Brief Calculus: An Applied Approach
Note: Each chapter includes an Algebra Review, Chapter Summary and Study Strategies, Review Exercises, and Sample Post-Graduation Exam Questions. A Precalculus Review 0.1 The Real Line and Order 0.2 Absolute Value and Distance on the Real Number Line 0.3 Exponents and Radicals 0.4 Factoring Polynomials 0.5 Fractions and Rationalization 1. Functions, Graphs, and Limits 1.1 The Cartesian Plane and the Distance Formula 1.2 Graphs of Equations 1.3 Lines in the Plane and Slope 1.4 Functions 1.5 Limits 1.6 Continuity 2. Differentiation 2.1 The Derivative and the Slope of a Graph 2.2 Some Rules for Differentiation 2.3 Rates of Change: Velocity and Marginals 2.4 The Product and Quotient Rules 2.5 The Chain Rule 2.6 Higher-Order Derivatives 2.7 Implicit Differentiation 2.8 Related Rates 3. Applications of the Derivative 3.1 Increasing and Decreasing Functions 3.2 Extrema and the First-Derivative Test 3.3 Concavity and the Second-Derivative Test 3.4 Optimization Problems 3.5 Business and Economics Applications 3.6 Asymptotes 3.7 Curve Sketching: A Summary 3.8 Differentials and Marginal Analysis 4. Exponential and Logarithmic Functions 4.1 Exponential Functions 4.2 Natural Exponential Functions 4.3 Derivatives of Exponential Functions 4.4 Logarithmic Functions 4.5 Derivatives of Logarithmic Functions 4.6 Exponential Growth and Decay 5. Integration and Its Applications 5.1 Antiderivatives and Indefinite Integrals 5.2 The General Power Rule 5.3 Exponential and Logarithmic Integrals 5.4 Area and the Fundamental Theorem of Calculus 5.5 The Area of a Region Bounded by Two Graphs 5.6 The Definite Integral as the Limit of a Sum 5.7 Volumes of Solids of Revolution 6. Techniques of Integration 6.1 Integration by Substitution 6.2 Integration by Parts and Present Value 6.3 Partial Fractions and Logistic Growth 6.4 Integration Tables and Completing the Square 6.5 Numerical Integration 6.6 Improper Integrals 7. Functions of Several Variables 7.1 The Three-Dimensional Coordinate System 7.2 Surfaces in Space 7.3 Functions of Several Variables 7.4 Partial Derivatives 7.5 Extrema of Functions of Two Variables 7.6 Lagrange Multipliers 7.7 Least Squares Regression Analysis 7.8 Double Integrals and Area in the Plane 7.9 Applications of Double Integrals Appendices