CALCULUS: APPLICATIONS AND TECHNOLOGY is a modern text that is guided by four basic principles: The Rule of Four, technology, the Way of Archimedes, and an exploratory teaching method. Where appropriate, each topic is presented graphically, numerically, algebraically, and verbally, helping students gain a richer, deeper understanding of the material. A pronounced emphasis in the text on technology, whether graphing calculators or computers, permits instructors to spend more time teaching concepts. Additionally, applications play a central role in the text and are woven into the development of the material. More than 500 referenced exercises and hundreds of data sets contained in the text make this text useful and practical for students. Most importantly, this text lets students investigate and explore calculus on their own, and discover concepts for themselves.
Author(s): Edmond C. Tomastik
Edition: 3rd Edition
Publisher: Brooks Cole
Year: 2004
Language: English
Pages: 769
Tags: Математика;Высшая математика (основы);Математика для инженерных и естественнонаучных специальностей;
Front Cover......Page 1
Title Page......Page 4
Copyright......Page 5
Table of Contents......Page 18
1. Functions......Page 21
1.0 Graphers Versus Calculus......Page 23
1.1 Functions......Page 24
1.2 Mathematical Models......Page 43
1.3 Exponential Models......Page 69
1.4 Combinations of Functions......Page 89
1.5 Logarithms......Page 97
2.1 Method of Least Squares......Page 119
2.2 Quadratic Regression......Page 131
2.3 Cubic, Quartic, and Power Regression......Page 137
2.4 Exponential and Logarithmic Regression......Page 142
2.5 Logistic Regression......Page 146
2.6 Selecting the Best Model......Page 150
3. Limits and the Derivative......Page 157
3.0 Introduction to Calculus......Page 158
3.1 Limits......Page 161
3.2 Rates of Change......Page 179
3.3 The Derivative......Page 207
3.4 Local Linearity......Page 224
4. Rules for the Derivative......Page 241
4.1 Derivatives of Powers, Exponents, and Sums......Page 242
4.2 Derivatives of Products and Quotients......Page 263
4.3 The Chain Rule......Page 273
4.4 Derivatives of Exponential and Logarithmic Functions......Page 283
4.5 Elasticity of Demand......Page 294
4.6 Management of Renewable Natural Resources......Page 303
5. Curve Sketching and Optimization......Page 313
5.1 The First Derivative......Page 314
5.2 The Second Derivative......Page 333
5.3 Limits at Infinity......Page 349
5.4 Additional Curve Sketching......Page 361
5.5 Absolute Extrema......Page 369
5.6 Optimization and Modeling......Page 379
5.7 The Logistic Model......Page 389
5.8 Implicit Differentiation and Related Rates......Page 399
6. Integration......Page 415
6.1 Antiderivatives......Page 417
6.2 Substitution......Page 427
6.3 Estimating Distance Traveled......Page 435
6.4 The Definite Integral......Page 451
6.5 The Fundamental Theorem of Calculus......Page 466
6.6 Area Between Two Curves......Page 480
6.7Additional Applications of the Integral......Page 492
7.1 Integration by Parts......Page 507
7.2 Integration Using Tables......Page 514
7.3 Numerical Integration......Page 519
7.4 Improper Integrals......Page 531
8. Functions of Several Variables......Page 541
8.1 Functions of Several Variables......Page 542
8.2 Partial Derivatives......Page 557
8.3 Extrema of Functions of Two Variables......Page 571
8.4 Lagrange Multipliers......Page 583
8.5 Tangent Plane Approximations......Page 591
8.6 Double Integrals......Page 597
A.1 Exponents and Roots......Page 617
A.2 Polynomials and Rational Expressions......Page 622
A.3 Equations......Page 627
A.4 Inequalities......Page 632
A.5 The Cartesian Coordinate System......Page 637
A.6 Lines......Page 645
A.7 Quadratic Functions......Page 659
A.8 Some Special Functions and Graphing Techniques......Page 670
B.1 Basic Geometric Formulas......Page 681
B.2 Tables of Integrals......Page 682
Answers to Selected Exercises......Page 686
Index......Page 752
