Calculus with Applications, 12th Edition Margaret Lial | eBook [PDF]

Title Page Copyright Page Contents Preface Acknowledgments Prerequisite Skills Diagnostic Test R Algebra Reference R.1 Polynomials R.2 Factoring R.3 Rational Expressions R.4 Equations R.5 Inequalities R.6 Exp ...

Title Page Copyright Page Contents Preface Acknowledgments Prerequisite Skills Diagnostic Test R Algebra Reference R.1 Polynomials R.2 Factoring R.3 Rational Expressions R.4 Equations R.5 Inequalities R.6 Exponents R.7 Radicals 1 Linear Functions 1.1 Slopes and Equations of Lines 1.2 Linear Functions and Applications 1.3 The Least Squares Line Chapter 1 Review Extended Application Predicting Life Expectancy 2 Nonlinear Functions 2.1 Properties of Functions 2.2 Quadratic Functions; Translation and Reflection 2.3 Polynomial and Rational Functions 2.4 Exponential Functions 2.5 Logarithmic Functions 2.6 Applications: Growth and Decay; Mathematics of Finance Chapter 2 Review Extended Application Power Functions 3 The Derivative 3.1 Limits 3.2 Continuity 3.3 Rates of Change 3.4 Definition of the Derivative 3.5 Graphical Differentiation Chapter 3 Review Extended Application A Model for Drugs Administered Intravenously 4 Calculating the Derivative 4.1 Techniques for Finding Derivatives 4.2 Derivatives of Products and Quotients 4.3 The Chain Rule 4.4 Derivatives of Exponential Functions 4.5 Derivatives of Logarithmic Functions Chapter 4 Review Extended Application Electric Potential and Electric Field 5 Graphs and the Derivative 5.1 Increasing and Decreasing Functions 5.2 Relative Extrema 5.3 Higher Derivatives, Concavity, and the Second Derivative Test 5.4 Curve Sketching Chapter 5 Review Extended Application A Drug Concentration Model for Orally Administered Medications 6 Applications of the Derivative 6.1 Absolute Extrema 6.2 Applications of Extrema 6.3 Further Business Applications 6.4 Implicit Differentiation 6.5 Related Rates 6.6 Differentials: Linear Approximation Chapter 6 Review Extended Application A Total Cost Model for a Training Program 7 Integration 7.1 Antiderivatives 7.2 Substitution 7.3 Area and the Definite Integral 7.4 The Fundamental Theorem of Calculus 7.5 The Area Between Two Curves 7.6 Numerical Integration Chapter 7 Review Extended Application Estimating Depletion Dates for Minerals 8 Further Techniques and Applications of Integration 8.1 Integration by Parts 8.2 Volume and Average Value 8.3 Continuous Money Flow 8.4 Improper Integrals Chapter 8 Review Extended Application Estimating Learning Curves in Manufacturing with Integrals 9 Multivariable Calculus 9.1 Functions of Several Variables 9.2 Partial Derivatives 9.3 Maxima and Minima 9.4 Lagrange Multipliers 9.5 Total Differentials and Approximations 9.6 Double Integrals Chapter 9 Review Extended Application Using Multivariable Fitting to Create a Response Surface Design 10 Differential Equations 10.1 Solutions of Elementary and Separable Differential Equations 10.2 Linear First-Order Differential Equations 10.3 Euler’s Method 10.4 Applications of Differential Equations Chapter 10 Review Extended Application Pollution of a Lake 11 Probability and Calculus 11.1 Continuous Probability Models 11.2 Expected Value and Variance of Continuous Random Variables 11.3 Special Probability Density Functions Chapter 11 Review Extended Application Exponential Waiting Times 12 Sequences and Series 12.1 Geometric Sequences 12.2 Annuities: An Application of Sequences 12.3 Taylor Polynomials at 0 12.4 Infinite Series 12.5 Taylor Series at 0 12.6 Newton’s Method 12.7 L’Hospital’s Rule Chapter 12 Review Extended Application Living Assistance and Subsidized Housing 13 The Trigonometric Functions 13.1 Definitions of the Trigonometric Functions 13.2 Derivatives of Trigonometric Functions 13.3 Integrals of Trigonometric Functions Chapter 13 Review Extended Application The Shortest Time and the Cheapest Path APPENDIX A Solutions to Prerequisite Skills Diagnostic Test APPENDIX B Tables 1 Formulas from Geometry 2 Area Under a Normal Curve to the Left of z, where z = x - μ/σ 3 Integrals 4 Integrals Involving Trigonometric Functions Answers to Selected Exercises Credits Index of Applications Business and Economics General Interest Life and Health Sciences Physical Sciences Social Sciences Index