Calculus for the life sciences
著者
書誌事項
Calculus for the life sciences
Wiley, c2014
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注記
Includes bibliographical references and indexes
内容説明・目次
内容説明
Authored by two distinguished researchers/teachers and an experiences, successful textbook author, Calculus for Life Sciences is a valuable resource for Life Science courses. As life-science departments increase the math requirements for their majors, there is a need for greater mathematic knowledge among students. This text balances rigorous mathematical training with extensive modeling of biological problems. The biological examples from health science, ecology, microbiology, genetics, and other domains, many based on cited data, are key features of this text.
目次
Preview of Modeling and Calculus
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
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
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'Ho pital's Rule
Group Projects
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
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
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
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
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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