Student Solutions Manual for Calculus for Biology and Medicine

<div class="c-section-headers-number-list_container"> <h4 class="h5">(NOTE: Each chapter concludes with Key Terms and Review Problems.)</h4> <h3>1. Preview and Review</h3> <ul> <li>1.1 Precalculus Skills Diagnostic Test</li> <li>1.2 Preliminaries</li> <li>1.3 Elementary Functions</li> <li>1.4 Graphing</li> </ul> <h3>2. Discrete-Time Models, Sequences, and Difference Equations</h3> <ul> <li>2.1 Exponential Growth and Decay</li> <li>2.2 Sequences</li> <li>2.3 Modeling with Recurrence Equations</li> </ul> <h3>3. Limits and Continuity</h3> <ul> <li>3.1 Limits</li> <li>3.2 Continuity</li> <li>3.3 Limits at Infinity</li> <li>3.4 Trigonometric Limits and the Sandwich Theorem</li> <li>3.5 Properties of Continuous Functions</li> <li>3.6 A Formal Definition of Limits (Optional)</li> </ul> <h3>4. Differentiation</h3> <ul> <li>4.1 Formal Definition of the Derivative</li> <li>4.2 Properties of the Derivative</li> <li>4.3 Power Rules and Basic Rules</li> <li>4.4 The Product and Quotient Rules, and the Derivatives of Rational and Power Functions</li> <li>4.5 Chain Rule</li> <li>4.6 Implicit Functions and Implicit Differentiation</li> <li>4.7 Higher Derivatives</li> <li>4.8 Derivatives of Trigonometric Functions</li> <li>4.9 Derivatives of Exponential Functions</li> <li>4.10 Inverse Functions and Logarithms</li> <li>4.11 Linear Approximation and Error Propagation</li> </ul> <h3>5. Applications of Differentiation</h3> <ul> <li>5.1 Extrema and the Mean-Value Theorem</li> <li>5.2 Monotonicity and Concavity</li> <li>5.3 Extrema and Inflection Points</li> <li>5.4 Optimization</li> <li>5.5 L'Hôpital's Rule</li> <li>5.6 Graphing and Asymptotes</li> <li>5.7 Recurrence Equations: Stability (Optional)</li> <li>5.8 Numerical Methods: The Newton - Raphson Method (Optional)</li> <li>5.9 Modeling Biological Systems Using Differential Equations (Optional)</li> <li>5.10 Antiderivatives</li> </ul> <h3>6. Integration</h3> <ul> <li>6.1 The Definite Integral</li> <li>6.2 The Fundamental Theorem of Calculus</li> <li>6.3 Applications of Integration</li> </ul> <h3>7. Integration Techniques and Computational Methods</h3> <ul> <li>7.1 The Substitution Rule</li> <li>7.2 Integration by Parts and Practicing Integration</li> <li>7.3 Rational Functions and Partial Fractions</li> <li>7.4 Improper Integrals (Optional)</li> <li>7.5 Numerical Integration</li> <li>7.6 The Taylor Approximation (optional)</li> <li>7.7 Tables of Integrals (Optional)</li> </ul> <h3>8. Differential Equations</h3> <ul> <li>8.1 Solving Separable Differential Equations</li> <li>8.2 Equilibria and Their Stability</li> <li>8.3 Differential Equation Models</li> <li>8.4 Integrating Factors and Two-Compartment Models</li> </ul> <h3>9. Linear Algebra and Analytic Geometry</h3> <ul> <li>9.1 Linear Systems</li> <li>9.2 Matrices</li> <li>9.3 Linear Maps, Eigenvectors, and Eigenvalues</li> <li>9.4 Demographic Modeling</li> <li>9.5 Analytic Geometry</li> </ul> <h3>10. Multivariable Calculus</h3> <ul> <li>10.1 Two or More Independent Variables</li> <li>10.2 Limits and Continuity (optional)</li> <li>10.3 Partial Derivatives</li> <li>10.4 Tangent Planes, Differentiability, and Linearization</li> <li>10.5 The Chain Rule and Implicit Differentiation (Optional)</li> <li>10.6 Directional Derivatives and Gradient Vectors (Optional)</li> <li>10.7 Maximization and Minimization of Functions (Optional)</li> <li>10.8 Diffusion (Optional)</li> <li>10.9 Systems of Difference Equations (Optional)</li> </ul> <h3>11. Systems of Differential Equations</h3> <ul> <li>11.1 Linear Systems: Theory</li> <li>11.2 Linear Systems: Applications</li> <li>11.3 Nonlinear Autonomous Systems: Theory</li> <li>11.4 Nonlinear Systems: Lotka - Volterra Model of Interspecific Interactions</li> <li>11.5 More Mathematical Models (Optional)</li> </ul> <h3>12. Probability and Statistics</h3> <ul> <li>12.1 Counting</li> <li>12.2 What Is Probability?</li> <li>12.3 Conditional Probability and Independence</li> <li>12.4 Discrete Random Variables and Discrete Distributions</li> <li>12.5 Continuous Distributions</li> <li>12.6 Limit Theorems</li> <li>12.7 Statistical Tools</li> </ul> <h3>Appendices</h3> <ul> <li>A: Frequently Used Symbols</li> <li>B: Table of the Standard Normal Distribution</li> </ul> <h4 class="h5">Answers to Odd-Numbered Problems</h4> <h4 class="h5">References</h4> <h4 class="h5">Photo Credits</h4> <h4 class="h5">Index</h4> </div>