Phu Xuan University Library
|
PXU E-LIB
Sign in
Introduction to Partial Differential Equations

External

Introduction to Partial Differential Equations

This is a self-published text book with excellent coverage and solid mathematics and theory to support applications. Each chapter is rich in applications, described in good detail and fine exercises which involve solution techniques, but many applications and variations. There are many applications of second order differential equations with complete and thorough discussion of damping, eigenvalues, and characteristic equation.

Differential EquationsMathematics
Author
Russell Herman
Publisher
University of North Carolina Wilmington
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 104 sections
  1. 01: First Order Partial Differential Equations
  2. 1.01: Introduction
  3. 1.02: Linear Constant Coefficient Equations
  4. 1.03: Quasilinear Equations- The Method of Characteristics
  5. 1.04: Applications
  6. 1.05: Nonlinear Advection Equations
  7. 1.06: General First Order PDEs
  8. 1.08: Problems
  9. 02: Second Order Partial Differential Equations
  10. 2.01: Introduction
  11. 2.02: Derivation of Generic 1D Equations
  12. 2.03: Boundary Value Problems
  13. 2.04: Separation of Variables
  14. 2.05: Laplaces Equation in 2D
  15. 2.06: Classification of Second Order PDEs
  16. 2.07: dAlemberts Solution of the Wave Equation
  17. 2.08: Problems
  18. 03: Trigonometric Fourier Series
  19. 3.01: Introduction to Fourier Series
  20. 3.02: Fourier Trigonometric Series
  21. 3.03: Fourier Series Over Other Intervals
  22. 3.04: Sine and Cosine Series
  23. 3.05: Solution of the Heat Equation
  24. 3.06: Finite Length Strings
  25. 3.07: The Gibbs Phenomenon
  26. 3.08: Problems
  27. 04: Sturm-Liouville Boundary Value Problems
  28. 4.01: Sturm-Liouville Operators
  29. 4.02: Properties of Sturm-Liouville Eigenvalue Problems
  30. 4.03: The Eigenfunction Expansion Method
  31. 4.04: Appendix- The Fredholm Alternative Theorem
  32. 4.05: Problems
  33. 05: Non-sinusoidal Harmonics and Special Functions
  34. 5.01: Function Spaces
  35. 5.02: Classical Orthogonal Polynomials
  36. 5.03: Fourier-Legendre Series
  37. 5.04: Gamma Function
  38. 5.05: Fourier-Bessel Series
  39. 5.06: Appendix- The Least Squares Approximation
  40. 5.07: Problems
  41. 06: Problems in Higher Dimensions
  42. 6.01: Vibrations of Rectangular Membranes
  43. 6.02: Vibrations of a Kettle Drum
  44. 6.03: Laplaces Equation in 2D
  45. 6.04: Three Dimensional Cake Baking
  46. 6.05: Laplaces Equation and Spherical Symmetry
  47. 6.06: Spherically Symmetric Vibrations
  48. 6.07: Baking a Spherical Turkey
  49. 6.08: Schrodinger Equation in Spherical Coordinates
  50. 6.09: Curvilinear Coordinates
  51. 6.10: Problems
  52. 07: Green's Functions
  53. 7.00: Prelude to Green's Functions and Nonhomogeneous Problems
  54. 7.01: Initial Value Greens Functions
  55. 7.02: Boundary Value Greens Functions
  56. 7.03: The Nonhomogeneous Heat Equation
  57. 7.04: Greens Functions for 1D Partial Differential Equations
  58. 7.05: Greens Functions for the 2D Poisson Equation
  59. 7.06: Method of Eigenfunction Expansions
  60. 7.07: Greens Function Solution of Nonhomogeneous Heat Equation
  61. 7.08: Summary
  62. 7.09: Problems
  63. 08: Complex Representations of Functions
  64. 8.01: Complex Representations of Waves
  65. 8.02: Complex Numbers
  66. 8.03: Complex Valued Functions
  67. 8.04: Complex Differentiation
  68. 8.05: Complex Integration
  69. 8.06: Laplaces Equation in 2D Revisited
  70. 8.07: Problems
  71. 09: Transform Techniques in Physics
  72. 9.01: Introduction
  73. 9.02: Complex Exponential Fourier Series
  74. 9.03: Exponential Fourier Transform
  75. 9.04: The Dirac Delta Function
  76. 9.05: Properties of the Fourier Transform
  77. 9.06: The Convolution Operation
  78. 9.07: The Laplace Transform
  79. 9.08: Applications of Laplace Transforms
  80. 9.09: The Convolution Theorem
  81. 9.10: The Inverse Laplace Transform
  82. 9.11: Transforms and Partial Differential Equations
  83. 9.12: Problems
  84. 10: Numerical Solutions of PDEs
  85. 10.01: Ordinary Differential Equations
  86. 10.02: The Heat Equation
  87. 10.03: Truncation Error
  88. 10.04: Stability
  89. 11: A - Calculus Review - What Do I Need to Know From Calculus?
  90. 11.01: What Do I Need To Know From Calculus
  91. 11.02: Hyperbolic Functions
  92. 11.03: Derivatives
  93. 11.04: Integrals
  94. 11.05: Geometric Series
  95. 11.06: Power Series
  96. 11.07: The Binomial Expansion
  97. 11.08: Problems
  98. 11.9: Problems
  99. 12: B - Ordinary Differential Equations Review
  100. 12.01: First Order Differential Equations
  101. 12.02: Second Order Linear Differential Equations
  102. 12.03: Forced Systems
  103. 12.04: Cauchy-Euler Equations
  104. 12.05: Problems