Calculus for the Life Sciences: A Modeling Approach 1st edition

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• Chapter 1: Mathematical Models of Biological Processes
  • 1.1: Experimental data, bacterial growth
  • 1.2: Solution to P_{t + 1} − P_t = rP_t
  • 1.3: Experimental data: Sunlight depletion below the surface of a lake or ocean
  • 1.4: Doubling time and half-life
  • 1.5: Quadratic solution equations: Mold growth
  • 1.6: Constructing a mathematical model of penicillin clearance
  • 1.7: Movement toward equilibrium
  • 1.8: Solution to the dynamic equation P_{t + 1} − P_t = rP_t + b
  • 1.9: Light decay with distance
  • 1.10: Data modeling vs mathematical models
  • 1.11: Summary
  • 1.12: Exercises for Chapter 1
  
  
• Chapter 2: Functions as Descriptions of Biological Patterns
  • 2.1: Environmental sex determination in turtles
  • 2.2: Functions and simple graphs
  • 2.3: Function notation
  • 2.4: Polynomial functions
  • 2.5: Least squares fit of polynomial to data
  • 2.6: New functions from old
  • 2.7: Composition of functions
  • 2.8: Periodic functions and oscillations
  
  
• Chapter 3: The Derivative
  • 3.1: Tangent to the graph of a function
  • 3.2: Limit and rate of change as a limit
  • 3.3: The derivative function, F'
  • 3.4: Mathematical models using the derivative
  • 3.5: Derivatives of polynomials, sum and constant factor rules
  • 3.6: The second derivative and higher order derivatives
  • 3.7: Left and right limits and derivatives; limits involving infinity
  • 3.8: Summary
  • 3.9: Exercises for Chapter 3
  
  
• Chapter 4: Continuity and the Power Chain Rule
  • 4.1: Continuity
  • 4.2: The derivative requires continuity
  • 4.3: The generalized power rule
  • 4.4: Applications of the power chain rule
  • 4.5: Some optimization problems
  • 4.6: Implicit differentiation
  • 4.7: Summary
  • 4.8: Exercises for Chapter 4
  
  
• Chapter 5: Derivatives of Exponential and Logarithmic Functions
  • 5.1: Derivatives of exponential functions
  • 5.2: The number e
  • 5.3: The natural logarithm
  • 5.4: The derivative of e^kt
  • 5.5: The derivative equation P' (t) = kP(t)
  • 5.6: Exponential and logarithm chain rules
  • 5.7: Summary
  
  
• Chapter 6: Derivatives of Products, Quotients and Compositions of Functions
  • 6.1: Derivatives of products and quotients
  • 6.2: The chain rule
  • 6.3: Derivatives of inverse functions
  • 6.4: Summary
  
  
• Chapter 7: Derivatives of the Trigonometric Functions
  • 7.1: Radian measure
  • 7.2: Derivatives of trigonometric functions
  • 7.3: The chain rule with trigonometric functions
  • 7.4: The equation y'' + ω²y
  • 7.5: Elementary predator-prey oscillation
  • 7.6: Periodic systems
  
  
• Chapter 8: Applications of Derivatives
  • 8.1: Some geometry of the derivative
  • 8.2: Some traditional max-min problems
  • 8.3: Life sciences optima
  • 8.4: Related rates
  • 8.5: Finding roots of f (x) = 0
  • 8.6: Harvesting of whales
  • 8.7: Summary and review of Chapters 3 to 8
  
  
• Chapter 9: The Integral
  • 9.1: Areas of irregular regions
  • 9.2: Areas under some algebraic curves
  • 9.3: A general procedure for computing areas
  • 9.4: The integral
  • 9.5: Properties of the integral
  • 9.6: Cardiac output
  • 9.7: Chlorophyll energy absorption
  
  
• Chapter 10: The Fundamental Theorem of Calculus
  • 10.1: An example
  • 10.2: The Fundamental Theorem of Calculus
  • 10.3: The Parallel Graph Theorem
  • 10.4: The second form of the Fundamental Theorem of Calculus
  • 10.5: Integral formulas
  
  
• Chapter 11: Applications of the Fundamental Theorem of Calculus and Multiple Integrals
  • 11.1: Volume
  • 11.2: Change the variable of integration
  • 11.3: Center of mass
  • 11.4: Arc length and surface area
  • 11.5: The improper integral,
  
  
• Chapter 12: The Mean Value Theorem and Taylor Polynomials
  • 12.1: The Mean Value Theorem
  • 12.2: Monotone functions; second derivative test for high points
  • 12.3: Approximating functions with quadratic polynomials
  • 12.4: Polynomial approximation anchored at 0
  • 12.5: Polynomial approximations to solutions of differential equations
  • 12.6: Polynomial approximation at anchor a ≠ 0
  • 12.7: Accuracy of the Taylor polynomial approximations
  
  
• Chapter 13: Two Variable Calculus and Diffusion
  • 13.1: Partial derivatives of functions of two variables
  • 13.2: Maxima and minima of functions of two variables
  • 13.3: Integrals of functions of two variables
  • 13.4: The diffusion equation u_t (x, t) = c²u_xx (x, t)
  
  
• Chapter 14: First Order Difference Equation Models of Populations
  • 14.1: Difference equations and solutions
  • 14.2: Graphical methods for difference equations
  • 14.3: Equilibrium points, stable and nonstable
  • 14.4: Cobwebbing
  • 14.5: Exponential growth and L'hôpital's rule
  • 14.6: Environmental carrying capacity
  • 14.7: Harvest of natural populations
  • 14.8: An alternate logistic equation
  
  
• Chapter 15: Discrete Dynamical Systems
  • 15.1: Infectious diseases: The SIR model
  • 15.2: Pharmacokinetics of penicillin
  • 15.3: Continuous infusion and oral administration of penicillin
  • 15.4: Solutions to pairs of difference equations
  • 15.5: Roots equal to zero, multiple roots, and complex roots
  • 15.6: Matrices
  
  
• Chapter 16: Nonlinear Dynamical Systems; Stable and Unstable Equilibria
  • 16.1: Equilibria of pairs of difference equations
  • 16.2: Stability of the equilibria of linear systems
  • 16.3: Asymptotic stability of equilibria of nonlinear systems
  • 16.4: Four examples of nonlinear dynamical systems
  
  
• Chapter 17: Differential Equations
  • 17.1: Differential equation models of biological processes
  • 17.2: Solutions to differential equations
  • 17.3: Direction fields
  • 17.4: Phase planes and stability of constant solutions
  • 17.5: Numerical approximations to solutions of differential equations
  • 17.6: Synopsis
  • 17.7: First order linear differential equations
  • 17.8: Separation of variables
  • 17.9: First order ordinary differential equation models
  
  
• Chapter 18: Second Order and Systems of Two First Order Differential Equations
  • 18.1: Constant coefficient linear second order differential equations
  • 18.2: Stability and asymptotic stability of equilibria of pairs of autonomous differential equations
  • 18.3: Two constant coefficient linear differential equations
  • 18.4: Systems of two first order differential equations
  • 18.5: Applications of Theorem 18.4.1 to biological systems
  
  
• Chapter A: Appendices
  • A.1: Summation notation
  • A.2: Mathematical induction
  • A.3: L'Hôpital's rule
  • A.4: The arithmetic mean is greater than or equal to the geometric mean
  • A.5: Stability of equilibrium of an autonomous differential equation