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 section of Applied Math 2 (MATH 5620) I taught in spring 1997. However, these notes are more appropriate for Introduction to Applied Math (MATH 4027/5027).

Applied Math 2 Syllabus, Spring 1997. Syllabus

Chapter 1. Where PDEs Come From.

• Section 1.1. What is a Partial Differential Equation? Section 1.1 notes
• Section 1.2. First-Order Linear Equations. Section 1.2 notes
• Section 1.3. Flows, Vibrations, and Diffusions. Section 1.3 notes
• Section 1.4. Initial and Boundary Conditions. Section 1.4 notes
• Section 1.5. Well-Posed Problems. Section 1.5 notes
• Section 1.6. Types of Second-Order Equations.

Chapter 2. Waves and Diffusions.

• Section 2.1. The Wave Equation. Section 2.1 notes
• Section 2.2. Causality and Energy. Section 2.2 notes
• Section 2.3. The Diffusion Equation. Section 2.3 notes
• Section 2.4. Diffusion on the Whole Line. Section 2.4 notes
• Section 2.5. Comparison of Waves and Diffusions.

Test 1 (1.1-1.5, 2.1-2.4). Test 1

Chapter 4. Boundary Problems.

• Section 4.1. Separation of Variables, the Dirichlet Condition. Section 4.1 notes
• Section 4.2. The Neumann Condition. Section 4.2 notes
• Section 4.3. The Robin Condition. Section 4.3 notes

Chapter 5. Fourier Series.

• Section 5.1. The Coefficients. Section 5.1 notes
• Section 5.2. Even, Odd, Periodic, and Complex Functions. Section 5.2 notes
• Section 5.3. Orthogonality and General Fourier Series. Section 5.3 notes
• Section 5.4. Completeness. Section 5.4 notes
• Section 5.5. Completeness and the Gibbs Phenomenon.
• Section 5.6. Inhomogeneous Boundary Conditions.

Chapter 6. Harmonic Functions.

• Section 6.1. Laplace's Equation. Section 6.1 notes
• Section 6.2. Rectangles and Cubes.
• Section 6.3. Poison's Formula.
• Section 6.4. Circles, Wedges, and Annuli.

Test 2 (4.1-4.3, 5.1-5.4, 6.1). Test 2

Additional Chapters.