Calculus for the life sciences

✍ Scribed by Greenwell, Raymond N.; Lial, Margaret L.; Ritchey, Nathan P

• Publisher: Pearson Education Limited
• Year: 2014;2015
• Tongue: English
• Leaves: 900
• Series: Always learning
• Edition: Global edition.,Second edition
• Category: Library

✦ Synopsis

Normal 0 false false falseCalculus for the Life Sciencesfeatures interesting, relevant applications that motivate students and highlight the utility of mathematics for the life sciences. This edition also features new ways to engage students with the material, such as Your Turn exercises.KEY TOPICS:Functions; Exponential, Logarithmic, and Trigonometric Functions; The Derivative; Calculating the Derivative; Graphs and the Derivative; Applications of the Derivative; Integration; Further Techniques and Applications of Integration; Multivariable Calculus; Matrices; Differential Equations; Probability; Probability and Calculus; Discrete Dynamical Systems; Special Topics (available online); Sequences and Series; Markov ChainsMARKET:For all readers interested in calculus for the life sciences.

✦ Table of Contents

Cover......Page 1
Title......Page 2
Copyright......Page 3
Contents......Page 4
Preface......Page 8
Prerequisite Skills Diagnostic Test......Page 18
Chapter R Algebra Reference......Page 20
R.1 Polynomials......Page 21
R.2 Factoring......Page 24
R.3 Rational Expressions......Page 27
R.4 Equations......Page 30
R.5 Inequalities......Page 35
R.6 Exponents......Page 40
R.7 Radicals......Page 44
Chapter 1 Functions......Page 50
1.1 Lines and Linear Functions......Page 51
1.2 the Least Squares Line......Page 66
1.3 Properties of Functions......Page 78
1.4 Quadratic Functions; translation and Reflection......Page 90
1.5 Polynomial and Rational Functions......Page 100
Chapter 1 Review......Page 112
Extended Application Using Extrapolation to Predict Life Expectancy......Page 119
Chapter 2 Exponential, Logarithmic, and Trigonometric Functions......Page 121
2.1 Exponential Functions......Page 122
2.2 Logarithmic Functions......Page 133
2.3 Applications: Growth and Decay......Page 145
2.4 trigonometric Functions......Page 151
Chapter 2 Review......Page 166
Extended Application Power Functions......Page 173
Chapter 3 The Derivative......Page 176
3.1 Limits......Page 177
3.2 Continuity......Page 195
3.3 Rates of Change......Page 204
3.4 Definition of the Derivative......Page 216
3.5 Graphical Differentiation......Page 234
Chapter 3 Review......Page 241
Extended Application A Model for Drugs Administered Intravenously......Page 246
Chapter 4 Calculating the Derivative......Page 250
4.1 Techniques for Finding Derivatives......Page 251
4.2 Derivatives of Products and Quotients......Page 263
4.3 The Chain Rule......Page 269
4.4 Derivatives of Exponential Functions......Page 279
4.5 Derivatives of Logarithmic Functions......Page 288
4.6 Derivatives of Trigonometric Functions......Page 296
Chapter 4 Review......Page 303
Extended Application Managing Renewable Resources......Page 307
Chapter 5 Graphs and the Derivative......Page 310
5.1 Increasing and Decreasing Functions......Page 311
5.2 Relative Extrema......Page 322
5.3 Higher Derivatives, Concavity, and the Second Derivative Test......Page 333
5.4 Curve Sketching......Page 347
Chapter 5 Review......Page 357
Extended Application A Drug Concentration Model for Orally Administered Medications......Page 363
Chapter 6 Applications of the Derivative......Page 365
6.1 Absolute Extrema......Page 366
6.2 Applications of Extrema......Page 375
6.3 Implicit Differentiation......Page 386
6.4 Related Rates......Page 392
6.5 Differentials: Linear Approximation......Page 399
Chapter 6 Review......Page 405
Extended Application A total Cost Model for a Training Program......Page 409
Chapter 7 Integration......Page 411
7.1 Antiderivatives......Page 412
7.2 Substitution......Page 424
7.3 Area and the Definite Integral......Page 434
7.4 The Fundamental Theorem of Calculus......Page 447
7.5 The Area Between Two Curves......Page 461
Chapter 7 Review......Page 467
Extended Application Estimating Depletion Dates for Minerals......Page 473
Chapter 8 Further Techniques and Applications of Integration......Page 476
8.1 Numerical Integration......Page 477
8.2 Integration by Parts......Page 485
8.3 Volume and Average Value......Page 495
8.4 Improper Integrals......Page 502
Chapter 8 Review......Page 507
Extended Application Flow Systems......Page 510
Chapter 9 Multivariable Calculus......Page 513
9.1 Functions of Several Variables......Page 514
9.2 Partial Derivatives......Page 525
9.3 Maxima and Minima......Page 536
9.4 Total Differentials and Approximations......Page 545
9.5 Double Integrals......Page 551
Chapter 9 Review......Page 561
Extended Application Optimization for a Predator......Page 567
Chapter 10 Matrices......Page 569
10.1 Solution of Linear Systems......Page 570
10.2 Addition and Subtraction of Matrices......Page 588
10.3 Multiplication of Matrices......Page 595
10.4 Matrix Inverses......Page 605
10.5 Eigenvalues and Eigenvectors......Page 616
Chapter 10 Review......Page 625
Extended Application Contagion......Page 631
Chapter 11 Differential Equations......Page 632
11.1 Solutions of Elementary and Separable Differential Equations......Page 633
11.2 Linear First-Order Differential Equations......Page 646
11.3 Euler’s Method......Page 652
11.4 Linear Systems of Differential Equations......Page 658
11.5 Nonlinear Systems of Differential Equations......Page 666
11.6 Applications of Differential Equations......Page 673
Chapter 11 Review......Page 677
Extended Application Pollution of the Great Lakes......Page 681
Chapter 12 Probability......Page 684
12.1 Sets......Page 685
12.2 Introduction to Probability......Page 699
12.3 Conditional Probability; Independent Events; Bayes’ Theorem......Page 717
12.4 Discrete Random Variables; Applications to Decision Making......Page 736
Chapter 12 Review......Page 748
Extended Application Medical Diagnosis......Page 756
13.1 Continuous Probability Models......Page 757
13.2 Expected Value and Variance of Continuous Random Variables......Page 768
13.3 Special Probability Density Functions......Page 777
Chapter 13 Review......Page 791
Extended Application Exponential Waiting Times......Page 796
Chapter 14 Discrete Dynamical Systems......Page 799
14.1 Sequences......Page 800
14.2 Equilibrium Points......Page 805
14.3 Determining Stability......Page 811
Chapter 14 Review......Page 815
Extended Application Mathematical Modeling in a Dynamic World......Page 817
A Solutions to Prerequisite Skills Diagnostic Test......Page 820
B Learning Objectives......Page 823
C MathPrint Operating System for TI-84 and TI-84 Plus Silver Edition......Page 827
1 Formulas of Geometry......Page 829
2 Area Under a normal Curve......Page 830
3 Integrals......Page 832
4 Integrals Involving Trigonometric Functions......Page 833
Answers to Selected Exercises......Page 834
Credits......Page 880
Index of Applications......Page 882
Index......Page 886
Sources......Page 894