Calculus with Applications, Brief Version

Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
Contents......Page 6
Chapter R: Algebra Reference......Page 22
R.1. Polynomials......Page 23
R.2. Factoring......Page 26
R.3. Rational Expressions......Page 29
R.4. Equations......Page 32
R.5. Inequalities......Page 38
R.6. Exponents......Page 42
R.7. Radicals......Page 47
Chapter 1: Linear Functions......Page 52
1.1. Slopes and Equations of Lines......Page 53
1.2. Linear Functions and Applications......Page 68
1.3. The Least Squares Line......Page 78
Chapter 1: Review......Page 91
Extended Application: Using Extrapolation to Predict Life Expectancy......Page 97
Chapter 2: Nonlinear Functions......Page 99
2.1. Properties of Functions......Page 100
2.2. Quadratic Functions; Translation and Reflection......Page 113
2.3. Polynomial and Rational Functions......Page 127
2.4. Exponential Functions......Page 140
2.5. Logarithmic Functions......Page 151
2.6. Applications: Growth and Decay; Mathematics of Finance......Page 164
Chapter 2: Review......Page 172
Extended Application: Power Functions......Page 180
Chapter 3: The Derivative......Page 184
3.1. Limits......Page 185
3.2. Continuity......Page 203
3.3. Rates of Change......Page 212
3.4. Definition of the Derivative......Page 225
3.5. Graphical Differentiation......Page 244
Chapter 3: Review......Page 251
Extended Application: A Model for Drugs Administered Intravenously......Page 257
Chapter 4: Calculating the Derivative......Page 260
4.1. Techniques for Finding Derivatives......Page 261
4.2. Derivatives of Products and Quotients......Page 277
4.3. The Chain Rule......Page 284
4.4. Derivatives of Exponential Functions......Page 294
4.5. Derivatives of Logarithmic Functions......Page 302
Chapter 4: Review......Page 309
Extended Application: Electric Potential and Electric Field......Page 314
Chapter 5: Graphs and the Derivative......Page 317
5.1. Increasing and Decreasing Functions......Page 318
5.2. Relative Extrema......Page 329
5.3. Higher Derivatives, Concavity, and the Second Derivative Test......Page 341
5.4. Curve Sketching......Page 356
Chapter 5: Review......Page 365
Extended Application: A Drug Concentration Model for Orally Administered Medications......Page 369
Chapter 6: Applications of the Derivative......Page 372
6.1. Absolute Extrema......Page 373
6.2. Applications of Extrema......Page 382
6.3. Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand......Page 392
6.4. Implicit Differentiation......Page 401
6.5. Related Rates......Page 407
6.6. Differentials: Linear Approximation......Page 414
Chapter 6: Review......Page 420
Extended Application: A Total Cost Model for a Training Program......Page 424
Chapter 7: Integration......Page 426
7.1. Antiderivatives......Page 427
7.2. Substitution......Page 439
7.3. Area and the Definite Integral......Page 447
7.4. The Fundamental Theorem of Calculus......Page 459
7.5. The Area Between Two Curves......Page 469
7.6. Numerical Integration......Page 478
Chapter 7: Review......Page 487
Extended Application: Estimating Depletion Dates for Minerals......Page 492
Chapter 8: Further Techniques and Applications of Integration......Page 496
8.1. Integration by Parts......Page 497
8.2. Volume and Average Value......Page 506
8.3. Continuous Money Flow......Page 513
8.4. Improper Integrals......Page 521
Chapter 8: Review......Page 527
Extended Application: Estimating Learning Curves in Manufacturing with Integrals......Page 530
Chapter 9: Multivariable Calculus......Page 533
9.1. Functions of Several Variables......Page 534
9.2. Partial Derivatives......Page 545
9.3. Maxima and Minima......Page 557
9.4. Lagrange Multipliers......Page 566
9.5. Total Differentials and Approximations......Page 575
9.6. Double Integrals......Page 580
Chapter 9: Review......Page 591
Extended Application: Using Multivariable Fitting to Create a Response Surface Design......Page 597
Appendix A: Solutions to Prerequisite Skills Diagnostic Test......Page 601
Appendix B: Tables......Page 604
Answers to Selected Exercises......Page 607
Credits......Page 635
Index of Applications......Page 636
Index......Page 640
Sources......Page 646