Partial Differential Equations

Part I. Background

1. Vector Fields and Ordinary Differential Equations
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2. Partial Differential Equations in Engineering
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Part II. The First-Order Equation

3. The Single First-Order Quasi-linear PDE
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4. Shock Waves
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5. The Genuinely Nonlinear First-Order Equation
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Part III. Classification of Equations and Systems

6. The Second-Order Quasi-linear Equation
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7. Systems of Equations
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Part IV. Paradigmatic Equations

8. The One-Dimensional Wave Equation
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9. Standing Waves and Separation of Variables
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10. The Diffusion Equation
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11. The Laplace Equation
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Keywords: Engineering, Theoretical and Applied Mechanics, Partial Differential Equations, Mathematical Modeling and Industrial Mathematics