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 sophomore differential equations class I taught at Louisiana State University in Shreveport (MATH 355) in spring 1992. A copy of the book can be browsed online here (accessed March 4, 2019).

Announcement for the LSUS Class
Syllabus for the LSUS Class

Chapter 1. Differential Equations and Their Solutions.

• Section 1.1. Classification of Differential Equations; Their Origin and Application. Section 1.1 notes
• Section 1.2. Solutions. Section 1.2 notes
• Section 1.3. Initial-Value Problems, Boundary-Value Problems and Existence of Solutions. Section 1.3 notes

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

• Section 2.1. Exact Differential Equations and Integrating Factors. Section 2.1 notes
• Section 2.2. Separable Equations and Equations Reducible to This Form. Section 2.2 notes
• Section 2.3. Linear Equations and Bernoulli Equations. Section 2.3 notes
• Section 2.4. Special Integrating Factors and Transformations.

Test 1 (1.1-1.3, 2.1-2.4)

Chapter 3. Applications of First-Order Equations.

• Section 3.1. Orthogonal and Oblique Trajectories.
• Section 3.2. Problems in Mechanics. Section 3.2 notes (This section contains a computation of escape velocity from a gravitational object.)
• Section 3.3. Rate Problems. Section 3.3 notes

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

• Section 4.1. Basic Theory of Linear Differential Equations. Section 4.1 notes
• Section 4.2. The Homogeneous Linear Equation with Constant Coefficients. Section 4.2 notes
• Section 4.3. The Method of Undetermined Coefficients. Section 4.3 notes
• Section 4.4. Variation of Parameters. Section 4.4 notes
• Section 4.5. The Cauchy-Euler Equation. Section 4.5 notes
• Section 4.6. Statements and Proofs of Theorems on the Second-Order Homogeneous Linear Equation.

Test 2 (3.1-1.3, 4.1-4.5)

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
• Section 5.3. Free, Damped Motion. Section 5.3 notes
• Section 5.4. Forced Motion. Section 5.4 notes
• Section 5.5. Resonance Phenomena.
• Section 5.6. Electric Circuit Problems. Section 5.6 notes

Test 3 (5.1-5.5)

Chapter 6. Series Solutions of Linear Equations.

• Section 6.1. Power Series Solutions About an Ordinary Point. Section 2.1 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.

Final, (Comprehensive, plus 5.6, 6.1, 6.2)

Additional Chapters.

• Chapter 7. Systems of Linear Differential Equations.
• Chapter 8. Approximate Methods of Solving First-Order Equations.
• Chapter 9. The Laplace Transform.

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