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Calculus with Analytic Geometry by Crowell and Slesnick



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Calculus with Analytic Geometry written by Crowell and Slesnick cover the following topics.

  • 1 Functions, Limits, and Derivatives
    1.1 Real Numbers, Inequalities, Absolute Values
    1.2 Ordered Pairs of Real Numbers, the xy-Plane, Functions
    1.3 Operations with Functions
    1.4 Limits and Continuity
    1.5 Straight Lines and Their Equations
    1.6 The Derivative
    1.7 Derivatives of Polynomials and Rational Functions
    1.8 The Chain Rule
    1.9 Implicit Di erentiation

  • 2 Applications of the Derivative
    2.1 Curve Sketching
    2.2 Maximum and Minimum Problems
    2.3 Rates of Change with respect to Time.
    2.4 Approximate Values.
    2.5 Rolle's Theorem and Its Consequences
    2.6 The Differential
    2.7 L'H^opital's Rule

  • 3 Conic Sections
    3.1 The Circle
    3.2 The Parabola
    3.3 The Ellipse
    3.4 The Hyperbola

  • 4 Integration
    4.1 The De nite Integral
    4.2 Sequences and Summations
    4.3 Integrability of Monotonic Functions
    4.4 Properties of the De nite Integral
    4.5 The Fundamental Theorem of Calculus
    4.6 Inde nite Integrals.
    4.7 Area between Curves
    4.8 Integrals of Velocity and Acceleration

  • 5 Logarithms and Exponential Functions
    5.1 The Natural Logarithm
    5.2 The Exponential Function.
    5.3 Inverse Function Theorems.
    5.4 Other Exponential and Logarithm Functions.
    5.5 Introduction to Di erential Equations

  • 6 Trigonometric Functions
    6.1 Sine and Cosine
    6.2 Calculus of Sine and Cosine.
    6.3 Other Trigonometric Functions.
    6.4 Inverse Trigonometric Functions.
    6.5 Algebraic and Transcendental Functions
    6.6 Complex Numbers.
    6.7 The Complex Exponential Function ez.
    6.8 Di erential Equations.

  • 7 Techniques of Integration
    7.1 Integration by Parts.
    7.2 Integrals of Trigonometric Functions
    7.3 Trigonometric Substitutions.
    7.4 Partial Fractions.
    7.5 Other Substitutions.

  • 8 The De nite Integral
    8.1 Average Value of a Function.
    8.2 Riemann Sums and the Trapezoid Rule
    8.3 Numerical Approximations (Continued)
    8.4 Volume.
    8.5 Work.
    8.6 Integration of Discontinuous Functions
    8.7 Improper Integrals

  • 9 Infinite Series
    9.1 Sequences and Their Limits
    9.2 In nite Series: De nition and Properties.
    9.3 Nonnegative Series.
    9.4 Alternating Series.
    9.5 Absolute and Conditional Convergence.
    9.6 Power Series.
    9.7 Functions De ned by Power Series
    9.8 Taylor Series

  • 10 Geometry in the Plane
    10.1 Parametrically De ned Curves.
    10.2 Arc Length of a Parametrized Curve
    10.3 Vectors in the Plane
    10.4 The Derived Vector of a Parametrized Curve.
    10.5 Vector Velocity and Acceleration.
    10.6 Polar Coordinates
    10.7 Area and Arc Length in Polar Coordinates

  • 11 Differential Equations
    11.1 Review
    11.2 First-Order Linear Di erential Equations.
    11.3 Linear Di erential Operators.
    11.4 Homogeneous Di erential Equations.
    11.5 Nonhomogeneous Equations.
    11.6 Hyperbolic Functions.

  • Appendix
    A. Properties of Limits
    B. Properties of the De nite Integral
    C. Equivalent De nitions of the Integral

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