Copies of the classnotes are on the internet in PDF format as given below. The "Examples, Exercises, and Proofs" files were prepared in Beamer. The "Printout of Examples, Exercises, and Proofs" are printable PDF files of the Beamer slides without the pauses. These notes and supplements have not been classroom tested (and so may have some typographical errors). John Wiley and Sons webpage for the textbook has more information, including purchasing information. A copy of the book can be browsed online on the Slideshare website (accessed January 13, 2025).

The 2024-25 catalog course description of Differential Equations (MATH 2120) is: "Offers first order differential equations and applications; second and higher order linear differential equations and applications; Laplace transforms; and systems of [linear] differential equations." These topics are covered in Chapters 1, 2, 3, 4, 5, 7, and 9. This is ambitious! In practice, we will likely cover Laplace transforms (Chapter 9) briefly and not have time to consider systems of linear differential equations (Chapter 7). We should cover series solutions (Chapter 6), though.

I taught sophomore differential equations class at Louisiana State University in Shreveport (MATH 355) in spring 1992. You can view the Announcement for the LSUS Class, the Syllabus for the LSUS Class, Test 1 (1.1-1.3, 2.1-2.4), Test 2 (3.1-1.3, 4.1-4.5), Test 3 (5.1-5.5), and Final (Comprehensive, plus 5.6, 6.1, 6.2) online.

Chapter 1. Differential Equations and Their Solutions. Chapter 1 introduction

• Section 1.1. Classification of Differential Equations; Their Origin and Application. Section 1.1 notes
• Section 1.2. Solutions. Section 1.2 notes
• Supplement. Examples, Exercises, and Proofs from Section 1.2. Beamer file of Section 1.2 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 1.2. Print file of Section 1.2 Proofs, Examples, and Exercises
• Section 1.3. Initial-Value Problems, Boundary-Value Problems and Existence of Solutions. Section 1.3 notes
• Supplement. Examples, Exercises, and Proofs from Section 1.3. Beamer file of Section 1.3 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 1.3. Print file of Section 1.3 Proofs, Examples, and Exercises
• Supplement. The Brachistochrone (from Section 1.6 of Simmon's Differential Equations with Applications and Historical Notes, CRC Press, 2023). Brachistochrone notes
• Supplement. Examples, Exercises, and Proofs from The Brachistochrone. Beamer file of The Brachistochrone, Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from The Brachistochrone. Print file of The Brachistochrone, Proofs, Examples, and Exercises
• Study Guide 1.

Chapter 2. First-Order Equations for Which Exact Solutions Are Obtainable. Chapter 2 introduction

• Section 2.1. Exact Differential Equations and Integrating Factors. Section 2.1 notes
• Supplement. Examples, Exercises, and Proofs from Section 2.1. Beamer file of Section 2.1 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 2.1. Print file of Section 2.1 Proofs, Examples, and Exercises
• Section 2.2. Separable Equations and Equations Reducible to This Form. Section 2.2 notes
• Supplement. Examples, Exercises, and Proofs from Section 2.2. Beamer file of Section 2.2 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 2.2. Print file of Section 2.2 Proofs, Examples, and Exercises
• Section 2.3. Linear Equations and Bernoulli Equations. Section 2.3 notes
• Supplement. Examples, Exercises, and Proofs from Section 2.3. Beamer file of Section 2.3 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 2.3. Print file of Section 2.3 Proofs, Examples, and Exercises
• Section 2.4. Special Integrating Factors and Transformations. Section 2.4 notes
• Supplement. Examples, Exercises, and Proofs from Section 2.4. Beamer file of Section 2.4 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 2.4. Print file of Section 2.4 Proofs, Examples, and Exercises
• Study Guide 2.

Chapter 3. Applications of First-Order Equations. Chapter 3 introduction

• Section 3.1. Orthogonal and Oblique Trajectories. Section 3.1 notes
• Supplement. Examples, Exercises, and Proofs from Section 3.1. Beamer file of Section 3.1 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 3.1. Print file of Section 3.1 Proofs, Examples, and Exercises
• Section 3.2. Problems in Mechanics. Section 3.2 notes (This section contains a computation of escape velocity from a gravitational object.)
• Supplement. Examples, Exercises, and Proofs from Section 3.2. Beamer file of Section 3.2 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 3.2. Print file of Section 3.2 Proofs, Examples, and Exercises
• Section 3.3. Rate Problems. Section 3.3 notes
• Supplement. Examples, Exercises, and Proofs from Section 3.3. Beamer file of Section 3.3 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 3.3. Print file of Section 3.3 Proofs, Examples, and Exercises
• Supplement. The Hanging Cable and Pursuit Curves (from Section 2.12 of Simmon's Differential Equations with Applications and Historical Notes, CRC Press, 2023). Hanging Cable and Pursuit Curve notes
  • Supplement. Examples, Exercises, and Proofs from The Hanging Cable and Pursuit Curves. Beamer file of The Hanging Cable and Pursuit Curves, Proofs, Examples, and Exercises
  • Supplement. Printout of Examples, Exercises, and Proofs from The Hanging Cable and Pursuit Curves. Print file of The Hanging Cable and Pursuit Curves, Proofs, Examples, and Exercises
• Study Guide 3.

Chapter 4. Explicit Methods of Solving Higher-Order Linear Differential Equations. Chapter 4 introduction

• Section 4.1. Basic Theory of Linear Differential Equations. Section 4.1 notes
• Supplement. Examples, Exercises, and Proofs from Section 4.1. Beamer file of Section 4.1 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 4.1. Print file of Section 4.1 Proofs, Examples, and Exercises
• Section 4.2. The Homogeneous Linear Equation with Constant Coefficients. Section 4.2 notes
• Supplement. Examples, Exercises, and Proofs from Section 4.2. Beamer file of Section 4.2 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 4.2. Print file of Section 4.2 Proofs, Examples, and Exercises
• Section 4.3. The Method of Undetermined Coefficients. Section 4.3 notes
• Supplement. Examples, Exercises, and Proofs from Section 4.3. Beamer file of Section 4.3 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 4.3. Print file of Section 4.3 Proofs, Examples, and Exercises
• Section 4.4. Variation of Parameters. Section 4.4 notes
• Supplement. Examples, Exercises, and Proofs from Section 4.4. Beamer file of Section 4.4 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 4.4. Print file of Section 4.4 Proofs, Examples, and Exercises
• Section 4.5. The Cauchy-Euler Equation. Section 4.5 notes
• Supplement. Examples, Exercises, and Proofs from Section 4.5. Beamer file of Section 4.5 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 4.5. Print file of Section 4.5 Proofs, Examples, and Exercises
• Section 4.6. Statements and Proofs of Theorems on the Second-Order Homogeneous Linear Equation. Section 4.6 notes
• Supplement. Examples, Exercises, and Proofs from Section 4.6. Beamer file of Section 4.6 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 4.6. Print file of Section 4.6 Proofs, Examples, and Exercises
• Study Guide 4.

Chapter 5. Applications of Second-Order Linear Differential Equations with Constant Coefficients.

• Section 5.1. The Differential Equation of the Vibrations of a Mass on a Spring. Section 5.1 notes
• Section 5.2. Free, Undamped Motion. Section 5.2 notes (This includes the pendulum equation and its approximation; see Exercise 5.2.10.)
• Supplement. Examples, Exercises, and Proofs from Section 5.2. Beamer file of Section 5.2 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 5.2. Print file of Section 5.2 Proofs, Examples, and Exercises
• Supplement. More on the Pendulum Equation (from Section 1.5 of Simmon's Differential Equations with Applications and Historical Notes, CRC Press, 2023). Pendulum Supplement notes (This includes some basic elliptic integrals.)
• Supplement. Examples, Exercises, and Proofs from More on the Pendulum Equation. Beamer file of More on the Pendulum Equation, Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from More on the Pendulum Equation. Print file of More on the Pendulum Equation, Proofs, Examples, and Exercises
• Supplement. Coupled Harmonic Oscillators (from Section 3.22 of Simmon's Differential Equations with Applications and Historical Notes, CRC Press, 2023). Coupled Harmonic Oscillators Supplement notes (This involves an mass oscillating on a frictionless surface.)
• Supplement. Examples, Exercises, and Proofs from More on Coupled Harmonic Oscillators. Beamer file on Coupled Harmonic Oscillators, Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from More on Coupled Harmonic Oscillators. Print file of More on Coupled Harmonic Oscillators, Proofs, Examples, and Exercises
• Section 5.3. Free, Damped Motion. Section 5.3 notes
• Supplement. Examples, Exercises, and Proofs from Section 5.3. Beamer file of Section 5.3 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 5.3. Print file of Section 5.3 Proofs, Examples, and Exercises
• Section 5.4. Forced Motion. Section 5.4 notes
• Supplement. Examples, Exercises, and Proofs from Section 5.4. Beamer file of Section 5.4 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 5.4. Print file of Section 5.4 Proofs, Examples, and Exercises
• Section 5.5. Resonance Phenomena. Section 5.5 notes
• Supplement. Examples, Exercises, and Proofs from Section 5.5. Beamer file of Section 5.5 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 5.5. Print file of Section 5.5 Proofs, Examples, and Exercises
• Section 5.6. Electric Circuit Problems. Section 5.6 notes
• Study Guide 5.

Chapter 6. Series Solutions of Linear Equations.

• Section 6.1. Power Series Solutions About an Ordinary Point. Section 6.1 notes
• Section 6.2. Solutions About Singular Points; The Method of Frobenius. Section 6.2 notes
• Section 6.3. Bessel's Equation and Bessel Functions.
• Study Guide 6.

Chapter 9. The Laplace Transform.

• Section 9.1. Definition, Existence, and Basic Properties of the Laplace Transform. Section 9.1 notes
• Supplement. Examples, Exercises, and Proofs from Section 9.1. Beamer file of Section 9.1 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 9.1. Print file of Section 9.1 Proofs, Examples, and Exercises
• Section 9.2. The Inverse Transform and the Convolution. Section 9.2 notes
• Supplement. Examples, Exercises, and Proofs from Section 9.2. Beamer file of Section 9.2 Proofs, Examples, and Exercises
• Supplement. Printout of Examples, Exercises, and Proofs from Section 9.2. Print file of Section 9.2 Proofs, Examples, and Exercises
• Section 9.3. Laplace Transform Solution of Linear Differential Equations with Constant Coefficients.
• Supplement. Abel's Mechanical Problem (from Section 9.52 of Simmon's Differential Equations with Applications and Historical Notes, CRC Press, 2023).
• Section 9.4. Laplace Transform Solution of Linear Differential Equations with Discontinuous Nonhomogeneous Terms.
• Section 9.5. Laplace Transform Solution of Linear Systems.
• Study Guide 9.

Additional Chapters.

• Chapter 7. Systems of Linear Differential Equations.
• Chapter 8. Approximate Methods of Solving First-Order Equations.

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