Calculus: Single Variable, Student Study and Solutions Companion

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.

• 1 Basics 1 1.1 Number Systems  11.2 Planar Coordinates and Graphing in the Pl ne  41.3 Lines and Their Slopes  101.4 Functions and Their Graphs  161.5 Combining Functions  211.6 Trigonometry 262 Limits 352.1 The Concept of Limit  352.2 Limit Theorems  412.3 Continuity 462.4 In nite Limits and Asymptotes  522.5 Limits of Sequences  572.6 Exponential Functions and Logarithms  603 The Derivative 683.1 Rates of Change and Tangent Lines  683.2 The Derivative  743.3 Rules for Dierentiation  803.4 Dierentiation of Some Basic Functions  883.5 The Chain Rule  933.6 Derivatives of Inverse Functions  993.7 Higher Derivatives  1043.8 Implicit Dierentiation  1093.9 Dierentials and Approximation of Functions  1173.10 Other Transcendental Functions  1224 Applications of the Derivative 1304.1 Related Rates 1304.2 The Mean Value Theorem  1334.3 Maxima and Minima of Functions  1394.4 Applied Maximum-Minimum Problems  1454.5 Concavity  1514.6 Graphing Functions  1564.7 L'H^opital's Rule  1624.8 The Newton-Raphson Method  1684.9 Antidierentiation and Applications  1725 The Integral 1825.1 Introduction to Integration|The Area Problem  1825.2 The Riemann Integral  1875.3 Properties of the Integral  1925.4 The Fundamental Theorem of Calculus  1975.5 A Calculus Approach to the Logarithm and Exponential Function 2025.6 Integration by Substitution  2085.7 More on the Calculation of Area  2165.8 Numerical Techniques of Integration  2236 Techniques of Integration 2396.1 Integration by Parts  2396.2 Powers and Products of Trigonometric Functions 2526.3 Trigonometric Substitution 2646.4 Partial Fractions|Linear Factors 2766.5 Partial Fractions|Irreducible Quadratic Factors  2856.6 Improper Integrals|Unbounded Integrands  2946.7 Improper Integrals|Unbounded Intervals  3047 Applications of the Integral 3257.1 Volumes  3257.2 Arc Length and Surface Area  3327.3 The Average Value of a Function 3377.4 Center of Mass  3417.5 Work  3467.6 First Order Dierential Equations{Separable Equations  3507.7 First Order Dierential Equations{Linear Equations  3588 In nite Series 3718.1 Series  3718.2 The Divergence Test and the Integral Test  3778.3 The Comparison Tests  3828.4 Alternating Series  3858.5 The Root and Ratio Tests  3888.6 Introduction to Power Series  3928.7 Representing Functions by Power Series  4038.8 Taylor Series  411