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Biocalculus : calculus, probability, and statistics for the life sciences / James Stewart, McMaster University and University of Toronto, Troy Day, Queen's University.
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Title:Biocalculus : calculus, probability, and statistics for the life sciences / James Stewart, McMaster University and University of Toronto, Troy Day, Queen's University.
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Author/Creator:Stewart, James, 1941- author.
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Other Contributors/Collections:Day, Troy, 1968- author.
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Published/Created:Boston, MA, USA : Cengage Learning, [2016]
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Holdings
Holdings Record Display
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Location:BMB LIBRARY (VGH) stacksWhere is this?
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Call Number: QH323.5 .S74 2016
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Number of Items:1
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Status:Available
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Location:WOODWARD LIBRARY stacksWhere is this?
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Call Number: QH323.5 .S74 2016
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Number of Items:1
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Status:Available
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Location:BMB LIBRARY (VGH) stacksWhere is this?
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Library of Congress Subjects:Life sciences--Mathematics.
Calculus.
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Description:xlvii, 973 pages : illustrations (some color) ; 27 cm
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Notes:Includes bibliographical references and indexes.
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ISBN:1305114035 hardcover
9781305114036 hardcover
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Contents:Machine generated contents note: Case Study 1 Kill Curves and Antibiotic Effectiveness
Case Study 2 Hosts, Parasites, and Time-Travel
1.1. Four Ways to Represent a Function
Representations of Functions
Piecewise Defined Functions
Symmetry
Periodic Functions
Increasing and Decreasing Functions
1.2. Catalog of Essential Functions
Linear Models
Polynomials
Power Functions
Rational Functions
Algebraic Functions
Trigonometric Functions
Exponential Functions
Logarithmic Functions
1.3. New Functions from Old Functions
Transformations of Functions
Combinations of Functions
Project: The Biomechanics of Human Movement
1.4. Exponential Functions
Growth of Malarial Parasites
Exponential Functions
Exponential Growth
HIV Density and Exponential Decay
Number e
1.5. Logarithms; Semilog and Log-Log Plots
Inverse Functions
Logarithmic Functions
Natural Logarithms
Graph and Growth of the Natural Logarithm
Semilog Plots
Log-Log Plots
Project: The Coding Function of DNA
1.6. Sequences and Difference Equations
Recursive Sequences: Difference Equations
Discrete-Time Models in the Life Sciences
Project: Drug Resistance in Malaria
Review
Case Study 1a Kill Curves and Antibiotic Effectiveness
2.1. Limits of Sequences
Long-Term Behavior of a Sequence
Definition of a Limit
Limit Laws
Geometric Sequences
Recursion for Medication
Geometric Series
Logistic Sequence in the Long Run
Project: Modeling the Dynamics of Viral Infections
2.2. Limits of Functions at Infinity
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
Velocity Is a Limit
Limits: Numerical and Graphical Methods
One-Sided Limits
Infinite Limits
2.4. Limits: Algebraic Methods
Limit Laws
Additional Properties of Limits
Limits of Trigonometric Functions
2.5. Continuity
Definition of a Continuous Function
Which Functions Are Continuous?
Approximating Discontinuous Functions by Continuous Ones
Review
Case Study 2a Hosts, Parasites, and Time-Travel
3.1. Derivatives and Rates of Change
Measuring the Rate of Increase of Blood Alcohol Concentration
Tangent Lines
Derivatives
Rates of Change
3.2. Derivative as a Function
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
Power Functions
New Derivatives from Old
Exponential Functions
Sine and Cosine Functions
3.4. Product and Quotient Rules
Product Rule
Quotient Rule
Trigonometric Functions
3.5. Chain Rule
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
Population Growth
Radioactive Decay
Newton's Law of Cooling
Project: Controlling Red Blood Cell Loss During Surgery
3.7. Derivatives of the Logarithmic and Inverse Tangent Functions
Differentiating Logarithmic Functions
Logarithmic Differentiation
Number e as a Limit
Differentiating the Inverse Tangent Function
3.8. Linear Approximations and Taylor Polynomials
Tangent Line Approximations
Newton's Method
Taylor Polynomials
Project: Harvesting Renewable Resources
Review
Case Study 1b Kill Curves and Antibiotic Effectiveness
4.1. Maximum and Minimum Values
Absolute and Local Extreme Values
Fermat's Theorem
Closed Interval Method
Project: The Calculus of Rainbows
4.2. How Derivatives Affect the Shape of a Graph
Mean Value Theorem
Increasing and Decreasing Functions
Concavity
Graphing with Technology
4.3. L'Hospital's Rule: Comparing Rates of Growth
Indeterminate Quotients
Which Functions Grow Fastest?
Indeterminate Products
Indeterminate Differences
Project: Mutation-Selection Balance in Genetic Diseases
4.4. Optimization Problems
Project: Flapping and Gliding
Project: The Tragedy of the Commons: An Introduction to Game Theory
4.5. Recursions: Equilibria and Stability
Equilibria
Cobwebbing
Stability Criterion
4.6. Antiderivatives
Review
5.1. Areas, Distances, and Pathogenesis
Area Problem
Distance Problem
Pathogenesis
5.2. Definite Integral
Calculating Integrals
Midpoint Rule
Properties of the Definite Integral
5.3. Fundamental Theorem of Calculus
Evaluating Definite Integrals
Indefinite Integrals
Net Change Theorem
Fundamental Theorem
Differentiation and Integration as Inverse Processes
Project: The Outbreak Size of an Infectious Disease
5.4. Substitution Rule
Substitution in Indefinite Integrals
Substitution in Definite Integrals
Symmetry
5.5. Integration by Parts
Indefinite Integrals
Definite Integrals
5.6. Partial Fractions
5.7. Integration Using Tables and Computer Algebra Systems
Tables of Integrals
Computer Algebra Systems
Can We Integrate All Continuous Functions?
5.8. Improper Integrals
Review
Case Study 1c Kill Curves and Antibiotic Effectiveness
6.1. Areas Between Curves
Cerebral Blood Flow
Project: Disease Progression and Immunity
Project: The Gini Index
6.2. Average Values
6.3. Further Applications to Biology
Survival and Renewal
Blood Flow
Cardiac Output
6.4. Volumes
Review
Case Study 1d Kill Curves and Antibiotic Effectiveness
Case Study 2b Hosts, Parasites, and Time-Travel
7.1. Modeling with Differential Equations
Models of Population Growth
Classifying Differential Equations
Project: Chaotic Blowflies and the Dynamics of Populations
7.2. Phase Plots, Equilibria, and Stability
Phase Plots
Equilibria and Stability
Mathematical Derivation of the Local Stability Criterion
Project: Catastrophic Population Collapse: An Introduction to Bifurcation Theory
7.3. Direction Fields and Euler's Method
Direction Fields
Euler's Method
7.4. Separable Equations
Project: Why Does Urea Concentration Rebound after Dialysis?
7.5. Systems of Differential Equations
Parametric Curves
Systems of Two Autonomous Differential Equations
Project: The Flight Path of Hunting Raptors
7.6. Phase Plane Analysis
Equilibria
Qualitative Dynamics in the Phase Plane
Project: Determining the Critical Vaccination Coverage
Review
Case Study 2c Hosts, Parasites, and Time-Travel
8.1. Coordinate Systems
Three-Dimensional Space
Higher-Dimensional Space
8.2. Vectors
Combining Vectors
Components
8.3. Dot Product
Projections
Project: Microarray Analysis of Genome Expression
Project: Vaccine Escape
8.4. Matrix Algebra
Matrix Notation
Matrix Addition and Scalar Multiplication
Matrix Multiplication
8.5. Matrices and the Dynamics of Vectors
Systems of Difference Equations: Matrix Models
Leslie Matrices
Summary
8.6. Inverse and Determinant of a Matrix
Inverse of a Matrix
Determinant of a Matrix
Solving Systems of Linear Equations
Project: Cubic Splines
8.7. Eigenvectors and Eigenvalues
Characterizing How Matrix Multiplication Changes Vectors
Eigenvectors and Eigenvalues
8.8. Iterated Matrix Models
Solving Matrix Models
Solutions with Complex Eigenvalues
Perron-Frobenius Theory
Project: The Emergence of Geometric Order in Proliferating Cells
Review
9.1. Functions of Several Variables
Functions of Two Variables
Graphs
Level Curves
Functions of Three Variables
Limits and Continuity
9.2. Partial Derivatives
Interpretations of Partial Derivatives
Functions of More Than Two Variables
Higher Derivatives
Partial Differential Equations
9.3. Tangent Planes and Linear Approximations
Tangent Planes
Linear Approximations
Project: The Speedo LZR Racer
9.4. Chain Rule
Implicit Differentiation
9.5. Directional Derivatives and the Gradient Vector
Directional Derivatives
Gradient Vector
Maximizing the Directional Derivative
9.6. Maximum and Minimum Values
Absolute Maximum and Minimum Values
Review
10.1. Qualitative Analysis of Linear Systems
Terminology
Saddles
Nodes
Spirals
10.2. Solving Systems of Linear Differential Equations
General Solution
Nullclines versus Eigenvectors
Saddles
Nodes
Spirals
Long-Term Behavior
10.3. Applications
Metapopulations
Natural Killer Cells and Immunity
Gene Regulation
Transport of Environmental Pollutants
Project: Pharmacokinetics of Antimicrobial Dosing
10.4. Systems of Nonlinear Differential Equations
Linear and Nonlinear Differential Equations
Local Stability Analyses
Linearization
Examples
Review
Case Study 2d: Hosts, Parasites, and Time-Travel
11.1. 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
11.2. Graphical Descriptions of Data
Contents note continued: Displaying Categorical Data
Displaying Numerical Data: Histograms
Interpreting Area in Histograms
Normal Curve
11.3. Relationships between Variables
Two Categorical Variables
Categorical and Numerical Variables
Two Numerical Variables
11.4. Populations, Samples, and Inference
Populations and Samples
Properties of Samples
Types of Data
Causation
Project: The Birth Weight Paradox
Review
12.1. Principles of Counting
Permutations
Combinations
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
Multiplication Rule and Independence
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
13.1. Sampling Distribution
Sums of Random Variables
Sampling Distribution of the Mean
Sampling Distribution of the Standard Deviation
13.2. Confidence Intervals
Interval Estimates
Student's t-Distribution
13.3. Hypothesis Testing
Null and Alternative Hypotheses
t-Statistic
P-Value
Summary
13.4. Contingency Table Analysis
Hypothesis Testing with Contingency Tables
Chi-Squared Test Statistic
Hypothesis Test
Summary
Review
A. Intervals, Inequalities, and Absolute Values
B. Coordinate Geometry
C. Trigonometry
D. Precise Definitions of Limits
E. Few Proofs
F. Sigma Notation
G. Complex Numbers
H. Statistical Tables.