Biocalculus: Calculus and Mathematical Models for the Biological Sciences
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Copyright: 2017
Pages: 703
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Biocalculus: Calculus and Mathematical Models for the Biological Sciences is designed to be a rigorous first-year calculus text primarily for students whose primary interests lie in the biological sciences.
Biocalculus: Calculus and Mathematical Models for the Biological Sciences by Timothy D. Comar, James Pierce, and Olcay Akman:
- Introduces many calculus concepts along with related biological models and applications.
- Discusses population models throughout to provide a theme connecting mathematical concepts in the text.
- Includes projects, examples and exercises with real data.
- Integrates discrete models (using difference equations) and continuous models (using differential equations).
- Uses discrete change to motivate change in the differentiable sense.
- Presents matrix algebra and multivariable differential calculus in Part Two to enable the study of the dynamics of higher-dimensional systems, including competition between competing species, predator-prey relations, and epidemic models.
- Examines calculus-based probability and statistics.
Chapter 1: Preliminaries: Functions and Models
1.1 Functions and Models
1.2 Power Functions, polynomial Functions, and Rational Functions
1.3 Geometric Transformations of Functions and Combinations of Functions
1.4 Exponential Functions
1.5 Trigonometric Functions
1.6 Inverse Functions, Logarithmic Functions, Nonlinear Scales
1.7 Parametric Curves
1.8 Fundamentals of Probability
1.9 Review
Chapter 2: Difference Equations, Sequences, and limits
2.1 Sequences and Their Limits
2.2 Limit Laws and the Formal Definition of a Limit
2.3 Discrete Change: Forward Differences
2.4 Biological Examples of Discrete Dynamical Systems
2.5 Difference Equations: Density Dependent Population Models
2.6 Review
Chapter 3: Limits and Continuity of Functions of a Real Variable
3.1 Limits: Numerical and Geometric Intuition
3.2 Limits: Rules for Computing Limits
3.3 Limits Involving Infinits
3.4 The Formal Definition of a Limit
3.5 Continuity
3.6 The Intermediate Value Theorem
3.7 Review
Chapter 4: The Derivative
4.1 Introduction to the Derivative: Geometric and Numerical Intuition
4.2 The Derivative as a Function
4.3 Interpretation of the Derivative: From Difference Equations to Differential Equations
4.4 Techniques of Differentiation I: Basic Differentiation Rules
4.5 Techniques of Differentiation II: The Product and Quotient Rules
4.6 Techniques of Differentiation III: The Chain Rule
4.7 Implicit Differentiation
4.8 Review
Chapter 5: Applications of the Derivative
5.1 Extrema
5.2 The Mean Value Theorem
5.3 Derivative and The Geometry of Curves
5.4 Optimization
5.5 Linear Approximation, Differentials, and Error
5.6 Models Using Simple Differential Equations
5.7 Stability of Equilibria of Differential Equations
5.8 Stability of Equilibria of Difference Equations
5.9 Newton’s Method (Optional)
5.10 L’Hôpital’s Rule
5.11 Related Rates
5.12 Antiderivatives
5.13 Review
Chapter 6: The Definite Integral
6.1 The Area Problem, The Distance Problem, and Riemann Sums
6.2 The Definite Integral
6.3 The Fundamental Theorem of Calculus
6.4 Interpretations and Applications of the Definite Integral
6.5 Numerical Integration
6.6 Review
Chapter 7: Basic Integration Techniques
7.1 Integration by Substitution
7.2 Using Integral Tables and Computer Algebra Systems
7.3 Integration by Parts
7.4 Partial Fractions
7.5 Additional Integration Techniques
7.6 Improper Integrals
7.7 Taylor Polynomial Approximations
7.8 Review
Additional Chapters to be included in the First Edition:
Chapter 8: Applications of the Definite Integral
Chapter 9: Ordinary Differential Equations
Chapter 10: Matrix Algebra and Models
Chapter 11: Differential Calculus of Functions of Several Variables
Chapter 12: Systems of Difference Equations
Chapter 13: Systems of Differential Equations
Chapter 14: Probability: Applications and Constructive Modeling
Chapter 15: Statistical Inference: Applications and Models
Timothy D. Comar is a professor of mathematics at Benedictine University in Lisle, IL. He earned his Ph.D. in mathematics at the University of Michigan specializing in low dimensional topology. He is currently working mathematical biology with interests in the dynamics of deterministic and stochastic models for pest management, vaccination strategies for epidemics, and gene regulatory networks using impulsive differential equations, difference equations, Boolean models, and agent-based models. He has taught biocalculus courses for many years, and mentored many undergraduate research projects in mathematical biology.
James Peirce is a Professor of Mathematics at the University of Wisconsin - La Crosse. He received his Ph.D. in Mathematics from U.C. Davis in 2004. As an applied mathematician, he loves incorporating problems from mathematical biology into his courses. His research focuses on host-parasite models in the field of Mathematical Ecology. He enjoys sampling host populations with his biology collaborators from sites within the Upper Mississippi River and the sandy beaches of California. Since 2004, he has directed numerous undergraduate research projects (often pairing mathematics and biology students) in the hope of developing the next generation of mathematical ecologists.
Olcay Akman is a professor of mathematics at Illinois State University in Normal, IL. He is the director of the intercollegiate Biomathematics Alliance, a consortium of universities collaborating and sharing resource in the pursuit of scholarships, teaching, and advanced research development. Olcay is currently Editor-in-Chief of the journal Letters in Biomathematics and a journal for undergraduate research, Spora. His research interests include computing-intensive modeling, using evolutionary computing or machine learning based methods.
New Publication Coming Soon!
Biocalculus: Calculus and Mathematical Models for the Biological Sciences is designed to be a rigorous first-year calculus text primarily for students whose primary interests lie in the biological sciences.
Biocalculus: Calculus and Mathematical Models for the Biological Sciences by Timothy D. Comar, James Pierce, and Olcay Akman:
- Introduces many calculus concepts along with related biological models and applications.
- Discusses population models throughout to provide a theme connecting mathematical concepts in the text.
- Includes projects, examples and exercises with real data.
- Integrates discrete models (using difference equations) and continuous models (using differential equations).
- Uses discrete change to motivate change in the differentiable sense.
- Presents matrix algebra and multivariable differential calculus in Part Two to enable the study of the dynamics of higher-dimensional systems, including competition between competing species, predator-prey relations, and epidemic models.
- Examines calculus-based probability and statistics.
Chapter 1: Preliminaries: Functions and Models
1.1 Functions and Models
1.2 Power Functions, polynomial Functions, and Rational Functions
1.3 Geometric Transformations of Functions and Combinations of Functions
1.4 Exponential Functions
1.5 Trigonometric Functions
1.6 Inverse Functions, Logarithmic Functions, Nonlinear Scales
1.7 Parametric Curves
1.8 Fundamentals of Probability
1.9 Review
Chapter 2: Difference Equations, Sequences, and limits
2.1 Sequences and Their Limits
2.2 Limit Laws and the Formal Definition of a Limit
2.3 Discrete Change: Forward Differences
2.4 Biological Examples of Discrete Dynamical Systems
2.5 Difference Equations: Density Dependent Population Models
2.6 Review
Chapter 3: Limits and Continuity of Functions of a Real Variable
3.1 Limits: Numerical and Geometric Intuition
3.2 Limits: Rules for Computing Limits
3.3 Limits Involving Infinits
3.4 The Formal Definition of a Limit
3.5 Continuity
3.6 The Intermediate Value Theorem
3.7 Review
Chapter 4: The Derivative
4.1 Introduction to the Derivative: Geometric and Numerical Intuition
4.2 The Derivative as a Function
4.3 Interpretation of the Derivative: From Difference Equations to Differential Equations
4.4 Techniques of Differentiation I: Basic Differentiation Rules
4.5 Techniques of Differentiation II: The Product and Quotient Rules
4.6 Techniques of Differentiation III: The Chain Rule
4.7 Implicit Differentiation
4.8 Review
Chapter 5: Applications of the Derivative
5.1 Extrema
5.2 The Mean Value Theorem
5.3 Derivative and The Geometry of Curves
5.4 Optimization
5.5 Linear Approximation, Differentials, and Error
5.6 Models Using Simple Differential Equations
5.7 Stability of Equilibria of Differential Equations
5.8 Stability of Equilibria of Difference Equations
5.9 Newton’s Method (Optional)
5.10 L’Hôpital’s Rule
5.11 Related Rates
5.12 Antiderivatives
5.13 Review
Chapter 6: The Definite Integral
6.1 The Area Problem, The Distance Problem, and Riemann Sums
6.2 The Definite Integral
6.3 The Fundamental Theorem of Calculus
6.4 Interpretations and Applications of the Definite Integral
6.5 Numerical Integration
6.6 Review
Chapter 7: Basic Integration Techniques
7.1 Integration by Substitution
7.2 Using Integral Tables and Computer Algebra Systems
7.3 Integration by Parts
7.4 Partial Fractions
7.5 Additional Integration Techniques
7.6 Improper Integrals
7.7 Taylor Polynomial Approximations
7.8 Review
Additional Chapters to be included in the First Edition:
Chapter 8: Applications of the Definite Integral
Chapter 9: Ordinary Differential Equations
Chapter 10: Matrix Algebra and Models
Chapter 11: Differential Calculus of Functions of Several Variables
Chapter 12: Systems of Difference Equations
Chapter 13: Systems of Differential Equations
Chapter 14: Probability: Applications and Constructive Modeling
Chapter 15: Statistical Inference: Applications and Models
Timothy D. Comar is a professor of mathematics at Benedictine University in Lisle, IL. He earned his Ph.D. in mathematics at the University of Michigan specializing in low dimensional topology. He is currently working mathematical biology with interests in the dynamics of deterministic and stochastic models for pest management, vaccination strategies for epidemics, and gene regulatory networks using impulsive differential equations, difference equations, Boolean models, and agent-based models. He has taught biocalculus courses for many years, and mentored many undergraduate research projects in mathematical biology.
James Peirce is a Professor of Mathematics at the University of Wisconsin - La Crosse. He received his Ph.D. in Mathematics from U.C. Davis in 2004. As an applied mathematician, he loves incorporating problems from mathematical biology into his courses. His research focuses on host-parasite models in the field of Mathematical Ecology. He enjoys sampling host populations with his biology collaborators from sites within the Upper Mississippi River and the sandy beaches of California. Since 2004, he has directed numerous undergraduate research projects (often pairing mathematics and biology students) in the hope of developing the next generation of mathematical ecologists.
Olcay Akman is a professor of mathematics at Illinois State University in Normal, IL. He is the director of the intercollegiate Biomathematics Alliance, a consortium of universities collaborating and sharing resource in the pursuit of scholarships, teaching, and advanced research development. Olcay is currently Editor-in-Chief of the journal Letters in Biomathematics and a journal for undergraduate research, Spora. His research interests include computing-intensive modeling, using evolutionary computing or machine learning based methods.