Calculus and Its Applications

<div class="c-un-numbered-headers-and-contents-list__container"> <p>Prerequisite Skills Diagnostic Test</p> <h3>R. Functions, Graphs, and Models</h3> <ul> <li>R.1 Graphs and Equations</li> <li>R.2 Functions and Models</li> <li>R.3 Finding Domain and Range</li> <li>R.4 Slope and Linear Functions</li> <li>R.5 Nonlinear Functions and Models</li> <li>R.6 Exponential and Logarithmic Functions</li> <li>R.7 Mathematical Modeling and Curve Fitting</li> <li>Chapter Summary</li> <li>Chapter Review Exercises</li> <li>Chapter Test</li> <li>Extended Technology Application: Average Price of a Movie Ticket</li> </ul> <h3>1. Differentiation</h3> <ul> <li>1.1 Limits: A Numerical and Graphical Approach</li> <li>1.2 Algebraic Limits and Continuity</li> <li>1.3 Average Rates of Change</li> <li>1.4 Differentiation Using Limits and Difference Quotients</li> <li>1.5 Leibniz Notation and the Power and Sum–Difference Rules</li> <li>1.6 The Product and Quotient Rules</li> <li>1.7 The Chain Rule</li> <li>1.8 Higher-Order Derivatives</li> <li>Chapter Summary</li> <li>Chapter Review Exercises</li> <li>Chapter Test</li> <li>Extended Technology Application: Path of a Baseball: The Tale of the Tape</li> </ul> <h3>2. Exponential and Logarithmic Functions</h3> <ul> <li>2.1 Exponential and Logarithmic Functions of the Natural Base, e</li> <li>2.2 Derivatives of Exponential (Base-e) Functions</li> <li>2.3 Derivatives of Natural Logarithmic Functions</li> <li>2.4 Applications: Uninhibited and Limited Growth Models</li> <li>2.5 Applications: Exponential Decay</li> <li>2.6 The Derivatives of ax and loga x</li> <li>Chapter Summary</li> <li>Chapter Review Exercises</li> <li>Chapter Test</li> <li>Extended Technology Application: The Business of Motion Picture Revenue and DVD Release</li> </ul> <h3>3. Applications of Differentiation</h3> <ul> <li>3.1 Using First Derivatives to Classify Maximum and Minimum Values and Sketch Graphs</li> <li>3.2 Using Second Derivatives to Classify Maximum and Minimum Values and Sketch Graphs</li> <li>3.3 Graph Sketching: Asymptotes and Rational Functions</li> <li>3.4 Optimization: Finding Absolute Maximum and Minimum Values</li> <li>3.5 Optimization: Business, Economics, and General Applications</li> <li>3.6 Marginals, Differentials, and Linearization</li> <li>3.7 Elasticity of Demand</li> <li>3.8 Implicit Differentiation and Logarithmic Differentiation</li> <li>3.9 Related Rates</li> <li>Chapter Summary</li> <li>Chapter Review Exercises</li> <li>Chapter Test</li> <li>Extended Technology Application: Maximum Sustainable Harvest</li> </ul> <h3>4. Integration</h3> <ul> <li>4.1 Antidifferentiation</li> <li>4.2 Antiderivatives as Areas</li> <li>4.3 Area and Definite Integrals</li> <li>4.4 Properties of Definite Integrals: Additive Property, Average Value, and Moving Average</li> <li>4.5 Integration Techniques: Substitution</li> <li>4.6 Integration Techniques: Integration by Parts</li> <li>4.7 Numerical Integration</li> <li>Chapter Summary</li> <li>Chapter Review Exercises</li> <li>Chapter Test</li> <li>Extended Technology Application: Business and Economics: Distribution of Wealth</li> </ul> <h3>5. Applications of Integration</h3> <ul> <li>5.1 Consumer and Producer Surplus; Price Floors, Price Ceilings, and Deadweight Loss</li> <li>5.2 Integrating Growth and Decay Models</li> <li>5.3 Improper Integrals</li> <li>5.4 Probability</li> <li>5.5 Probability: Expected Value; the Normal Distribution</li> <li>5.6 Volume</li> <li>5.7 Differential Equations</li> <li>Chapter Summary</li> <li>Chapter Review Exercises</li> <li>Chapter Test</li> <li>Extended Technology Application: Curve Fitting and Volumes of Containers</li> </ul> <h3>6. Functions of Several Variables</h3> <ul> <li>6.1 Functions of Several Variables</li> <li>6.2 Partial Derivatives</li> <li>6.3 Maximum–Minimum Problems</li> <li>6.4 An Application: The Least-Squares Technique</li> <li>6.5 Constrained Optimization: Lagrange Multipliers and the Extreme-Value Theorem</li> <li>6.6 Double Integrals</li> <li>Chapter Summary</li> <li>Chapter Review Exercises</li> <li>Chapter Test</li> <li>Extended Technology Application: Minimizing Employees' Travel Time in a Building</li> </ul> <h3>7. Trigonometric Functions</h3> <ul> <li>7.1 Basics of Trigonometry</li> <li>7.2 Derivatives of Trigonometric Functions</li> <li>7.3 Integration of Trigonometric Functions</li> <li>7.4 Inverse Trigonometric Functions and Applications</li> <li>Chapter Summary</li> <li>Chapter Review Exercises</li> <li>Chapter Test</li> <li>Extended Technology Application</li> </ul> <h3>8. Differential Equations</h3> <ul> <li>8.1 Direction Fields, Autonomic Forms, and Population Models</li> <li>8.2 Applications: Inhibited Growth Models</li> <li>8.3 First-Order Linear Differential Equations</li> <li>8.4 Higher-Order Differential Equations and a Trigonometry Connection</li> <li>Chapter Summary</li> <li>Chapter Review Exercises</li> <li>Chapter Test</li> <li>Extended Technology Application</li> </ul> <h3>9. Sequences and Series</h3> <ul> <li>9.1 Arithmetic Sequences and Series</li> <li>9.2 Geometric Sequences and Series</li> <li>9.3 Simple and Compound Interest</li> <li>9.4 Annuities and Amortization</li> <li>9.5 Power Series and Linearization</li> <li>9.6 Taylor Series and a Trigonometry Connection</li> <li>Chapter Summary</li> <li>Chapter Review Exercises</li> <li>Chapter Test</li> <li>Extended Technology Application</li> </ul> <h3>10. Probability Distributions</h3> <ul> <li>10.1 A Review of Sets</li> <li>10.2 Theoretical Probability</li> <li>10.3 Discrete Probability Distributions</li> <li>10.4 Continuous Probability Distributions: Mean, Variance, and Standard Deviation</li> <li>Chapter Summary</li> <li>Chapter Review Exercises</li> <li>Chapter Test</li> <li>Extended Technology Application</li> </ul> <h3>11. Systems and Matrices (online only)</h3> <ul> <li>11.1 Systems of Linear Equations</li> <li>11.2 Gaussian Elimination</li> <li>11.3 Matrices and Row Operations</li> <li>11.4 Matrix Arithmetic: Equality, Addition, and Scalar Multiples</li> <li>11.5 Matrix Multiplication, Multiplicative Identities, and Inverses</li> <li>11.6 Determinants and Cramer's Rule</li> <li>11.7 Systems of Linear Inequalities and Linear Programming</li> <li>Chapter Summary</li> <li>Chapter Review Exercises</li> <li>Chapter Test</li> <li>Extended Technology Application</li> </ul> <h3>12. Combinatorics and Probability (online only)</h3> <ul> <li>12.1 Compound Events and Odds</li> <li>12.2 Combinatorics: The Multiplication Principle and Factorial Notation</li> <li>12.3 Permutations and Distinguishable Arrangements</li> <li>12.4 Combinations and the Binomial Theorem</li> <li>12.5 Conditional Probability and the Hypergeometric Probability Distribution Model</li> <li>12.6 Independent Events, Bernoulli Trials, and the Binomial Probability Model</li> <li>12.7 Bayes Theorem</li> <li>Chapter Summary</li> <li>Chapter Review Exercises</li> <li>Chapter Test</li> <li>Extended Technology Application</li> <br> <li>Cumulative Review</li> </ul> <h3>Appendices</h3> <ul> <li>A. Review of Basic Algebra</li> <li>B. Indeterminate Forms and l'Hôpital's Rule</li> <li>C. Regression and Microsoft Excel</li> <li>D. Areas for a Standard Normal Distribution</li> <li>E. Using Tables of Integration Formulas</li> </ul> <h4 class="h5">Answers</h4> <h4 class="h5">Index of Applications</h4> <h4 class="h5">Index</h4> </div>