PART I

Section 1: Introduction

Section 2: First-order Equations

Section 3: Conservation Laws

Section 4: Second-order Equations

Section 5: Wave Equation on the Real Line

Section 6: Wave Equation on an Interval

Section 7: Wave Equation in Higher Dimensions

Section 8: Hyperbolic Systems of First-Order Equations

PART II

Section 1: Introduction

Section 2: Heat Equation

Section 3: Laplace's Equation

Section 4: Green's Functions

Section 5: Potential Theory 

Section 5 Addendum: Physical Interpretation of Single and Double-Layer Potentials 

Section 6: Eigenvalues of the Laplacian

Section 6 Addendum: Comments on Rayleigh-Ritz Approximation and Minimax Principle 

Section 7: Calculus of Variations