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Schaum's Outline of Theory and Problems of Beginning Calculus (Second Edition) by Elliott Mendelson



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Schaum's Outline of Theory and Problems of Beginning Calculus (Second Edition) written by Elliott Mendelson, Ph.D., Professor of Mathematics, Queens College, City University of New York, New Yark.

Schaum's Outline of Theory and Problems of Beginning Calculus (Second Edition) written by Elliott Mendelson cover the following topics.

  • 1. Coordinate Systems on a Line
    1.1 The Coordinates of a Point
    1.2 Absolute Value

  • 2. Coordinate Systems in a Plane
    2.1 The Coordinates of a Point
    2.2 The Distance Formula
    2.3 The Midpoint Formulas

  • 3. Graphs of Equations

  • 4. Straight Lines
    4.1 Slope
    4.2 Equations of a Line
    4.3 Parallel Lines
    4.4 Perpendicular Lines

  • 5. Intersections of Graphs

  • 6. Symmetry
    6.1 Symmetry about a Line

  • 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

  • 8. Limits
    8.1 Introduction
    8.2 Properties of Limits
    8.3 Existence or Nonexistence of the Limit

  • 9. Special Limits
    9.1 One-Sided Limits
    9.2 Infinite Limits: Vertical Asymptotes
    9.3 Limits at Infinity: Horizontal Asymptotes

  • 10. Continuity
    10.1 Definition and Properties
    10.2 One-Sided Continuity
    10.3 Continuity over a Closed Interval

  • 11. The Slope of a Tangent Line

  • 12. The Derivative

  • 13. More on the Derivative
    13.1 Differentiability and Continuity
    13.2 Further Rules for Derivatives

  • 14. Maximum and Minimum Problems
    14.1 Relative Extrema
    14.2 Absolute Extrema

  • 15. The Chain Rule
    15.1 Composite Functions
    15.2 Differentiation of Composite Functions

  • 16. Implicit Differentiation

  • 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

  • 18. Rectilinear Motion and Instantaneous Velocity

  • 19. Instantaneous Rate of Change

  • 20. Related Rates

  • 21. Approximation by Differentials; Newton's Method
    21.1 Estimating the Value of a Function
    21.2 The Differential
    21.3 Newton's Method

  • 22. Higher-Order Derivatives

  • 23. Applications of the Second Derivative and Graph Sketching
    23.1 Concavity
    23.2 Test for Relative Extrema
    23.3 Graph Sketching

  • 24. More Maximum and Minimum Problems

  • 25. Angle Measure
    25.1 Arc Length and Radian Measure
    25.2 Directed Angles

  • 26. Sine and Cosine Functions
    26.1 General Definition
    26.2 Properties

  • 27. Graphs and Derivatives of Sine and Cosine Functions
    27.1 Graphs
    27.2 Derivatives

  • 28. The Tangent and Other Trigonometric Functions

  • 29. Antiderivatives
    29.1 Definition and Notation
    29.2 Rules for Antiderivatives

  • 30. The Definite Integral
    30.1 Sigma Notation
    30.2 Area under a Curve
    30.3 Properties of the Definite Integral

  • 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

  • 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

  • 33. Applications of Integration II: Volume
    33.1 Solids of Revolution
    33.2 Volume Based on Cross Sections

  • 34. The Natural Logarithm
    34.1 Definition
    34.2 Properties

  • 35. Exponential Functions
    35.1 Introduction
    35.2 Properties of ax
    35.3 The Function ex
    36.1 L'Hôpital's Rule
    36.2 Exponential Growth and Decay

  • 36. L'Hôpital's Rule; Exponential Growth and Decay

  • 37. Inverse Trigonometric Functions
    37.1 One-One Functions 292
    37.2 Inverses of Restricted Trigonometric Functions

  • 38. Integration by Parts

  • 39. Trigonometric Integrands and Trigonometric Substitutions
    39.1 Integration of Trigonometric Functions
    39.2 Trigonometric Substitutions

  • 40. Integration of Rational Functions; The Method of Partial Fractions

  • Appendix
    A Trigonometric Formulas
    B Basic Integration Formulas
    C Geometric Formulas
    D Trigonometric Functions
    E Natural Logarithms
    F Exponential Functions

  • Answers to Supplementary Problem

  • Index

  • This page intentionally left blank

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