Biocalculus: calculus, probability, and statistics for the life sciences
Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston, Ma.
Cengage Learning
2016 [2015 erschienen]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XLVII, 973 S. graph. Darst. 26 cm |
| ISBN: | 9781305114036 |
Internformat
MARC
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| 245 | 1 | 0 | |a Biocalculus |b calculus, probability, and statistics for the life sciences |c James Stewart ; Troy Day |
| 264 | 1 | |a Boston, Ma. |b Cengage Learning |c 2016 [2015 erschienen] | |
| 300 | |a XLVII, 973 S. |b graph. Darst. |c 26 cm | ||
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| 650 | 7 | |a calculation |2 cabt | |
| 650 | 7 | |a biometry |2 cabt | |
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Datensatz im Suchindex
| _version_ | 1804174720485031936 |
|---|---|
| adam_text | iBBsigeiSig
Calculus for the Life Sciences
lames Stewart
McMaster University and University of Toronto
Troy Day
Queen s University
CENGAGE
QCJ Learning*
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
Contents
Preface xv
To thelstudent xxv
Calculators, Computers, and Other Graphing Devices xxvi
Diagnostic Tests xxviii
Prologue: Mathematics and Biology xxxiii
Case Studies in Mathematical Modeling xli
CASE STUDY 1 Kill Curves and Antibiotic Effectiveness xlii
CASE STUDY2 Hosts, Parasites, and Time-Travel xlvi
1 Functions and Sequences 1
1 1 Four Ways to Represent a Function 2
• Representations of Functions • Piecewise Defined Functions • Symmetry
• Periodic Functions • Increasing and Decreasing Functions
12A Catalog of Essential Functions 17
• Linear Models • Polynomials • Power Functions • Rational Functions
• Algebraic Functions • Trigonometric Functions • Exponential Functions
• Logarithmic Functions
1 3 New Functions from Old Functions 31
• Transformations of Functions • Combinations of Functions
PROJECT The Biomechanics of Human Movement 40
1 4 Exponential Functions 41
• The Growth of Malarial Parasites • Exponential Functions • Exponential Growth
• HIV Density and Exponential Decay • The Number e
1 5 Logarithms; Semilog and Log-Log Plots 52
• Inverse Functions • Logarithmic Functions • Natural Logarithms
• Graph and Growth of the Natural Logarithm • Semilog Plots • Log-Log Plots
PROJECT The Coding Function of DNA 69
1 6 Sequences and Difference Equations 70
• Recursive Sequences: Difference Equations
• Discrete-Time Models in the Life Sciences
PROJECT Drug Resistance in Malaria 78
Review 80
CASE STUDY la Kill Curves and Antibiotic Effectiveness 84
vii
viii CONTENTS
Limits 89
2 1 Limits of Sequences 90
• The Long-Term Behavior of a Sequence • Definition of a Limit • Limit Laws
• Geometric Sequences • Recursion for Medication • Geometric Series
• The Logistic Sequence in the Long Run
PROJECT Modeling the Dynamics of Viral Infections 101
2 2 Limits of Functions at Infinity 102
• The Monod Growth Function • Definition of a Limit at Infinity
• LirTMts Involving Exponential Functions • Infinite Limits at Infinity
2 3 Limits of Functions at Finite Numbers 111
• Velocity Is a Limit • Limits: Numerical and Graphical Methods
• One-Sided Limits • Infinite Limits
2 4 Limits: Algebraic Methods 125
• The Limit Laws • Additional Properties of Limits
• Limits of Trigonometric Functions
2 5 Continuity 137
• Definition of a Continuous Function • Which Functions Are Continuous?
• Approximating Discontinuous Functions by Continuous Ones
Review 149
CASE STUDY 2a Hosts, Parasites, and Time-Travel 151
Derivatives 155
Derivatives and Rates of Change 156
• Measuring the Rate of Increase of Blood Alcohol Concentration
• Derivatives • Rates of Change
• Tangent Lines
The Derivative as a Function 168
• Graphing a Derivative from a Function s Graph • Finding a Derivative from a
Function s Formula • Differentiability • Higher Derivatives • What a Derivative
Tells Us about a Function
Basic Differentiation Formulas 181
• Power Functions • New Derivatives from Old
• Sine and Cosine Functions
Exponential Functions
3 4 The Product and Quotient Rules 194
• The Product Rule • The Quotient Rule • Trigonometric Functions
3 5 The Chain Rule 202
• Combining the Chain Rule with Other Rules • Exponential Functions with
Arbitrary Bases • Longer Chains • Implicit Differentiation • Related Rates
• How To Prove the Chain Rule
CONTENTS ix
3 6 Exponential Growth and Decay 215
• Population Growth • Radioactive Decay • Newton s Law of Cooling
PROJECT: Controlling Red Blood Cell Loss During Surgery 222
3 7 Derivatives of the Logarithmic and Inverse Tangent Functions 222
• Differentiating Logarithmic Functions • Logarithmic Differentiation
• The Number e as a Limit • Differentiating the Inverse Tangent Function
3 8 Linear Approximations and Taylor Polynomials 230
• Tangent Line Approximations • Newton s Method • Taylor Polynomials
PROJECT: Harvesting Renewable Resources 239
Review 240
CASE STUDY lb Kill Curves and Antibiotic Effectiveness 245
Applications of Derivatives 249
4 1 Maximum and Minimum Values 250
• Absolute and Local Extreme Values • Fermat s Theorem
• The Closed Interval Method
PROJECT: The Calculus of Rainbows 259
4 2 How Derivatives Affect the Shape of a Graph 261
• The Mean Value Theorem • Increasing and Decreasing Functions • Concavity
• Graphing with Technology
4 3 L Hospital s Rule; Comparing Rates of Growth 274
• Indeterminate Quotients • Which Functions Grow Fastest?
• Indeterminate Products • Indeterminate Differences
PROJECT: Mutation-Selection Balance in Genetic Diseases 284
4 4 Optimization Problems 285
PROJECT: Flapping and Gliding 297
PROJECT: The Tragedy of the Commons: An Introduction to Game Theory 298
4 5 Recursions: Equilibria and Stability 299
« Equilibria • Cobwebbing • Stability Criterion
4 6 Antiderivatives 306
Review 312
5 Integrals 315
5 1 Areas, Distances, and Pathogenesis 316
• The Area Problem • The Distance Problem • Pathogenesis
5 2 The Definite Integral 329
• Calculating Integrals • The Midpoint Rule • Properties of the Definite Integral
5 3 The Fundamental Theorem of Calculus 342
• Evaluating Definite Integrals • Indefinite Integrals • The Net Change Theorem
• The Fundamental Theorem • Differentiation and Integration as Inverse Processes
PROJECT: The Outbreak Size of an Infectious Disease 354
5 4 The Substitution Rule 354
• Substitution in Indefinite Integrals • Substitution in Definite Integrals • Symmetry
5 5 Integration by Parts 362
• Indefinite Integrals • Definite Integrals
5 6 Partial Fractions 368
5 7 Integration Using Tables and Computer Algebra Systems 371
• Tables of Integrals • Computer Algebra Systems
• Can We Integrate All Continuous Functions?
5 8 Improper Integrals 376
Review 381
CASE STUDY lc Kill Curves and Antibiotic Effectiveness 385
Applications of Integrals 387
6 1 Areas Between Curves 388
«Cerebral Blood Flow
PROJECT: Disease Progression and Immunity 394
PROJECT: The Gini Index 395
6 2 Average Values 397
6 3 Further Applications to Biology 400
• Survival and Renewal • Blood Flow • Cardiac Output
6 4 Volumes 405
Review 412
CASE STUDY Id Kill Curves and Antibiotic Effectiveness 414
CASE STUDY 2b Hosts, Parasites, and Time-Travel 416
Differential Equations 419
7 1 Modeling with Differential Equations 420
• Models of Population Growth
• Classifying Differential Equations
PROJECT: Chaotic Blowflies and the Dynamics of Populations 430
CONTENTS xi
7 2 Phase Plots, Equilibria, and Stability 431
« Phase Plots • Equilibria and Stability
• A Mathematical Derivation of the Local Stability Criterion
PROJECT: Catastrophic Population Collapse:
An Introduction to Bifurcation Theory 438
7 3 Direction Fields and Euler s Method 440
• Direction Fields • Euler s Method
7 4 Separable Equations 449
PROJECT: Why Does Urea Concentration Rebound after Dialysis? 458
7 5 Systems of Differential Equations 459
« Parametric Curves • Systems of Two Autonomous Differential Equations
PROJECT: The Flight Path of Hunting Raptors 467
7 6 Phase Plane Analysis 468
• Equilibria • Qualitative Dynamics in the Phase Plane
PROJECT: Determining the Critical Vaccination Coverage 479
Review 480
CASE STUDY 2c Hosts, Parasites, and Time-Travel 484
8 Vectors and Matrix Models 487
356-TW98 (C2)
NWKO-TW
Coordinate Systems 488
• Three-Dimensional Space • Higher-Dimensional Space
Vectors 496
• Combining Vectors • Components
The Dot Product 505
• Projections
PROJECT: Microarray Analysis of Genome Expression 513
PROJECT: Vaccine Escape 514
• Matrix Addition and Scalar Multiplication
Matrices and the Dynamics of Vectors 520
• Systems of Difference Equations: Matrix Models • Leslie Matrices
The Inverse and Determinant of a Matrix 528
• The Inverse of a Matrix • The Determinant of a Matrix
• Solving Systems of Linear Equations
PROJECT: Cubic Splines 536
Eigenvectors and Eigenvalues 537
• Characterizing How Matrix Multiplication Changes Vectors
• Eigenvectors and Eigenvalues
Matrix Algebra
• Matrix Notation Matrix Multiplication
Summary
xii CONTENTS
8 8 Iterated Matrix Models 547
• Solving Matrix Models • Solutions with Complex Eigenvalues
• Perron-Frobenius Theory
PROJECT:The Emergence of Geometric Order in Proliferating Cells 559
Review 560
Multivariable Calculus 565
9 1 Functions of Several Variables 566
» Functions of Two Variables • Graphs • Level Curves
• Functions of Three Variables • Limits and Continuity
9 2 Partial Derivatives 585
• Interpretations of Partial Derivatives • Functions of More Than Two Variables
« Higher Derivatives • Partial Differential Equations
9 3 Tangent Planes and Linear Approximations 596
• Tangent Planes • Linear Approximations
PROJECT: The Speedo LZR Racer 603
9 4 The Chain Rule 604
• Implicit Differentiation
9 5 Directional Derivatives and the Gradient Vector 610
• Directional Derivatives • The Gradient Vector
• Maximizing the Directional Derivative
9 6 Maximum and Minimum Values 619
• Absolute Maximum and Minimum Values
Review 628
10 Systems of Linear Differential Equations 631
10 1 Qualitative Analysis of Linear Systems 632
• Terminology Saddles Nodes Spirals
10 2 Solving Systems of Linear Differential Equations 640
• The General Solution • Nullclines versus Eigenvectors Saddles
• Nodes • Spirals • Long-Term Behavior
10 3 Applications 652
• Metapopulations • Natural Killer Cells and Immunity • Gene Regulation
• Transport of Environmental Pollutants
PROJECT: Pharmacokinetics of Antimicrobial Dosing 664
10 4 Systems of Nonlinear Differential Equations 665
• Linear and Nonlinear Differential Equations • Local Stability Analyses
• Linearization • Examples
Review 676
CASE STUDY 2d: Hosts, Parasites, and Time-Travel 679
CONTENTS xiii
The content listed in the shaded areas appears only in
Biocalculus: Calculus, Probability, and Statistics for the Life Sciences
11 Descriptive Statistics
Numerical Descriptions of Data
• Types of Variables Categorical Data • Numerical Data: Measures
of Central Tendency •, Numerical Data: Measures of Spread
• Numerical Data: The Five-Number Summary • Outliers
Graphical Descriptions of Data
• Displaying Categorical Data • Displaying Numerical Data: Histograms
• Interpreting Area in Histograms • The Normal Curve
Relationships between Variables
• Two Categorical Variables • Categorical and Numerical Variables
• Two Numerical Variables
Populations, Samples, and Inference
• Populations and Samples • Properties of Samples
PROJECT:The Birth Weight Paradox
Review
• Types of Data • Causation
12 Probability
12 1 Principles of Counting
• Permutations •Combinations
- ;lll|pt
12 2 What Is Probability?
• Experiments, Trials, Outcomes, and Events • Probability When Outcomes
Are Equally Likely • Probability in General
12 3 Conditional Probability
• Conditional Probability • The Multiplication Rule and Independence
• The Law of Total Probability • Bayes Rule
PROJECT: Testing for Rare Diseases
12 4 Discrete Random Variables
• Describing Discrete Random Variables • Mean and Variance of Discrete
Random Variables ° Bernoulli Random Variables • Binomial Random Variables
PROJECT: DNA Supercoiling
PROJECT:The Probability of an Avian Influenza Pandemic in Humans
12 5 Continuous Random Variables
• Describing Continuous Random Variables • Mean and Variance of Continuous
Random Variables • Exponential Random Variables • Normal Random Variables
Review
Ff,|jn:jf • : • |1 ( • I
Inferential (Statistics • i! i! •
y 1^ ii i !
13 1 The Sampling Distribution
•;Sums of Random Variables • The Sampling Distribution of the Mean
• The Sampling Distribution of the Standard Deviation
13 2 Confidence Intervals j
• Interval Estimates • Student s f-Distribution
E If !!!! |! tl: i • ! •; 1 I
I 13 3 Hypothesis Testing
• Tlie Null and Alternative Hypotheses • The t Statistic • The P-Value • Summary
13 4 Contingency Table Analysis
; « Hypothesis Testing with Contingency Tables • The Chi^Squared Test Statistic
• The Hypothesis Test • Summary
j j r ! !M i
Review , , i
:|f:r! • V • • V
APPENDIXES 683
A Intervals, Inequalities, and Absolute Values 684
B Coordinate Geometry 689
C Trigonometry 699
D Precise Definitions of Limits 708
E A Few Proofs 714
F Sigma Notation 718
G Complex Numbers 724
H Statistical Tables
GLOSSARY OF BIOLOGICAL TERMS 733
ANSWERS TO ODD-NUMBERED EXERCISES 735
BIOLOGICAL INDEX 779
INDEX 789
|
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| illustrated | Illustrated |
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| isbn | 9781305114036 |
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| spelling | Stewart, James 1941- Verfasser (DE-588)124089097 aut Biocalculus calculus, probability, and statistics for the life sciences James Stewart ; Troy Day Boston, Ma. Cengage Learning 2016 [2015 erschienen] XLVII, 973 S. graph. Darst. 26 cm txt rdacontent n rdamedia nc rdacarrier factor analysis cabt calculation cabt biometry cabt statistical analysis cabt Day, Troy 1968- Verfasser (DE-588)132966883 aut HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028002155&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stewart, James 1941- Day, Troy 1968- Biocalculus calculus, probability, and statistics for the life sciences factor analysis cabt calculation cabt biometry cabt statistical analysis cabt |
| title | Biocalculus calculus, probability, and statistics for the life sciences |
| title_auth | Biocalculus calculus, probability, and statistics for the life sciences |
| title_exact_search | Biocalculus calculus, probability, and statistics for the life sciences |
| title_full | Biocalculus calculus, probability, and statistics for the life sciences James Stewart ; Troy Day |
| title_fullStr | Biocalculus calculus, probability, and statistics for the life sciences James Stewart ; Troy Day |
| title_full_unstemmed | Biocalculus calculus, probability, and statistics for the life sciences James Stewart ; Troy Day |
| title_short | Biocalculus |
| title_sort | biocalculus calculus probability and statistics for the life sciences |
| title_sub | calculus, probability, and statistics for the life sciences |
| topic | factor analysis cabt calculation cabt biometry cabt statistical analysis cabt |
| topic_facet | factor analysis calculation biometry statistical analysis |
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