Solutions Manual to Accompany Beginning Partial Differential Equations [Paperback]

Solutions Manual to Accompany Beginning Partial Differential Equations, 3rd Edition

Featuring a challenging, yet accessible, introduction to partial differential equations, Beginning Partial Differential Equations provides a solid introduction to partial differential equations, particularly methods of solution based on characteristics, separation of variables, as well as Fourier series, integrals, and transforms. Thoroughly updated with novel applications, such as Poe's pendulum and Kepler's problem in astronomy, this third edition is updated to include the latest version of Maples, which is integrated throughout the text. New topical coverage includes novel applications, such as Poe's pendulum and Kepler's problem in astronomy.Preface vii

1 First Ideas 1

1.1 Two Partial Differential Equations 1

1.2 Fourier Series 4

1.3 Two Eigenvalue Problems 12

1.4 A Proof of the Convergence Theorem 14

2 Solutions of the Heat Equation 15

2.1 Solutions on an Interval [0, L] 15

2.2 A Nonhomogeneous Problem 19

3 Solutions of the Wave Equation 25

3.1 Solutions on Bounded Intervals 25

3.2 The Cauchy Problem 32

3.2.1 d’Alembert’s Solution 32

3.2.2 The Cauchy Problem on a Half Line 36

3.2.3 Characteristic Triangles and Quadrilaterals 41

3.2.4 A Cauchy Problem with a Forcing Term 41

3.2.5 String with Moving Ends 42

3.3 The Wave Equation in Higher Dimensions 46

3.3.1 Vibrations ilS.