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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 . This book 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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