Calculus Study Guide v12.2

Calculus Study Guide v.12.2

Requirements: 1.5+

Overview:



You will use it from high school all the way to graduate school and beyond.



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



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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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https://play.google.com/store/apps/details?id=com.mobilereference.calculus






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trmpereira — Thu Mar 14, 2013 10:14 pm


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