Applied Mathematics Body and Soul, Volume 1: Derivatives and Geometry in R3

Rating:
Summary: Calculus + Linear Algebra in One Series
Review: I wish Amazon would put a text list of the "Table of Contents" for books.

Sorry about the length: Amazon does not allow postings for each volume in a series!

Volume 1: Derivatives and Geometry in R^3
1. What is Mathematics?
2. The Mathematics Library
3. Introduction to Modeling
4. A Very Short Calculus Course
5. Natural Numbers and Integers
6. Mathematical Induction
7. Rational Numbers
8. Pythagoras and Euclid
9. What is a Function?
10. Polynomial Functions
11. Combinations of Functions
12. Lipschitz Continuity
13. Sequences and Limits
14. The Square Root of Two
15. Real Numbers
16. The Bisection Algorithm for f(x) = 0
17. Do Mathematicians Quarrel?
18. The Function y = x^r
19. Fixed Points and Contraction Mappings
20. Analytic Geometry in R^2
21. Analytic Geometry in R^3
22. Complex Numbers
23. The Derivative
24. Differentiation Rules
25. Newton's Method
26. Galileo, Newton, Hooke, Malthus and Fourier

Volume 2: Integrals and Geometry in R^n
27: The Integral
28: Properties of the Integral
29. The Logarithm log(x)
30. Numerical Quadrature
31. The Exponential Function exp(x) = e^x
32. Trigonometric Functions
33. The Functions exp(z), log(z), sin(z) and cos(z) for z e C
34. Techniques of Integration
35. Solving Differential Equations Using the Exponential
36. Improper Integrals
37. Series
38. Scalar Autonomous Initial Value Problems
39. Separable Scalar Initial Value Problems
40. The General Initial Value Problem
41. Calculus Tool Bag I
42. Analytic Geometry in R^n
43. The Spectral Theorem
44. Solving Linear Algebraic Systems
45. Linear Algebra Tool Bag
46. The Matrix Exponential exp(xA)
47. Lagrange and the Principle of Least Action
48. N-Body Systems
49. The Crash Model
50. Electrical Circuits
51. String Theory
52. Piecewise Linear Approximation
53. FEM for Two-Point Boundary Value Problems

Volume 3: Calculus in Several Dimensions
54. Vector-Valued Functions of Several Real Variables
55. Level Curves/Surfaces and the Gradient
56. Linearization and Stability of Initial Value Problems
57. Adaptive Solvers for IVPs
58. Lorenz and the Essence of Chaos
59. The Solar System
60. Optimization
61. The Divergence, Rotation and Laplacian
62. Meteorology and Coriolis Forces
63. Curve Integrals
64. Double Integrals
65. Surface Integrals
66. Multiple Integrals
67. Gauss' Theorem and Green's Formula in R^2
68. Gauss' Theorem and Green's Formula in R^3
69. Stoke's Theorem
70. Potential Fields
71. Center of Mass and Archimedes' Principle
72. Newton's Nightmare
73. Laplacian Models
74. Chemical Reactions
75. Calculus Tool Bag II
76. Piecewise Linear Polynomials in R^2 and R^3
77. FEM for Boundary Value Problems in R^2 and R^3
78. Inverse Problems
79. Optimal Control
80. Differential Equations Tool Bag
81. Applications Tool Bag
82. Analytic Functions
83. Fourier Series
84. Fourier Transforms
85. Analytic Functions Tool Bag
86. Fourier Analysis Tool Bag
87. Incompressible Navier-Stokes: Quick and Easy

This book/series has some problems; however, the attempt to wed Mathematical Analysis, Numerical Computation, and Application AND to also talk about Calculus and Linear Algebra at the same time -- makes these three books worth a look.