Calculus and its applications

Library	Materyal Türü	Barkod	Yer Numarası	Durum
Searching... Pamukkale Merkez Kütüphanesi	Kitap	0048356	QA303G625 1999	Searching... Unknown
Searching... Pamukkale Merkez Kütüphanesi	Kitap	0048355	QA303G625 1999	Searching... Unknown

This text presents innovative ways of applying calculus to real-world situations in business, economics, life science, and social science disciplines. It aims to present a way in which technology can be used to foster understanding of several topics while it facilitates computation.

Preface	p. ix
Introduction	p. 1
0 Functions	p. 3
0.1 Functions and Their Graphs	p. 3
0.2 Some Important Functions	p. 18
0.3 The Algebra of Functions	p. 27
0.4 Zeros of Functions--The Quadratic Formula and Factoring	p. 34
0.5 Exponents and Power Functions	p. 42
0.6 Functions and Graphs in Applications	p. 49
Graphing Functions Using Technology	p. 62
Chapter Project	p. 68
1 The Derivative	p. 70
1.1 The Slope of a Straight Line	p. 72
1.2 The Slope of a Curve at a Point	p. 83
1.3 The Derivative	p. 89
1.4 Limits and the Derivative	p. 101
1.5 Differentiability and Continuity	p. 111
1.6 Some Rules for Differentiation	p. 116
1.7 More About Derivatives	p. 123
1.8 The Derivative as a Rate of Change	p. 128
Chapter Project	p. 143
2 Applications of the Derivative	p. 144
2.1 Describing Graphs of Functions	p. 144
2.2 The First and Second Derivative Rules	p. 156
2.3 Curve Sketching (Introduction)	p. 166
2.4 Curve Sketching (Conclusion)	p. 173
2.5 Optimization Problems	p. 180
2.6 Further Optimization Problems	p. 189
2.7 Applications of Derivatives to Business and Economics	p. 198
Chapter Project	p. 213
3 Techniques of Differentiation	p. 214
3.1 The Product and Quotient Rules	p. 214
3.2 The Chain Rule and the General Power Rule	p. 222
3.3 Implicit Differentiation and Related Rates	p. 228
Chapter Project	p. 242
4 The Exponential and Natural Logarithm Functions	p. 243
4.1 Exponential Functions	p. 243
4.2 The Exponential Function e[superscript x]	p. 247
4.3 Differentiation of Exponential Functions	p. 252
4.4 The Natural Logarithm Function	p. 257
4.5 The Derivative of ln x	p. 262
4.6 Properties of the Natural Logarithm Function	p. 266
Chapter Project	p. 272
5 Applications of the Exponential and Natural Logarithm Functions	p. 274
5.1 Exponential Growth and Decay	p. 274
5.2 Compound Interest	p. 284
5.3 Applications of the Natural Logarithm Function to Economics	p. 292
5.4 Further Exponential Models	p. 298
Chapter Project	p. 312
6 The Definite Integral	p. 313
6.1 Antidifferentiation	p. 314
6.2 Areas and Riemann Sums	p. 323
6.3 Definite Integrals and the Fundamental Theorem	p. 332
6.4 Areas in the xy-Plane	p. 344
6.5 Applications of the Definite Integral	p. 354
Chapter Project	p. 366
7 Functions of Several Variables	p. 367
7.1 Examples of Functions of Several Variables	p. 367
7.2 Partial Derivatives	p. 374
7.3 Maxima and Minima of Functions of Several Variables	p. 383
7.4 Lagrange Multipliers and Constrained Optimization	p. 391
7.5 The Method of Least Squares	p. 402
7.6 Nonlinear Regression	p. 409
7.7 Double Integrals	p. 421
Chapter Project	p. 429
8 The Trigonometric Functions	p. 430
8.1 Radian Measure of Angles	p. 430
8.2 The Sine and the Cosine	p. 434
8.3 Differentiation and Integration of sin t and cos t	p. 442
8.4 The Tangent and Other Trigonometric Functions	p. 452
Chapter Project	p. 459
9 Techniques of Integration	p. 460
9.1 Integration by Substitution	p. 461
9.2 Integration by Parts	p. 468
9.3 Evaluation of Definite Integrals	p. 472
9.4 Approximation of Definite Integrals	p. 477
9.5 Some Applications of the Integral	p. 488
9.6 Improper Integrals	p. 493
Chapter Project	p. 502
10 Differential Equations	p. 503
10.1 Solutions of Differential Equations	p. 503
10.2 Separation of Variables	p. 510
10.3 Numerical Solution of Differential Equations	p. 519
10.4 Graphing Solutions of Differential Equations	p. 525
10.5 Applications of Differential Equations	p. 535
Chapter Project	p. 547
11 Taylor Polynomials and Infinite Series	p. 548
11.1 Taylor Polynomials	p. 548
11.2 The Newton-Raphson Algorithm	p. 556
11.3 Infinite Series	p. 565
11.4 Series with Positive Terms	p. 575
11.5 Taylor Series	p. 581
Chapter Project	p. 592
12 Probability and Calculus	p. 593
12.1 Discrete Random Variables	p. 593
12.2 Continuous Random Variables	p. 601
12.3 Expected Value and Variance	p. 610
12.4 Exponential and Normal Random Variables	p. 616
12.5 Poisson and Geometric Random Variables	p. 626
Chapter Project	p. 639
Appendix A Calculus and the TI-82 Calculator	p. A1
Appendix B Calculus and the TI-83/TI-83 Plus Calculators	p. A6
Appendix C Calculus and the TI-85 Calculator	p. A11
Appendix D Calculus and the TI-86 Calculator	p. A16
Appendix E Areas under the Standard Normal Curve	p. A22
Answers to Exercises	p. A23
Index	p. I1

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