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Biocalculus: Calculus, Probability, and Statistics for the Life Sciences New edition [Kõva köide]

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(McMaster University)
  • Formaat: Hardback, 1032 pages, kõrgus x laius x paksus: 45x220x256 mm, kaal: 2267 g
  • Ilmumisaeg: 22-Jul-2015
  • Kirjastus: Brooks/Cole
  • ISBN-10: 1305114035
  • ISBN-13: 9781305114036
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Biocalculus: Calculus, Probability, and Statistics for the Life Sciences New editionSuurem pilt
  • Formaat: Hardback, 1032 pages, kõrgus x laius x paksus: 45x220x256 mm, kaal: 2267 g
  • Ilmumisaeg: 22-Jul-2015
  • Kirjastus: Brooks/Cole
  • ISBN-10: 1305114035
  • ISBN-13: 9781305114036
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781305114036.html
Märksõnad:
BIOCALCULUS: CALCULUS, PROBABILITY, AND STATISTICS FOR THE LIFE SCIENCES shows students how calculus relates to biology, with a style that maintains rigor without being overly formal. The text motivates and illustrates the topics of calculus with examples drawn from many areas of biology, including genetics, biomechanics, medicine, pharmacology, physiology, ecology, epidemiology, and evolution, to name a few. Particular attention has been paid to ensuring that all applications of the mathematics are genuine, and references to the primary biological literature for many of these has been provided so that students and instructors 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 book is motivated by the mathematical material. Students will come away with a sound knowledge of mathematics, an understanding of the importance of mathematical arguments, and a clear understanding of how these mathematical concepts and techniques are central in the life sciences.
Preface xv
To the Student 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 Study 2 Hosts, Parasites, and Time-Travel
xlvi
1 Functions and Sequences 1(88)
1.1 Four Ways to Represent a Function
2(15)
Representations of Functions
Piecewise Defined Functions
Symmetry
Periodic Functions
Increasing and Decreasing Functions
1.2 A Catalog of Essential Functions
17(14)
Linear Models
Polynomials
Power Functions
Rational Functions
Algebraic Functions
Trigonometric Functions
Exponential Functions
Logarithmic Functions
1.3 New Functions from Old Functions
31(10)
Transformations of Functions
Combinations of Functions
Project: The Biomechanics of Human Movement
40(1)
1.4 Exponential Functions
41(11)
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(18)
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)
1.6 Sequences and Difference Equations
70(10)
Recursive Sequences: Difference Equations
Discrete-Time Models in the Life Sciences
Project: Drug Resistance in Malaria
78(2)
Review
80(4)
Case Study 1a Kill Curves and Antibiotic Effectiveness
84(5)
2 Limits 89(66)
2.1 Limits of Sequences
90(12)
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(1)
2.2 Limits of Functions at Infinity
102(9)
The Monod Growth Function
Definition of a Limit at Infinity
Limits Involving Exponential Functions
Infinite Limits at Infinity
2.3 Limits of Functions at Finite Numbers
111(14)
Velocity Is a Limit
Limits: Numerical and Graphical Methods
One-Sided Limits
Infinite Limits
2.4 Limits: Algebraic Methods
125(12)
The Limit Laws
Additional Properties of Limits
Limits of Trigonometric Functions
2.5 Continuity
137(12)
Definition of a Continuous Function
Which Functions Are Continuous?
Approximating Discontinuous Functions by Continuous Ones
Review
149(2)
Case Study 2a Hosts, Parasites, and Time-Travel
151(4)
3 Derivatives 155(94)
3.1 Derivatives and Rates of Change
156(12)
Measuring the Rate of Increase of Blood Alcohol Concentration
Tangent Lines
Derivatives
Rates of Change
3.2 The Derivative as a Function
168(13)
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
3.3 Basic Differentiation Formulas
181(13)
Power Functions
New Derivatives from Old
Exponential Functions
Sine and Cosine Functions
3.4 The Product and Quotient Rules
194(8)
The Product Rule
The Quotient Rule
Trigonometric Functions
3.5 The Chain Rule
202(13)
Combining the Chain Rule with Other Rules
Exponential Functions with Arbitrary Bases
Longer Chains
Implicit Differentiation
Related Rates
How To Prove the Chain Rule
3.6 Exponential Growth and Decay
215(7)
Population Growth
Radioactive Decay
Newton's Law of Cooling
Project: Controlling Red Blood Cell Loss During Surgery
222(1)
3.7 Derivatives of the Logarithmic and Inverse Tangent Functions
222(8)
Differentiating Logarithmic Functions
Logarithmic Differentiation
The Number e as a Limit
Differentiating the Inverse Tangent Function
3.8 Linear Approximations and Taylor Polynomials
230(10)
Tangent Line Approximations
Newton's Method
Taylor Polynomials
Project: Harvesting Renewable Resources
239(1)
Review
240(5)
Case Study 1b Kill Curves and Antibiotic Effectiveness
245(4)
4 Applications of Derivatives 249(66)
4.1 Maximum and Minimum Values
250(11)
Absolute and Local Extreme Values
Fermat's Theorem
The Closed Interval Method
Project: The Calculus of Rainbows
259(2)
4.2 How Derivatives Affect the Shape of a Graph
261(13)
The Mean Value Theorem
Increasing and Decreasing Functions
Concavity
Graphing with Technology
4.3 L'Hospital's Rule: Comparing Rates of Growth
274(11)
Indeterminate Quotients
Which Functions Grow Fastest?
Indeterminate Products
Indeterminate Differences
Project: Mutation-Selection Balance in Genetic Diseases
284(1)
4.4 Optimization Problems
285(14)
Project: Flapping and Gliding
297(1)
Project: The Tragedy of the Commons: An Introduction to Game Theory
298(1)
4.5 Recursions: Equilibria and Stability
299(7)
Equilibria
Cobwebbing
Stability Criterion
4.6 Antiderivatives
306(6)
Review
312(3)
5 Integrals 315(72)
5.1 Areas, Distances, and Pathogenesis
316(13)
The Area Problem
The Distance Problem
Pathogenesis
5.2 The Definite Integral
329(13)
Calculating Integrals
The Midpoint Rule
Properties of the Definite Integral
5.3 The Fundamental Theorem of Calculus
342(12)
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(1)
5.4 The Substitution Rule
354(8)
Substitution in Indefinite Integrals
Substitution in Definite Integrals
Symmetry
5.5 Integration by Parts
362(6)
Indefinite Integrals
Definite Integrals
5.6 Partial Fractions
368(3)
5.7 Integration Using Tables and Computer Algebra Systems
371(5)
Tables of Integrals
Computer Algebra Systems
Can We Integrate All Continuous Functions?
5.8 Improper Integrals
376(5)
Review
381(4)
Case Study 1c Kill Curves and Antibiotic Effectiveness
385(2)
6 Applications of Integrals 387(32)
6.1 Areas Between Curves
388(9)
Cerebral Blood Flow
Project: Disease Progression and Immunity
394(1)
Project: The Gini Index
395(2)
6.2 Average Values
397(3)
6.3 Further Applications to Biology
400(5)
Survival and Renewal
Blood Flow
Cardiac Output
6.4 Volumes
405(7)
Review
412(2)
Case Study 1d Kill Curves and Antibiotic Effectiveness
414(2)
Case Study 2b Hosts, Parasites, and Time-Travel
416(3)
7 Differential Equations 419(68)
7.1 Modeling with Differential Equations
420(11)
Models of Population Growth
Classifying Differential Equations
Project: Chaotic Blowflies and the Dynamics of Populations
430(1)
7.2 Phase Plots, Equilibria, and Stability
431(9)
Phase Plots
Equilibria and Stability
A Mathematical Derivation of the Local Stability Criterion
Project: Catastrophic Population Collapse: An Introduction to Bifurcation Theory
438(2)
7.3 Direction Fields and Euler's Method
440(9)
Direction Fields
Euler's Method
7.4 Separable Equations
449(10)
Project: Why Does Urea Concentration Rebound after Dialysis?
458(1)
7.5 Systems of Differential Equations
459(9)
Parametric Curves
Systems of Two Autonomous Differential Equations
Project: The Flight Path of Hunting Raptors
467(1)
7.6 Phase Plane Analysis
468(12)
Equilibria
Qualitative Dynamics in the Phase Plane
Project: Determining the Critical Vaccination Coverage
479(1)
Review
480(4)
Case Study 2c Hosts, Parasites, and Time-Travel
484(3)
8 Vectors and Matrix Models 487(78)
8.1 Coordinate Systems
488(8)
Three-Dimensional Space
Higher-Dimensional Space
8.2 Vectors
496(9)
Combining Vectors
Components
8.3 The Dot Product
505(9)
Projections
Project: Microarray Analysis of Genome Expression
513(1)
Project: Vaccine Escape
514(1)
8.4 Matrix Algebra
514(6)
Matrix Notation
Matrix Addition and Scalar Multiplication
Matrix Multiplication
8.5 Matrices and the Dynamics of Vectors
520(8)
Systems of Difference Equations: Matrix Models
Leslie Matrices
Summary
8.6 The Inverse and Determinant of a Matrix
528(9)
The Inverse of a Matrix
The Determinant of a Matrix
Solving Systems of Linear Equations
Project: Cubic Splines
536(1)
8.7 Eigenvectors and Eigenvalues
537(10)
Characterizing How Matrix Multiplication Changes Vectors
Eigenvectors and Eigenvalues
8.8 Iterated Matrix Models
547(13)
Solving Matrix Models
Solutions with Complex Eigenvalues
Perron-Frobenius Theory
Project: The Emergence of Geometric Order in Proliferating Cells
559(1)
Review
560(5)
9 Multivariable Calculus 565(66)
9.1 Functions of Several Variables
566(19)
Functions of Two Variables
Graphs
Level Curves
Functions of Three Variables
Limits and Continuity
9.2 Partial Derivatives
585(11)
Interpretations of Partial Derivatives
Functions of More Than Two Variables
Higher Derivatives
Partial Differential Equations
9.3 Tangent Planes and Linear Approximations
596(8)
Tangent Planes
Linear Approximations
Project: The Speedo LZR Racer
603(1)
9.4 The Chain Rule
604(6)
Implicit Differentiation
9.5 Directional Derivatives and the Gradient Vector
610(9)
Directional Derivatives
The Gradient Vector
Maximizing the Directional Derivative
9.6 Maximum and Minimum Values
619(9)
Absolute Maximum and Minimum Values
Review
628(3)
10 Systems of Linear Differential Equations 631(52)
10.1 Qualitative Analysis of Linear Systems
632(8)
Terminology
Saddles
Nodes
Spirals
10.2 Solving Systems of Linear Differential Equations
640(12)
The General Solution
Nullclines versus Eigenvectors
Saddles
Nodes
Spirals
Long-Term Behavior
10.3 Applications
652(13)
Metapopulations
Natural Killer Cells and Immunity
Gene Regulation
Transport of Environmental Pollutants
Project: Pharmacokinetics of Antimicrobial Dosing
664(1)
10.4 Systems of Nonlinear Differential Equations
665(11)
Linear and Nonlinear Differential Equations
Local Stability Analyses
Linearization
Examples
Review
676(3)
Case Study 2d: Hosts, Parasites, and Time-Travel
679(4)
11 Descriptive Statistics 683(44)
11.1 Numerical Descriptions of Data
684(9)
Types of Variables
Categorical Data
Numerical Data: Measures of Central Tendency
Numerical Data: Measures of Spread
Numerical Data: The Five-Number Summary
Outliers
11.2 Graphical Descriptions of Data
693(10)
Displaying Categorical Data
Displaying Numerical Data: Histograms
Interpreting Area in Histograms
The Normal Curve
11.3 Relationships between Variables
703(10)
Two Categorical Variables
Categorical and Numerical Variables
Two Numerical Variables
11.4 Populations, Samples, and Inference
713(9)
Populations and Samples
Properties of Samples
Types of Data
Causation
Project: The Birth Weight Paradox
720(2)
Review
722(5)
12 Probability 727(76)
12.1 Principles of Counting
728(9)
Permutations
Combinations
12.2 What Is Probability?
737(14)
Experiments, Trials, Outcomes, and Events
Probability When Outcomes Are Equally Likely
Probability in General
12.3 Conditional Probability
751(16)
Conditional Probability
The Multiplication Rule and Independence
The Law of Total Probability
Bayes' Rule
Project: Testing for Rare Diseases
766(1)
12.4 Discrete Random Variables
767(19)
Describing Discrete Random Variables
Mean and Variance of Discrete Random Variables
Bernoulli Random Variables
Binomial Random Variables
Project: DNA Supercoiling
783(1)
Project: The Probability of an Avian Influenza Pandemic in Humans
784(2)
12.5 Continuous Random Variables
786(13)
Describing Continuous Random Variables
Mean and Variance of Continuous Random Variables
Exponential Random Variables
Normal Random Variables
Review
799(4)
13 Inferential Statistics 803(36)
13.1 The Sampling Distribution
804(8)
Sums of Random Variables
The Sampling Distribution of the Mean
The Sampling Distribution of the Standard Deviation
13.2 Confidence Intervals
812(9)
Interval Estimates
Student's t-Distribution
13.3 Hypothesis Testing
821(8)
The Null and Alternative Hypotheses
The t-Statistic
The P-Value
Summary
13.4 Contingency Table Analysis
829(6)
Hypothesis Testing with Contingency Tables
The Chi-Squared Test Statistic
The Hypothesis Test
Summary
Review
835(4)
Appendixes 839(52)
A Intervals, Inequalities, and Absolute Values
840(5)
B Coordinate Geometry
845(10)
C Trigonometry
855(9)
D Precise Definitions of Limits
864(6)
E A Few Proofs
870(4)
F Sigma Notation
874(6)
G Complex Numbers
880(8)
H Statistical Tables
888(3)
Glossary Of Biological Terms 891(2)
Answers To Odd-Numbered Exercises 893(54)
Biological Index 947(10)
Index 957
James Stewart received the M.S. degree from Stanford University and the Ph.D. from the University of Toronto. After two years as a postdoctoral fellow at the University of London, he became Professor of Mathematics at McMaster University. His research has been in harmonic analysis and functional analysis. Stewarts books include a series of high school textbooks as well as a best-selling series of calculus textbooks published by Cengage Learning. He is also co-author, with Lothar Redlin and Saleem Watson, of a series of college algebra and precalculus textbooks. Translations of his books include those into Spanish, Portuguese, French, Italian, Korean, Chinese, Greek, Indonesian and Japanese. A talented violinist, Stewart was concertmaster of the McMaster Symphony Orchestra for many years and played professionally in the Hamilton Philharmonic Orchestra. He has given more than 20 talks worldwide on mathematics and music. Stewart was named a Fellow of the Fields Institute in 2002 and was awarded an honorary D.Sc. in 2003 by McMaster University. The library of the Fields Institute is named after him. The James Stewart Mathematics Centre was opened in October, 2003, at McMaster University.