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CITATION

Mendelson, Elliott. Schaum's Outline of Beginning Calculus, Third Edition. US: McGraw-Hill, 2009.

Schaum's Outline of Beginning Calculus, Third Edition

Authors: Elliott Mendelson

Published:  August 2009

eISBN: 9780071815239 0071815236 | ISBN: 9780071635356
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  • Contents
  • Chapter 1 Coordinate Systems on a Line
  • 1.1 The Coordinates of a Point
  • 1.2 Absolute Value
  • Chapter 2 Coordinate Systems in a Plane
  • 2.1 The Coordinates of a Point
  • 2.2 The Distance Formula
  • 2.3 The Midpoint Formulas
  • Chapter 3 Graphs of Equations
  • Chapter 4 Straight Lines
  • 4.1 Slope
  • 4.2 Equations of a Line
  • 4.3 Parallel Lines
  • 4.4 Perpendicular Lines
  • Chapter 5 Intersections of Graphs
  • Chapter 6 Symmetry
  • 6.1 Symmetry about a Line
  • 6.2 Symmetry about a Point
  • Chapter 7 Functions and Their Graphs
  • 7.1 The Notion of a Function
  • 7.2 Intervals
  • 7.3 Even and Odd Functions
  • 7.4 Algebra Review: Zeros of Polynomials
  • Chapter 8 Limits
  • 8.1 Introduction
  • 8.2 Properties of Limits
  • 8.3 Existence or Nonexistence of the Limit
  • Chapter 9 Special Limits
  • 9.1 One-Sided Limits
  • 9.2 Infinite Limits: Vertical Asymptotes
  • 9.3 Limits at Infinity: Horizontal Asymptotes
  • Chapter 10 Continuity
  • 10.1 Definition and Properties
  • 10.2 One-Sided Continuity
  • 10.3 Continuity over a Closed Interval
  • Chapter 11 The Slope of a Tangent Line
  • Chapter 12 The Derivative
  • Chapter 13 More on the Derivative
  • 13.1 Differentiability and Continuity
  • 13.2 Further Rules for Derivatives
  • Chapter 14 Maximum and Minimum Problems
  • 14.1 Relative Extrema
  • 14.2 Absolute Extrema
  • Chapter 15 The Chain Rule
  • 15.1 Composite Functions
  • 15.2 Differentiation of Composite Functions
  • Chapter 16 Implicit Differentiation
  • Chapter 17 The Mean-Value Theorem and the Sign of the Derivative
  • 17.1 Rolle’s Theorem and the Mean-Value Theorem
  • 17.2 The Sign of the Derivative
  • Chapter 18 Rectilinear Motion and Instantaneous Velocity
  • Chapter 19 Instantaneous Rate of Change
  • Chapter 20 Related Rates
  • Chapter 21 Approximation by Differentials; Newton’s Method
  • 21.1 Estimating the Value of a Function
  • 21.2 The Differential
  • 21.3 Newton’s Method
  • Chapter 22 Higher-Order Derivatives
  • Chapter 23 Applications of the Second Derivative and Graph Sketching
  • 23.1 Concavity
  • 23.2 Test for Relative Extrema
  • 23.3 Graph Sketching
  • Chapter 24 More Maximum and Minimum Problems
  • Chapter 25 Angle Measure
  • 25.1 Arc Length and Radian Measure
  • 25.2 Directed Angles
  • Chapter 26 Sine and Cosine Functions
  • 26.1 General Definition
  • 26.2 Properties
  • Chapter 27 Graphs and Derivatives of sine and Cosine Functions
  • 27.1 Graphs
  • 27.2 Derivatives
  • Chapter 28 The Tangent and Other Trigonometric Functions
  • Chapter 29 Antiderivatives
  • 29.1 Definition and Notation
  • 29.2 Rules for Antiderivatives
  • Chapter 30 The Definite Integral
  • 30.1 Sigma Notation
  • 30.2 Area under a Curve
  • 30.3 Properties of the Definite Integral
  • Chapter 31 The Fundamental Theorem of Calculus
  • 31.1 Calculation of the Definite Integral
  • 31.2 Average Value of a Function
  • 31.3 Change of Variable in a Definite Integral
  • Chapter 32 Applications of Integration I: Area and Arc Length
  • 32.1 Area between a Curve and the y-Axis
  • 32.2 Area between Two Curves
  • 32.3 Arc Length
  • Chapter 33 Applications of Integration II: Volume
  • 33.1 Solids of Revolution
  • 33.2 Volume Based on Cross Sections
  • Chapter 34 The Natural Logarithm
  • 34.1 Definition
  • 34.2 Properties
  • Chapter 35 Exponential Functions
  • 35.1 Introduction
  • 35.2 Properties of a[sup(x)]
  • 35.3 The Function e[sup(x)]
  • Chapter 36 L’Hôpital’s Rule; Exponential Growth and Decay
  • 36.1 L’Hôpital’s Rule
  • 36.2 Exponential Growth and Decay
  • Chapter 37 Inverse Trigonometric Functions
  • 37.1 One-One Functions
  • 37.2 Inverses of Restricted Trigonometric Functions
  • Chapter 38 Integration by Parts
  • Chapter 39 Trigonometric Integrands and Trigonometric Substitutions
  • 39.1 Integration of Trigonometric Functions
  • 39.2 Trigonometric Substitutions
  • Chapter 40 Integration of Rational Functions; The Method of Partial Fractions
  • Appendix A: Trigonometric Formulas
  • Appendix B: Basic Integration Formulas
  • Appendix C: Geometric Formulas
  • Appendix D: Trigonometric Functions
  • Appendix E: Natural Logarithms
  • Appendix F: Exponential Functions
  • Answers to Supplementary Problems
  • Index