Biocalculus: Calculus, Probability, and Statistics for the Life Sciences
Innbundet /
2025
/ Engelsk
Produktdetaljer
ISBN
9798214002576
Publisert
2025-05-15
Utgave
2. utgave
Utgiver
Vendor
Brooks/Cole
Aldersnivå
U, 05
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
1024
Biografisk notat
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. Stewart’s 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. Troy Day received the M.S. degree in biology from the University of British Columbia and the Ph.D. in mathematics from Queen’s University. His first academic position was at the University of Toronto before being recruited back to Queen’s University as a Canada Research Chair in Mathematical Biology. He is currently Professor of Mathematics and Statistics and Professor of Biology. His research group works in areas ranging from applied mathematics to experimental biology. Day is also co-author of the widely used book, "A Biologist’s Guide to Mathematical Modeling," published by Princeton University Press in 2007.
Stewart/Day’s “Biocalculus: Calculus, Probability, and Statistics for the Life Sciences” 2nd Edition, shows you how calculus, probability and statistics relate to biology, illustrating the topics of calculus with real-world genuine examples drawn from many areas of biology, including genetics, biomechanics, physiology, medicine, ecology, epidemiology and evolutionary biology.
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CHAPTER 1: FUNCTIONS AND SEQUENCES.
1.1 Four Ways to Represent a Function.
1.2 A Catalog of Essential Functions.
1.3 New Functions from Old Functions.
Project: The Biomechanics of Human Movement.
1.4 Exponential Functions.
1.5 Logarithms; Semilog and Log-Log Plots.
Project: The Coding Function of DNA.
1.6 Sequences and Difference Equations.
Project: Drug Resistance in Malaria.
Review.
Case Study 1a: Kill Curves and Antibiotic Effectiveness.
Case Study 3a: Vaccines and The Evolution of Disease Severity.
CHAPTER 2: LIMITS.
2.1 Limits of Functions.
2.2 Limits: Algebraic Methods.
2.3 Continuity.
2.4 Limits of Functions at Infinity.
2.5 Limits of Sequences.
Project: Modeling the Dynamics of Viral Infections.
Review.
Case Study 2a: Hosts, Parasites, and Time-Travel.
Case Study 3b: Vaccines and the Evolution of Disease Severity.
CHAPTER 3: DERIVATIVES.
3.1 Derivatives and Rates of Change.
3.2 The Derivative as a Function.
3.3 Basic Differentiation Formulas.
3.4 The Product and Quotient Rules.
3.5 The Chain Rule.
3.6 Exponential Growth and Decay.
Project: Controlling Red Blood Cell Loss During Surgery.
3.7 Derivatives of the Logarithmic and Inverse Tangent Functions.
3.8 Linear Approximations and Differentials.
Project: Harvesting Renewable Resources.
Review.
Case Study 1b: Kill Curves and Antibiotic Effectiveness.
CHAPTER 4: APPLICATIONS AND DERIVATIVES.
4.1 Maximum and Minimum Values.
Project: The Calculus of Rainbows.
4.2 How Derivatives Affect the Shape of a Graph.
4.3 L’Hospital’s Rule: Comparing Rates of Growth.
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.
4.6 Antiderivatives.
Review.
Case Study 3c: Vaccines and the Evolution of Disease Severity.
CHAPTER 5: INTEGRALS.
5.1 Areas, Distances, and Pathogenesis.
5.2 The Definite Integral.
5.3 The Fundamental Theorem of Calculus.
Project: The Outbreak Size of an Infectious Disease.
5.4 The Substitution Rule.
5.5 Integration by Parts.
5.6 Partial Fractions.
5.7 Integration Using Tables and Computer Algebra Systems.
5.8 Improper Integrals.
Review.
Case Study 1c: Kill Curves and Antibiotic Effectiveness.
CHAPTER 6: APPLICATIONS OF INTEGRALS.
6.1 Areas Between Curves.
Project: Disease Progression and Immunity.
Project: The Gini Index.
6.2 Average Values.
6.3 Further Applications to Biology.
6.4 Numerical Integration.
6.5 Volumes.
Review.
Case Study 1d: Kill Curves and Antibiotic Effectiveness.
Case Study 2b: Hosts, Parasites, and Time-Travel.
CHAPTER 7: DIFFERENTIAL EQUATIONS.
7.1 Modeling with Differential Equations.
Project: Sterile Insect Technique.
7.2 Separable Equations.
Project: Why Does Urea Concentration Rebound After Dialysis?
7.3 Phase Plots, Equilibria, and Stability.
Project: Catastrophic Population Collapse: An Introduction to Bifurcation Theory.
7.4 Direction Fields and Euler’s Method.
7.5 Systems of Differential Equations.
Project: The Flight Path of Hunting Raptors.
7.6 Phase Plane Analysis.
Project: Determining the Critical Vaccination Coverage.
Review.
Case Study 2c: Hosts, Parasites, and Time-Travel.
Case Study 3d: Vaccines and the Evolution of Disease Severity.
CHAPTER 8: VECTORS AND MATRIX MODELS.
8.1 Coordinate Systems.
8.2 Vectors.
8.3 The Dot Product.
Project: Microarray Analysis of Genome Expression.
Project: Vaccine Escape.
8.4 Matrix Algebra.
8.5 Matrix Models.
8.6 The Inverse and Determinant of a Matrix.
Project: Cubic Splines.
Project: Color Vision and Chromaticity Diagrams.
8.7 Eigenvectors and Eigenvalues.
8.8 Iterated Matrix Models.
Project: The Emergence of Geometric Order in Proliferating Cells.
Review.
CHAPTER 9: MULTIVARIATE CALCULUS.
9.1 Functions of Several Variables.
9.2 Partial Derivatives.
9.3 Tangent Planes and Linear Approximations.
Project: The Speedo LZR Racer.
9.4 The Chain Rule.
9.5 Directional Derivatives and the Gradient Vector.
9.6 Maximum and Minimum Values.
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Les mer
Produktdetaljer
ISBN
9798214002576
Publisert
2025-05-15
Utgave
2. utgave
Utgiver
Vendor
Brooks/Cole
Aldersnivå
U, 05
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
1024