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