# Calculus Study Guide (Mobi Study Guides)

## Overview

Calculus Study GuideFEATURES:- 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: FunctionsLimits and Continuity: Limit of a Sequence Limit of a Function Limit of a function at infinity Continuity Classification of DiscontinuitiesDerivative: 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 FunctionsIntegration (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 ruleLogarithms and Exponentials: E - base of natural logarithm Ln(x) Hiperbolic functionsApplications of the Definite Integral in Geometry: Area of a Surface of Revolution Solid of RevolutionTechniques of Integration: Integration by Parts The ILATE rule Integration by Substitution Trigonometric Substitution Partial Fractions in Integration of Rational Function Numeric Integration Simpson RulePrinciples of Integral Evaluation: Methods of Contour Integration Cauchy's Integral Formula Improper Integrals L'Hopital's RuleDifferential 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 EquationNumerical Integration Methods: Numerical Ordinary Differential Equations Euler's Method Runge-Kutta Methods Multistep MethodSeries: Taylor Polynomials Taylor Series List of Taylor series Lagrange Polynomial