Mathematical Methods in Chemistry

by Marcia Levitus

Read here Read at LibreTextsPDF

This text introduces student to mathematical/computational methods in chemical kinetics, thermodynamics, quantum chemistry.

Description from LibreTexts.

Publisher
Arizona State University
Subjects
Chemistry, Physical and Theoretical Chemistry Textbook Maps
Licence
CC BY-NC-SA 4.0, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. About this Book
  7. Preface
  8. 1: Before We Begin...
  9. 1.1: Things to review
  10. 1.2: Odd and Even Functions
  11. 1.3: The Exponential Function
  12. 1.4: The Period of a Periodic Function
  13. 1.5: Exercises
  14. 2: Complex Numbers
  15. 2.1: Algebra with Complex Numbers
  16. 2.2: Graphical Representation and Euler Relationship
  17. 2.3: Complex Functions
  18. 2.4: Problems
  19. 3: Series
  20. 3.1: Maclaurin Series
  21. 3.2: Linear Approximations
  22. 3.3: Taylor Series
  23. 3.4: Other Applications of Mclaurin and Taylor series
  24. 3.5: Problems
  25. 4: First Order Ordinary Differential Equations
  26. 4.1: Definitions and General Concepts
  27. 4.2: 1st Order Ordinary Differential Equations
  28. 4.3: Chemical Kinetics
  29. 4.4: Problems
  30. 5: Second Order Ordinary Differential Equations
  31. 5.1: Second Order Ordinary Differential Equations
  32. 5.2: Second Order Ordinary Differential Equations - Oscillations
  33. 5.3: Second Order Ordinary Differential Equations with Boundary Conditions
  34. 5.4: An example in Quantum Mechanics
  35. 5.5: Problems
  36. 6: Power Series Solutions of Differential Equations
  37. 6.1: Introduction to Power Series Solutions of Differential Equations
  38. 6.2: The Power Series Method
  39. 6.3: The Laguerre Equation
  40. 6.4: Problems
  41. 7: Fourier Series
  42. 7.1: Introduction to Fourier Series
  43. 7.2: Fourier Series
  44. 7.3: Orthogonal Expansions
  45. 7.4: Problems
  46. 8: Calculus in More than One Variable
  47. 8.1: Functions of Two Independent Variables
  48. 8.2: The Equation of State
  49. 8.3: The Chain Rule
  50. 8.4: Double and Triple Integrals
  51. 8.5: Real Gases
  52. 8.6: Problems
  53. 9: Exact and Inexact Differentials
  54. 9.1: The Total Differential
  55. 9.2: Exact and Inexact Differentials
  56. 9.3: Differentials in Thermodynamics - State and Path Functions
  57. 9.4: A Mathematical Toolbox
  58. 9.5: Line Integrals
  59. 9.6: Exact and Inexact Differentials (Summary)
  60. 9.7: Problems
  61. 10: Plane Polar and Spherical Coordinates
  62. 10.1: Coordinate Systems
  63. 10.2: Area and Volume Elements
  64. 10.3: A Refresher on Electronic Quantum Numbers
  65. 10.4: A Brief Introduction to Probability
  66. 10.5: Problems
  67. 11: Operators
  68. 11.1: Definitions
  69. 11.2: Operator Algebra
  70. 11.3: Operators and Quantum Mechanics - an Introduction
  71. 11.4: Problems
  72. 12: Partial Differential Equations
  73. 12.1: Introduction to Partial Differential Equations
  74. 12.2: The Method of Separation of Variables
  75. 12.3: The Wave Equation in One Dimension
  76. 12.4: Molecular Diffusion
  77. 12.5: Problems
  78. 13: Determinants
  79. 13.1: The Solutions of Simultaneous Linear Equations
  80. 13.2: Calculation of a 3 × 3 determinant
  81. 13.3: The Determinant as a Volume
  82. 13.4: Properties of Determinants
  83. 13.5: Problems
  84. 14: Vectors
  85. 14.1: Introduction to Vectors
  86. 14.2: The Scalar Product
  87. 14.3: The Vector Product
  88. 14.4: Vector Normalization
  89. 14.5: Problems
  90. 15: Matrices
  91. 15.1: Definitions
  92. 15.2: Matrix Addition
  93. 15.3: Matrix Multiplication
  94. 15.4: Symmetry Operators
  95. 15.5: Matrix Inversion
  96. 15.6: Orthogonal Matrices
  97. 15.7: Eigenvalues and Eigenvectors
  98. 15.8: Hermitian Matrices
  99. 15.9: Problems
  100. 16: Formula Sheets
  101. 16.1: Some Important Numbers
  102. 16.2: Quadratic Equation
  103. 16.3: Logarithms and Exponentials
  104. 16.4: Trigonometric Identities
  105. 16.5: Complex Numbers
  106. 16.6: Operators
  107. 16.7: Taylor Series
  108. 16.8: Fourier Series
  109. 16.9: Derivatives and Primitives (Indefinite Integrals)
  110. 16.10: Definite integrals
  111. 16.11: Differentiation Rules
  112. 16.12: Partial Derivatives
  113. 16.13: Coordinate Systems
  114. Back Matter
  115. Index
  116. Glossary
  117. Detailed Licensing