Name: Calculus for The Life Sciences
Price: 128.95 USD
Availability: InStock
ISBN: 9781118169827

Calculus for The Life Sciences, 1st Edition, is a textbook that pairs rigorous mathematical instruction with extensive biological modeling. The work presents fundamental mathematical concepts through four distinct perspectives: visual, numerical, algebraic, and verbal.

Core topics include modeling with functions, limits, derivative rules, and applications of differentiation. The text also examines integration techniques, differential equations, probabilistic applications of integration, and multivariable extensions, connecting mathematical principles to life science questions.

Whenever possible, formal definitions, computational procedures, and theoretical results are motivated by biological applications and real-world data. To support collaborative or independent study, each chapter includes projects covering applied scenarios such as the dynamics of disease outbreaks.

Table of Contents

Chapter 1: Modeling with Functions
- • 1.1 Real Numbers and Functions
- • 1.2 Data Fitting with Linear and Periodic Functions
- • 1.3 Power Functions and Scaling Laws
- • 1.4 Exponential Growth
- • 1.5 Function Building
- • 1.6 Inverse Functions and Logarithms
- • 1.7 Sequences and Difference Equations
Chapter 2: Limits and Derivatives
- • 2.1 Rates of Change and Tangent Lines
- • 2.2 Limits
- • 2.3 Limit Laws and Continuity
- • 2.4 Asymptotes and Infinity
- • 2.5 Sequential Limits
- • 2.6 Derivative at a Point
- • 2.7 Derivatives as Functions
- • Group Projects
Chapter 3: Derivative Rules and Tools
- • 3.1 Derivatives of Polynomials and Exponentials
- • 3.2 Product and Quotient Rules
- • 3.3 Chain Rule and Implicit Differentiation
- • 3.4 Derivatives of Trigonometric Functions
- • 3.5 Linear Approximation
- • 3.6 Higher Derivatives and Approximations
- • 3.7 l’Hoˆ pital’s Rule
- • Group Projects
Chapter 4: Applications of Differentiation
- • 4.1 Graphing Using Calculus
- • 4.2 Getting Extreme
- • 4.3 Optimization in Biology
- • 4.4 Decisions and Optimization
- • 4.5 Linearization and Difference Equations
- • Group Projects
Chapter 5: Integration
- • 5.1 Antiderivatives
- • 5.2 Accumulated Change and Area under a Curve
- • 5.3 The Definite Integral
- • 5.4 The Fundamental Theorem of Calculus
- • 5.5 Substitution
- • 5.6 Integration by Parts and Partial Fractions
- • 5.7 Numerical Integration
- • 5.8 Applications of Integration
- • Group Projects
Chapter 6: Differential Equations
- • 6.1 A Modeling Introduction to Differential Equations
- • 6.2 Solutions and Separable Equations
- • 6.3 Linear Models in Biology
- • 6.4 Slope Fields and Euler’s Method
- • 6.5 Phase Lines and Classifying Equilibria
- • 6.6 Bifurcations
- • Group Projects
Chapter 7: Probabilistic Applications of Integration
- • 7.1 Histograms, PDFs, and CDFs
- • 7.2 Improper Integrals
- • 7.3 Mean and Variance
- • 7.4 Bell-Shaped Distributions
- • 7.5 Life Tables
- • Group Projects
Chapter 8: Multivariable Extensions
- • 8.1 Multivariate Modeling
- • 8.2 Matrices and Vectors
- • 8.3 Eigenvalues and Eigenvectors
- • 8.4 Systems of Linear Differential Equations
- • 8.5 Nonlinear Systems
- • Group Projects

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