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CALCULUS STUDY GUIDE

Boost Your grades with this illustrated study guide. You will use it from high school all the way to graduate school and beyond. FREE chapters on Limits, Derivatives, Table of Derivatives in the trial version.


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Audience:

Intended for everyone interested in Math and Science, particularly high school, undergraduate, and graduate students.

Features:

  • Includes both Calculus I and II
  • Clear and concise explanations
  • Difficult concepts are explained in simple terms
  • Illustrated with graphs and diagrams
  • Search for the words or phrases
  • Access the guide anytime, anywhere - at home, on the train, in the subway.
  • Use your down time to prepare for an exam.
  • Always have the guide available for a quick reference.
  • Automatic synchronization between the handheld and the desktop PC. You could read half of the book on the handheld, then finish reading on the desktop. Annotations and drawings are also synchronized.

Table of Contents:

Introduction: Functions

Limits and Continuity: Limit of a Sequence | Limit of a Function | Limit of a function at infinity | Continuity | Classification of Discontinuities

Derivative: Computing the derivative | Quotient Rules | The Chain Rule | Implicit Function | Related Rates | Product Rule
Table of derivatives: General differentiation rules | Derivatives of simple functions | Derivatives of exponential and logarithmic functions | Derivatives of trigonometric functions | Derivatives of hyperbolic functions | Derivatives of Inverse Trigonometric Functions

Integration (Antiderivative): Integral | Arbitrary Constant of Integration | The Fundamental Theorem of Calculus
Table of Integrals: Rules for integration of general functions | Integrals of simple functions | Rational functions | Irrational functions | Logarithms | Exponential functions | Trigonometric functions | Inverse Trigonometric Functions | Hyperbolic functions | Inverse hyperbolic functions | Definite integrals lacking closed-form antiderivatives | The "sophomore's dream" | Integral Curve | Euler-Maclaurin Formula | Trapezium rule

Logarithms and Exponentials: E - base of natural logarithm | Ln(x) | Hiperbolic functions

Applications of the Definite Integral in Geometry: Area of a Surface of Revolution | Solid of Revolution

Techniques of Integration: Integration by Parts | The ILATE rule | Integration by Substitution | Trigonometric Substitution | Partial Fractions in Integration of Rational Function | Numeric Integration | Simpson Rule

Principles of Integral Evaluation: Methods of Contour Integration | Cauchy's Integral Formula | Improper Integrals | L'Hopital's Rule

Differential Equations: First-Order Differential Equation | Linear Differential Equation
Examples: A separable first order linear ordinary differential equation | Non-separable first order linear ordinary differential equations | A simple mathematical model | Harmonic Oscillator | Stiff Equation

Numerical Integration Methods: Numerical Ordinary Differential Equations | Euler's Method | Runge-Kutta Methods | Multistep Method

Series: Taylor Polynomials | Taylor Series | List of Taylor series | Lagrange Polynomial

 

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