Calculus

Brian Erf Blank is an associate professor of mathematics at Washington University in St. Louis. He received his Ph.D. in 1980 at Cornell University, with Anthony Knapp as advisor. His 20th century work involved harmonic analysis.Steven George Krantz is an American scholar, mathematician, and writer. He has authored more than 235 research papers and more than 125 books. Additionally, Krantz has edited journals such as the Notices of the American Mathematical Society and The Journal of Geometric Analysis.

• Preface. Supplementary Resources.Acknowledgments.About the Authors.C H A P T E R 1 Basics.Preview.1 Number Systems.2 Planar Coordinates and Graphing in the Plane.3 Lines and Their Slopes.4 Functions and Their Graphs.5 Combining Functions.6 Trigonometry.Summary of Key Topics.Review Exercises.Genesis & Development 1.C H A P T E R 2 Limits.Preview.1 The Concept of Limit.2 Limit Theorems.3 Continuity.4 Infinite Limits and Asymptotes.5 Limits of Sequences.6 Exponential Functions and Logarithms.Summary of Key Topics.Review Exercises.Genesis & Development 2.C H A P T E R 3 The Derivative.Preview.1 Rates of Change and Tangent Lines.2 The Derivative.3 Rules for Differentiation.4 Differentiation of Some Basic Functions.5 The Chain Rule.6 Derivatives of Inverse Functions.7 Higher Derivatives.8 Implicit Differentiation.9 Differentials and Approximation of Functions.10 Other Transcendental Functions.Summary of Key Topics.Review Exercises.Genesis & Development 3.C H A P T E R 4 Applications of the Derivative.Preview.1 Related Rates.2 The Mean Value Theorem.3 Maxima and Minima of Functions.4 Applied Maximum-Minimum Problems.5 Concavity.6 Graphing Functions.7 l’Hoˆ pital’s Rule.8 The Newton-Raphson Method.9 Antidifferentiation and Applications.Summary of Key Topics.Review Exercises.Genesis & Development 4.C H A P T E R 5 The Integral.Preview.1 Introduction to Integration—The Area Problem.2 The Riemann Integral.3 Rules for Integration.4 The Fundamental Theorem of Calculus.5 A Calculus Approach to the Logarithm and Exponential Functions.6 Integration by Substitution.7 More on the Calculation of Area.8 Numerical Techniques of Integration.Summary of Key Topics.Review Exercises.Genesis & Development 5.C H A P T E R 6 Techniques of Integration.Preview.1 Integration by Parts.2 Powers and Products of Trigonometric Functions.3 Trigonometric Substitution.4 Partial Fractions—Linear Factors.5 Partial Fractions—Irreducible Quadratic Factors.6 Improper Integrals—Unbounded Integrands.7 Improper Integrals—Unbounded Intervals.Summary of Key Topics.Review Exercises.Genesis & Development 6.C H A P T E R 7 Applications of the Integral.Preview.1 Volumes.2 Arc Length and Surface Area.3 The Average Value of a Function.4 Center of Mass.5 Work.6 First Order Differential Equations—Separable Equations.7 First Order Differential Equations—Linear Equations.Summary of Key Topics.Review Exercises.Genesis & Development 7.C H A P T E R 8 Infinite Series.Preview.1 Series.2 The Divergence Test and the Integral Test.3 The Comparison Tests.4 Alternating Series.5 The Ratio and Root Tests.6 Introduction to Power Series.7 Representing Functions by Power Series.8 Taylor Series.Summary of Key Topics.Review Exercises.Genesis & Development 8.Table of Integrals.Answers to Selected Exercises.Index.