis of damped pendulum equation.
Section 9.4. Competing Species. Section 9.4 notes
Section 9.5. Predator-Prey Equations. Section 9.5 notes
Section 9.6. Liapunov's Second Method. Section 9.6 notes
Section 9.7. Periodic Solutions and Limit Cycles. Section 9.7 notes
Section 9.8. Chaos and Strange Attractors; the Lorenz Equations. Section 9.8 notes

Test 2 (9.1-9.8). Test 2

Chapter 10. Partial Differential Equations and Fourier Series.

Section 10.1. Separation of Variables; Heat Conduction. Section 10.1 notes
Section 10.2 and 10.5. Fourier Series (Partial). Section 10.2 notes

Final (Comprehensive, plus 10.1-10.2). Final

Additional Chapters.

Chapter 1. Introduction.

Chapter 2. First Order Differential Equations.

Chapter 3. Second Order Linear Equations.

Chapter 4. Higher Order Linear Equations.

Chapter 5. Series Solutions of Second Order Linear Equations.

Chapter 8. Numerical Methods.

Chapter 10. Partial Differential Equations and Fourier Series.

Chapter 11. Boundary Value Problems and Sturm-Liouville Theory.

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