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

James Cornette and Ralph Ackerman
Publisher: Mathematical Association of America

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• Chapter 1: Mathematical Models of Biological Processes
• 1.1: Experimental data, bacterial growth (5)
• 1.2: Solution to Pt + 1Pt = rPt (8)
• 1.3: Experimental data: Sunlight depletion below the surface of a lake or ocean (2)
• 1.4: Doubling time and half-life (11)
• 1.5: Quadratic solution equations: Mold growth (4)
• 1.6: Constructing a mathematical model of penicillin clearance (3)
• 1.7: Movement toward equilibrium (9)
• 1.8: Solution to the dynamic equation Pt + 1Pt = rPt + b (5)
• 1.9: Light decay with distance
• 1.10: Data modeling vs mathematical models (2)
• 1.11: Summary
• 1.12: Exercises for Chapter 1 (7)

• Chapter 2: Functions as Descriptions of Biological Patterns
• 2.1: Environmental sex determination in turtles (1)
• 2.2: Functions and simple graphs (5)
• 2.3: Function notation (12)
• 2.4: Polynomial functions (1)
• 2.5: Least squares fit of polynomial to data (2)
• 2.6: New functions from old (11)
• 2.7: Composition of functions (18)
• 2.8: Periodic functions and oscillations (9)

• Chapter 3: The Derivative
• 3.1: Tangent to the graph of a function (19)
• 3.2: Limit and rate of change as a limit (25)
• 3.3: The derivative function, F' (16)
• 3.4: Mathematical models using the derivative (6)
• 3.5: Derivatives of polynomials, sum and constant factor rules (26)
• 3.6: The second derivative and higher order derivatives (20)
• 3.7: Left and right limits and derivatives; limits involving infinity (3)
• 3.8: Summary
• 3.9: Exercises for Chapter 3 (10)

• Chapter 4: Continuity and the Power Chain Rule
• 4.1: Continuity (13)
• 4.2: The derivative requires continuity (2)
• 4.3: The generalized power rule (3)
• 4.4: Applications of the power chain rule (8)
• 4.5: Some optimization problems (2)
• 4.6: Implicit differentiation (6)
• 4.7: Summary
• 4.8: Exercises for Chapter 4 (7)

• Chapter 5: Derivatives of Exponential and Logarithmic Functions
• 5.1: Derivatives of exponential functions (7)
• 5.2: The number e (16)
• 5.3: The natural logarithm (7)
• 5.4: The derivative of ekt (13)
• 5.5: The derivative equation P' (t) = kP(t) (27)
• 5.6: Exponential and logarithm chain rules (14)
• 5.7: Summary (14)

• Chapter 6: Derivatives of Products, Quotients and Compositions of Functions
• 6.1: Derivatives of products and quotients (23)
• 6.2: The chain rule (15)
• 6.3: Derivatives of inverse functions (4)
• 6.4: Summary (5)

• Chapter 7: Derivatives of the Trigonometric Functions
• 7.1: Radian measure (3)
• 7.2: Derivatives of trigonometric functions (11)
• 7.3: The chain rule with trigonometric functions (10)
• 7.4: The equation y'' + ω2y (8)
• 7.5: Elementary predator-prey oscillation (3)
• 7.6: Periodic systems (4)

• Chapter 8: Applications of Derivatives
• 8.1: Some geometry of the derivative (8)
• 8.2: Some traditional max-min problems (21)
• 8.3: Life sciences optima (1)
• 8.4: Related rates (9)
• 8.5: Finding roots of f (x) = 0 (6)
• 8.6: Harvesting of whales (3)
• 8.7: Summary and review of Chapters 3 to 8 (18)

• Chapter 9: The Integral
• 9.1: Areas of irregular regions (6)
• 9.2: Areas under some algebraic curves (12)
• 9.3: A general procedure for computing areas (9)
• 9.4: The integral (17)
• 9.5: Properties of the integral (6)
• 9.6: Cardiac output (4)
• 9.7: Chlorophyll energy absorption

• Chapter 10: The Fundamental Theorem of Calculus
• 10.1: An example
• 10.2: The Fundamental Theorem of Calculus (5)
• 10.3: The Parallel Graph Theorem (4)
• 10.4: The second form of the Fundamental Theorem of Calculus (8)
• 10.5: Integral formulas (19)

• Chapter 11: Applications of the Fundamental Theorem of Calculus and Multiple Integrals
• 11.1: Volume (8)
• 11.2: Change the variable of integration (3)
• 11.3: Center of mass (2)
• 11.4: Arc length and surface area (5)
• 11.5: The improper integral, (8)

• Chapter 12: The Mean Value Theorem and Taylor Polynomials
• 12.1: The Mean Value Theorem (6)
• 12.2: Monotone functions; second derivative test for high points (6)
• 12.3: Approximating functions with quadratic polynomials (7)
• 12.4: Polynomial approximation anchored at 0 (4)
• 12.5: Polynomial approximations to solutions of differential equations (2)
• 12.6: Polynomial approximation at anchor a ≠ 0 (6)
• 12.7: Accuracy of the Taylor polynomial approximations (4)

• Chapter 13: Two Variable Calculus and Diffusion
• 13.1: Partial derivatives of functions of two variables (13)
• 13.2: Maxima and minima of functions of two variables (9)
• 13.3: Integrals of functions of two variables (10)
• 13.4: The diffusion equation ut (x, t) = c2uxx (x, t) (3)

• Chapter 14: First Order Difference Equation Models of Populations
• 14.1: Difference equations and solutions (26)
• 14.2: Graphical methods for difference equations (6)
• 14.3: Equilibrium points, stable and nonstable (6)
• 14.4: Cobwebbing (7)
• 14.5: Exponential growth and L'hôpital's rule (10)
• 14.6: Environmental carrying capacity (6)
• 14.7: Harvest of natural populations (6)
• 14.8: An alternate logistic equation (5)

• Chapter 15: Discrete Dynamical Systems
• 15.1: Infectious diseases: The SIR model (9)
• 15.2: Pharmacokinetics of penicillin (6)
• 15.3: Continuous infusion and oral administration of penicillin (2)
• 15.4: Solutions to pairs of difference equations (8)
• 15.5: Roots equal to zero, multiple roots, and complex roots (3)
• 15.6: Matrices (11)

• 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 (12)
• 16.3: Asymptotic stability of equilibria of nonlinear systems (3)
• 16.4: Four examples of nonlinear dynamical systems (17)

• Chapter 17: Differential Equations
• 17.1: Differential equation models of biological processes (10)
• 17.2: Solutions to differential equations (5)
• 17.3: Direction fields (5)
• 17.4: Phase planes and stability of constant solutions (9)
• 17.5: Numerical approximations to solutions of differential equations (3)
• 17.6: Synopsis (2)
• 17.7: First order linear differential equations (8)
• 17.8: Separation of variables (10)
• 17.9: First order ordinary differential equation models (9)

• Chapter 18: Second Order and Systems of Two First Order Differential Equations
• 18.1: Constant coefficient linear second order differential equations (8)
• 18.2: Stability and asymptotic stability of equilibria of pairs of autonomous differential equations (1)
• 18.3: Two constant coefficient linear differential equations (6)
• 18.4: Systems of two first order differential equations (3)
• 18.5: Applications of Theorem 18.4.1 to biological systems (7)

• Chapter A: Appendices
• A.1: Summation notation
• A.2: Mathematical induction
• A.3: L'Hôpital's rule (4)
• A.4: The arithmetic mean is greater than or equal to the geometric mean
• A.5: Stability of equilibrium of an autonomous differential equation

Calculus for the Life Sciences: A Modeling Approach, by James L. Cornette and Ralph A. Ackerman, helps life science students understand the relevance and importance of mathematics to their world and involves modeling living systems with difference and differential equations. Through partnership with the Mathematical Association of America, WebAssign is pleased to offer online question content alongside interactive step-by-step tutorials for this title. All questions include reading links to the eBook for an integrated student experience.

## Questions Available within WebAssign

Most questions from this textbook are available in WebAssign. The online questions are identical to the textbook questions except for minor wording changes necessary for Web use. Whenever possible, variables, numbers, or words have been randomized so that each student receives a unique version of the question. This list is updated nightly.

##### Question Availability Color Key
BLACK questions are available now
GRAY questions are under development

Group Quantity Questions
Chapter A: Appendices
A.3 4 002e 003b 008f 008h
Chapter 1: Mathematical Models of Biological Processes
1.1 5 001a 001e 002a 002e 006
1.2 8 001a 001b 001f 002 003 004 005 006
1.3 2 003 004
1.4 11 001b 001c 002 003 004c 004e 004g 005 006 007 009
1.5 4 003 004 005 006
1.6 3 001 002 005
1.7 9 001a 001c 002a 002b 003a 003b 004 006 007
1.8 5 001a 001b 001c 002 003
1.10 2 001 003
1.12 7 001 002 003 004 005 006 007
Chapter 2: Functions as Descriptions of Biological Patterns
2.1 1 001
2.2 5 001 002 005 006 008
2.3 12 001 002a 003 004 005 006a 006b 006c 006d 008a 008b.WA.Tut 008b.WA.Tut.SA
2.4 1 001
2.5 2 001 002
2.6 11 001 005 006 008 009 010 011 012 012.WA.Tut 012.WA.Tut.SA 013
2.7 18 002 005a 005b 006a 006b 007a 007b 007c 008a 008b 009 010 011 012 013a 013b 013c 501.WA.Tut
2.8 9 001 002 003 006 007a 007b 008a 011 013
Chapter 3: The Derivative
3.1 19 001 002 003 004 005 006a 006b 007 008 009 010 011 012-013.WA.Tut 012-013.WA.Tut.SA 012b 012d 013c 013e 014
3.2 25 001-002.WA.Tut 001-002.WA.Tut.SA 001a 001b 001c 002a 005a 005b 005c 005d 005m.WA.Tut 005n.WA.Tut 006 007 008 009a 009b 009c 009d 010a 010b 010c 010d 010e 011
3.3 16 001.WA.Tut 001.WA.Tut.SA 001b 001c 001e 001f 001g 001i 002c 002e 003a 004 005 006 007 008
3.4 6 001 002 003 004 005 006b
3.5 26 001a 001b 001c 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017a 017b 017c 018a 018b 018c 019 020
3.6 20 001a 001c 001g 001j.WA.Tut 002.WA.Tut 002.WA.Tut.SA 002b 003 004 005 006 007 008 009a 010a 010c 010e 011 012 013
3.7 3 001a 002a 003
3.9 10 001a 001b 001c 001d 003a 003b 003c 003d 004a 004b
Chapter 4: Continuity and the Power Chain Rule
4.1 13 002 003.WA.Tut 003.WA.Tut.SA 003a 003c 005 007 008 009 010 011 012 014
4.2 2 001 003
4.3 3 001a 001b 001c
4.4 8 001a 001b 001c 001d 001e 002 003 004
4.5 2 001 003
4.6 6 001a 002 003 004a 004c 004g
4.8 7 001a 001b 001c 001d 003 004 005
Chapter 5: Derivatives of Exponential and Logarithmic Functions
5.1 7 001 002 003 004 005a 006 007
5.2 16 002a 002c 002e 003 004 005 007 008a 008b 008c 008d 008i 010 013 014 015
5.3 7 001 002 003 004a 004e 005a 005c
5.4 13 003 004a 005a 005b 005c 005g 005o 005r 007 008a 008b 009 010
5.5 27 001a 001b 001c 002a 002b 002c 003a 003b 003c 005 006 007 008 009c 010 011 012 013 014 015 016 017 019 024 025 026 028
5.6 14 001a 001b 001c 002a 002c 002e 003 004 005 008a 008d 009a 009c 009f
5.7 14 001b 001c 001d 001e 001f 002b 002c 002d 003 004 005 006 007 008
Chapter 6: Derivatives of Products, Quotients and Compositions of Functions
6.1 23 001a 001a.WA.Tut 001a.WA.Tut.SA 001b 001c 001h.WA.Tut 001h.WA.Tut.SA 002a 002c 002d 002d.WA.Tut 002d.WA.Tut.SA 002e 006 007 008 010 011 014 015 016 018a 019
6.2 15 001a 001b 001c 001d 001k.WA.Tut 001k.WA.Tut.SA 002a 002b 003a 003b 003c 003c.WA.Tut 003c.WA.Tut.SA 004 005
6.3 4 001a 001b 002 003
6.4 5 001a 001b 001c 001d 002
Chapter 7: Derivatives of the Trigonometric Functions
7.1 3 001 002 003
7.2 11 001 002 003a 003b 003c 003h 004a 004b 005 009 011
7.3 10 001a 001b 001g 001h 002 003a 003c 004 005 007
7.4 8 001a 001b 001c 002a 002b 003a 003b 005
7.5 3 002 004 007
7.6 4 001 002 004 007
Chapter 8: Applications of Derivatives
8.1 8 001 002 003 004 005a 005b 005c 006
8.2 21 002 003 004 005 009 010 011 012 013 014 015 016 017 018 019 020 021 023 024 025 027
8.3 1 001
8.4 9 001 002 003 004 005 007 009 010 011
8.5 6 001 002 003 004 005a 008
8.6 3 001 005 006
8.7 18 002 003 006a 006b 006c 007a 007b 008a 008b 008c 008d 008e 009 010 012 013 014 015
Chapter 9: The Integral
9.1 6 001 002 003 005 010a 011a
9.2 12 003a 003b 004a 005a 005b 005c 006 007 008 009 011 012
9.3 9 003 004 006 007 008 010 012 013 014
9.4 17 001 002 003 004 005 006 009 010 011a 011b 012 013 014 015 016 018a 021
9.5 6 004 005 006 007a 008 009
9.6 4 002 003 005 008
Chapter 10: The Fundamental Theorem of Calculus
10.2 5 003 004 005 006 007
10.3 4 001 002 004 005c
10.4 8 002a 002b 002c 002j 003a 003b 003c 004
10.5 19 001 002a 003 004 005a 005c 005d 006a 006b 006c 007a 007b 007c 007d 008a 009a 009b 009c 010
Chapter 11: Applications of the Fundamental Theorem of Calculus and Multiple Integrals
11.1 8 001 003 004 006 007 008 009 010
11.2 3 001a 001c 001g
11.3 2 001 002
11.4 5 001 002 004 005 006
11.5 8 001 003 006 007 008 010 011 013
Chapter 12: The Mean Value Theorem and Taylor Polynomials
12.1 6 001a 002 003a 004a 006 007
12.2 6 001a 001b 001c 002a 002b 002c
12.3 7 001 002 003a 003b 003c 004a 004b
12.4 4 001 003 004 006
12.5 2 001a 001b
12.6 6 001 002 003a 004 005 006
12.7 4 001a 001b 003 004
Chapter 13: Two Variable Calculus and Diffusion
13.1 13 001a 001b 001c 001d 001e 002a 002b 002c 004a 005a 005b 006 008
13.2 9 001a 001b 001c 002a 003 005 007 009 011
13.3 10 001a 002a 002b 004a 004b 004c 005a 005b 005c 006
13.4 3 005 009 010
Chapter 14: First Order Difference Equation Models of Populations
14.1 26 001 002a 002b 003 004 005a 005b 005c 005d 006a 006c 006d 007a 009a 009b 010a 011 012a 012b 013a 013b 014a 014b 017 018a 018b
14.2 6 001 002 003a 003b 004a 004b
14.3 6 002 003a 003b 004a 004b 005
14.4 7 001a 001b 002a 003a 003c 006 007
14.5 10 002a 004a 004b 005a 008 010a 011a 011b 011c 011d
14.6 6 001 003a 003b 004 005 006
14.7 6 002 003 004 006 007 008
14.8 5 002 003a 003b 004 005
Chapter 15: Discrete Dynamical Systems
15.1 9 001 002 006 007 008 009 010 011 012
15.2 6 001 002 003 004 005 006
15.3 2 002 005
15.4 8 002 003c 004a 004b 005a 006 008 010
15.5 3 003a 003b 003c
15.6 11 003a 004 005a 005b 005c 005d 005e 005f 006 007 009
Chapter 16: Nonlinear Dynamical Systems; Stable and Unstable Equilibria
16.2 12 001 002 005 007a 007b 008a 008b 008c 009a 009b 009c 011
16.3 3 001a 001b 004
16.4 17 001 002 003 005 006 007a 008 010 013 015 016 017 018a 018b 020 021a 021b
Chapter 17: Differential Equations
17.1 10 001 003 004 005 007 009 011 013 014 015
17.2 5 001a 001b 001c 002a 002b
17.3 5 002a 003a 004a 005 006
17.4 9 001 002a 002c 002e 003 004 005 009 010
17.5 3 002 004a 004c
17.6 2 001 002
17.7 8 001a 001c 001g 002a 002b 004 008 009
17.8 10 003a 004a 004b 004c 005 007 008 009 010 011
17.9 9 001 002 003 004 005 007 010 011 012
Chapter 18: Second Order and Systems of Two First Order Differential Equations
18.1 8 002 004 006 008 011 013 015a 016a
18.2 1 002
18.3 6 001 002a 003a 004a 004c 004e
18.4 3 001 002a 003
18.5 7 001a 003 004 006a 006b 009 010
Total 950