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Biocalculus: Calculus; Probability; and Statistics for the Life Sciences

Download Biocalculus: Calculus; Probability; and Statistics for the Life Sciences written by James Stewart, Troy Day in PDF format. This book is under the category Biology and bearing the isbn/isbn13 number 1305114035/978-1305114036. You may reffer the table below for additional details of the book.

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Specifications

book-author

James Stewart, Troy Day

publisher

Cengage Learning; 1st edition (July 22; 2015)

file-type

PDF

pages

1032 pages

language

English

asin

B012TL2O1K

isbn10

1305114035

isbn13

978-1305114036


Book Description

Biocalculus: Calculus; Probability; And Statistics For The Life Sciences shows college students how calculus relates to biology; with a style that maintains rigor without being overly formal. This etextbook motivates and illustrates the topics of calculus with examples drawn from many areas of biology; including pharmacology; biomechanics; genetics; physiology; ecology; epidemiology; medicine; and evolution; to name a few. Particular attention has been paid to ensuring that all applications of the maths are genuine; and references to the primary biological literature for many of these has been provided so that instructors and college students can explore the applications in greater depth. Although the focus is on the interface between mathematics and the life sciences; the logical structure of the etextbook is motivated by the mathematical material. Most students will come away with a sound knowledge of mathematics; an understanding of the importance of math arguments; and a clear understanding of how these math concepts and techniques are central in life sciences.

book-author

James Stewart, Troy Day

publisher

Cengage Learning; 1st edition (July 22; 2015)

file-type

PDF

pages

1032 pages

language

English

asin

B012TL2O1K

isbn10

1305114035

isbn13

978-1305114036

Table of contents


Table of contents :
About the Cover Images……Page 3
About the Authors……Page 8
Contents……Page 9
Preface……Page 17
To the Student……Page 27
Calculators, Computers, and Other Graphing Devices……Page 28
Diagnostic Tests……Page 30
Prologue: Mathematics and Biology……Page 35
Case Studies in Mathematical Modeling……Page 43
Case Study 1: Kill Curves and Antibiotic Effectiveness……Page 44
Case Study 2: Hosts, Parasites, and Time-Travel……Page 48
Ch 1: Functions and Sequences……Page 51
1.1: Four Ways to Represent a Function……Page 52
1.2: A Catalog of Essential Functions……Page 67
1.3: New Functions from Old Functions……Page 81
1.4: Exponential Functions……Page 91
1.5: Logarithms; Semilog and Log-Log Plots……Page 102
1.6: Sequences and Difference Equations……Page 120
Chapter 1: Review……Page 130
Ch 2: Limits……Page 139
2.1: Limits of Sequences……Page 140
2.2: Limits of Functions at Infinity……Page 152
2.3: Limits of Functions at Finite Numbers……Page 161
2.4: Limits: Algebraic Methods……Page 175
2.5: Continuity……Page 187
Chapter 2: Review……Page 199
Ch 3: Derivatives……Page 205
3.1: Derivatives and Rates of Change……Page 206
3.2: The Derivative as a Function……Page 218
3.3: Basic Differentiation Formulas……Page 231
3.4: The Product and Quotient Rules……Page 244
3.5: The Chain Rule……Page 252
3.6: Exponential Growth and Decay……Page 265
3.7: Derivatives of the Logarithmic and Inverse Tangent Functions……Page 272
3.8: Linear Approximations and Taylor Polynomials……Page 280
Chapter 3: Review……Page 290
Ch 4: Applications of Derivatives……Page 299
4.1: Maximum and Minimum Values……Page 300
4.2: How Derivatives Affect the Shape of a Graph……Page 311
4.3: L’Hospital’s Rule: Comparing Rates of Growth……Page 324
4.4: Optimization Problems……Page 335
4.5: Recursions: Equilibria and Stability……Page 349
4.6: Antiderivatives……Page 356
Chapter 4: Review……Page 362
Ch 5: Integrals……Page 365
5.1: Areas, Distances, and Pathogenesis……Page 366
5.2: The Definite Integral……Page 379
5.3: The Fundamental Theorem of Calculus……Page 392
5.4: The Substitution Rule……Page 404
5.5: Integration by Parts……Page 412
5.6: Partial Fractions……Page 418
5.7: Integration Using Tables and Computer Algebra Systems……Page 421
5.8: Improper Integrals……Page 426
Chapter 5: Review……Page 431
Ch 6: Applications of Integrals……Page 437
6.1: Areas between Curves……Page 438
6.2: Average Values……Page 447
6.3: Further Applications to Biology……Page 450
6.4: Volumes……Page 455
Chapter 6: Review……Page 462
Ch 7: Differential Equations……Page 469
7.1: Modeling with Differential Equations……Page 470
7.2: Phase Plots, Equilibria, and Stability……Page 481
7.3: Direction Fields and Euler’s Method……Page 490
7.4: Separable Equations……Page 499
7.5: Systems of Differential Equations……Page 509
7.6: Phase Plane Analysis……Page 518
Chapter 7: Review……Page 530
Ch 8: Vectors and Matrix Models……Page 537
8.1: Coordinate Systems……Page 538
8.2: Vectors……Page 546
8.3: The Dot Product……Page 555
8.4: Matrix Algebra……Page 564
8.5: Matrices and the Dynamics of Vectors……Page 570
8.6: The Inverse and Determinant of a Matrix……Page 578
8.7: Eigenvectors and Eigenvalues……Page 587
8.8: Iterated Matrix Models……Page 597
Chapter 8: Review……Page 610
Ch 9: Multivariable Calculus……Page 615
9.1: Functions of Several Variables……Page 616
9.2: Partial Derivatives……Page 635
9.3: Tangent Planes and Linear Approximations……Page 646
9.4: The Chain Rule……Page 654
9.5: Directional Derivatives and the Gradient Vector……Page 660
9.6: Maximum and Minimum Values……Page 669
Chapter 9: Review……Page 678
Ch 10: Systems of Linear Differential Equations……Page 681
10.1: Qualitative Analysis of Linear Systems……Page 682
10.2: Solving Systems of Linear Differential Equations……Page 690
10.3: Applications……Page 702
10.4: Systems of Nonlinear Differential Equations……Page 715
Chapter 10: Review……Page 726
Ch 11: Descriptive Statistics……Page 733
11.1: Numerical Descriptions of Data……Page 734
11.2: Graphical Descriptions of Data……Page 743
11.3: Relationships between Variables……Page 753
11.4: Populations, Samples, and Inference……Page 763
Chapter 11: Review……Page 772
Ch 12: Probability……Page 777
12.1: Principles of Counting……Page 778
12.2: What is Probability?……Page 787
12.3: Conditional Probability……Page 801
12.4: Discrete Random Variables……Page 817
12.5: Continuous Random Variables……Page 836
Chapter 12: Review……Page 849
Ch 13: Inferential Statistics……Page 853
13.1: The Sampling Distribution……Page 854
13.2: Confidence Intervals……Page 862
13.3: Hypothesis Testing……Page 871
13.4: Contingency Table Analysis……Page 879
Chapter 13: Review……Page 885
Appendixes……Page 889
Appendix A: Intervals, Inequalities, and Absolute Values……Page 890
Appendix B: Coordinate Geometry……Page 895
Appendix C: Trigonometry……Page 905
Appendix D: Precise Definitions of Limits……Page 914
Appendix E: A Few Proofs……Page 920
Appendix F: Sigma Notation……Page 924
Appendix G: Complex Numbers……Page 930
Appendix H: Statistical Tables……Page 938
Glossary of Biological Terms……Page 941
Answers to Odd-Numbered Exercises……Page 943
Biological Index……Page 997
Index……Page 1007

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