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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.
  
• Other Contributors/Collections:Day, Troy, 1968- author.
  
• Published/Created:Boston, MA, USA : Cengage Learning, [2016]
  

• Holdings

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  • Location:BMB LIBRARY (VGH) stacksWhere is this?
    
  • Call Number: QH323.5 .S74 2016
    
  • Number of Items:1
    
  • Status:Available
    

  • Location:WOODWARD LIBRARY stacksWhere is this?
    
  • Call Number: QH323.5 .S74 2016
    
  • Number of Items:1
    
  • Status:Available
    

   
• Library of Congress Subjects:Life sciences--Mathematics.
  Calculus.
  
• Description:xlvii, 973 pages : illustrations (some color) ; 27 cm
  
• Notes:Includes bibliographical references and indexes.
  
• ISBN:1305114035 hardcover
  9781305114036 hardcover
  
• 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.