Practical Analysis in One Variable Book

	Preface
	Introduction	1
I	Numbers and Functions, Sequences and Limits	5
1	Mathematical Modeling	7
2	Natural Numbers Just Aren't Enough	15
3	Infinity and Mathematical Induction	29
4	Rational Numbers	37
5	Functions	51
6	Polynomials	61
7	Functions, Functions, and More Functions	73
8	Lipschitz Continuity	83
9	Sequences and Limits	99
10	Solving the Muddy Yard Model	125
11	Real Numbers	135
12	Functions of Real Numbers	153
13	The Bisection Algorithm	165
14	Inverse Functions	179
15	Fixed Points and Contraction Maps	191
II	Differential and Integral Calculus	215
16	The Linearization of a Function at a Point	217
17	Analyzing the Behavior of a Population Model	231
18	Interpretations of the Derivative	237
19	Differentiability on Intervals	245
20	Useful Properties of the Derivative	259
21	The Mean Value Theorem	269
22	Derivatives of Inverse Functions	279
23	Modeling with Differential Equations	285
24	Antidifferentiation	301
25	Integration	315
26	Properties of the Integral	339
27	Applications of the Integral	345
28	Rocket Propulsion and the Logarithm	355
29	Constant Relative Rate of Change and the Exponential	369
30	A Mass-Spring System and the Trigonometric Functions	387
31	Fixed Point Iteration and Newton's Method	407
	Calculus Quagmires	435
III	You Want Analysis? We've Got Your Analysis Right Here	439
32	Notions of Continuity and Differentiability	441
33	Sequences of Functions	463
34	Relaxing Integration	477
35	Delicate Limits and Gross Behavior	493
36	The Weierstrass: Approximation Theorem	509
37	The Taylor Polynomial	525
38	Polynomial Interpolation	543
39	Nonlinear Differential Equations	559
40	The Picard Iteration	569
41	The Forward Euler Method	583
	A Conclusion or an Introduction?	605
	References	607
	Index	609