Applied Calculus for the Life and Social Sciences

• 0. A PRECALCULUS REVIEW. The Real Number Line and Order. Absolute Value and Distance on the Real Number Line. Exponents and Radicals. Factoring Polynomials. Fractions and Rationalization. 1. FUNCTIONS, GRAPHS, AND LIMITS. The Cartesian Plane and the Distance Formula. Graphs of Equations. Lines in the Plane and Slope. Functions. Limits. Continuity. 2. DIFFERENTIATION. The Derivative and the Slope of a Graph. Some Rules for Differentiation. Rates of Change. The Product and Quotient Rules. The Chain Rule. Higher-Order Derivatives. 3. APPLICATIONS OF THE DERIVATIVE. Increasing and Decreasing Functions. Extrema and the First-Derivative Test. Concavity and the Second-Derivative. Optimization Problems. Asymptotes. Curve Sketching: A Summary. Differentials: Linear Approximation. 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Natural Exponential Functions. Derivatives of Exponential Functions. Logarithmic Functions. Derivatives of Logarithmic Functions. Exponential Growth and Decay. 5. TRIGONOMETRIC FUNCTIONS. Radian Measure of Angles. The Trigonometric Functions. Graphs of Trigonometric Functions. Derivatives of Trigonometric Functions. 6. INTEGRATION AND ITS APPLICATIONS. Antiderivatives and Indefinite Integrals. Integration by Substitution and The General Power Rule. Exponential and Logarithmic Integrals. Area and the Fundamental Theorem of Calculus. The Area of a Region Bounded by Two Graphs. Volumes of Solids of Revolution. 7. TECHNIQUES OF INTEGRATION. Integration by Parts. Partial Fractions and Logistic Growth. Integrals of Trigonometric Functions. The Definite Integral as the Limit of a Sum. Numerical Integration. Improper Integrals 8. MATRICES. Systems of Linear Equations in Two Variables. Systems of Linear Equations in More Than Two Variables. Matrices and Systems of Linear Equations. Operations with Matrices. The Inverse of a Matrix. 9. FUNCTIONS OF SEVERAL VARIABLES. The Three-Dimensional Coordinate System. Surfaces in Space. Functions of Several Variables. Partial Derivatives. Extrema of Functions of Two Variables. Least Squares Regression Analysis. Double Integrals and Area in the Plane. Applications of Double Integrals. 10. DIFFERENTIAL EQUATIONS. Solutions of Differential Equations. Separation of Variables. First-Order Linear Differential Equations. Applications of Differential Equations. 11. PROBABILITY AND CALCULUS. Discrete Probability. Continuous Random Variables. Expected Value and Variance. Appendix A. Differentiation and Integration Formulas. Appendix B. Additional Topics in Differentiation. Implicit Differentiation. Related Rates. Appendix C. Probability and Probability Distributions (web only). Probability. Probability Computations. Conditional Probability. Tree Diagrams and Bayes' Theorem. Probability Distributions. Normal Distribution. Binomial Distribution. Appendix D. Properties and Measurement (web only). Review of Algebra. Units of Measurements. Appendix E. Graphing Utility Programs (web only). Graphing Utility Programs.

0. A PRECALCULUS REVIEW. The Real Number Line and Order. Absolute Value and Distance on the Real Number Line. Exponents and Radicals. Factoring Polynomials. Fractions and Rationalization. 1. FUNCTIONS, GRAPHS, AND LIMITS. The Cartesian Plane and the Distance Formula. Graphs of Equations. Lines in the Plane and Slope. Functions. Limits. Continuity. 2. DIFFERENTIATION. The Derivative and the Slope of a Graph. Some Rules for Differentiation. Rates of Change. The Product and Quotient Rules. The Chain Rule. Higher-Order Derivatives. 3. APPLICATIONS OF THE DERIVATIVE. Increasing and Decreasing Functions. Extrema and the First-Derivative Test. Concavity and the Second-Derivative. Optimization Problems. Asymptotes. Curve Sketching: A Summary. Differentials: Linear Approximation. 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Natural Exponential Functions. Derivatives of Exponential Functions. Logarithmic Functions. Derivatives of Logarithmic Functions. Exponential Growth and Decay. 5. TRIGONOMETRIC FUNCTIONS. Radian Measure of Angles. The Trigonometric Functions. Graphs of Trigonometric Functions. Derivatives of Trigonometric Functions. 6. INTEGRATION AND ITS APPLICATIONS. Antiderivatives and Indefinite Integrals. Integration by Substitution and The General Power Rule. Exponential and Logarithmic Integrals. Area and the Fundamental Theorem of Calculus. The Area of a Region Bounded by Two Graphs. Volumes of Solids of Revolution. 7. TECHNIQUES OF INTEGRATION. Integration by Parts. Partial Fractions and Logistic Growth. Integrals of Trigonometric Functions. The Definite Integral as the Limit of a Sum. Numerical Integration. Improper Integrals 8. MATRICES. Systems of Linear Equations in Two Variables. Systems of Linear Equations in More Than Two Variables. Matrices and Systems of Linear Equations. Operations with Matrices. The Inverse of a Matrix. 9. FUNCTIONS OF SEVERAL VARIABLES. The Three-Dimensional Coordinate System. Surfaces in Space. Functions of Several Variables. Partial Derivatives. Extrema of Functions of Two Variables. Least Squares Regression Analysis. Double Integrals and Area in the Plane. Applications of Double Integrals. 10. DIFFERENTIAL EQUATIONS. Solutions of Differential Equations. Separation of Variables. First-Order Linear Differential Equations. Applications of Differential Equations. 11. PROBABILITY AND CALCULUS. Discrete Probability. Continuous Random Variables. Expected Value and Variance. Appendix A. Differentiation and Integration Formulas. Appendix B. Additional Topics in Differentiation. Implicit Differentiation. Related Rates. Appendix C. Probability and Probability Distributions (web only). Probability. Probability Computations. Conditional Probability. Tree Diagrams and Bayes' Theorem. Probability Distributions. Normal Distribution. Binomial Distribution. Appendix D. Properties and Measurement (web only). Review of Algebra. Units of Measurements. Appendix E. Graphing Utility Programs (web only). Graphing Utility Programs.