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Calculus by Paul Dawkins



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Calculus written by Paul Dawkins cover the following topics.

  • Review
    Introduction, Functions, Inverse Functions, Trig Functions, Solving Trig Equations, Solving Trig Equations with Calculators, Part I, Solving Trig Equations with Calculators, Part II, Exponential Functions, Logarithm Functions, Exponential and Logarithm Equations, Common Graphs

  • Limits
    Introduction, Rates of Change and Tangent Lines, The Limit, One‐Sided Limits, Limit Properties, Computing Limits, Infinite Limits, Limits At Infinity, Part I, Limits At Infinity, Part II, Continuity, The Definition of the Limit

  • Derivatives
    Introduction, The Definition of the Derivative, Interpretations of the Derivative, Differentiation Formulas, Product and Quotient Rule, Derivatives of Trig Functions, Derivatives of Exponential and Logarithm Functions, Derivatives of Inverse Trig Functions, Derivatives of Hyperbolic Functions, Chain Rule, Implicit Differentiation, Related Rates, Higher Order Derivatives, Logarithmic Differentiation

  • Applications of Derivatives
    Introduction, Rates of Change, Critical Points, Minimum and Maximum Values, Finding Absolute Extrema, The Shape of a Graph, Part I, The Shape of a Graph, Part II, The Mean Value Theorem, Optimization, More Optimization Problems, Indeterminate Forms and L’Hospital’s Rule, Linear Approximations, Differentials, Newton’s Method, Business Applications

  • Integrals
    Introduction, Indefinite Integrals, Computing Indefinite Integrals, Substitution Rule for Indefinite Integrals, More Substitution Rule, Area Problem, The Definition of the Definite Integral, Computing Definite Integrals, Substitution Rule for Definite Integrals

  • Applications of Integrals
    Introduction, Average Function Value, Area Between Curves, Volumes of Solids of Revolution / Method of Rings, Volumes of Solids of Revolution / Method of Cylinders, Work

  • Extras
    Introduction, Proof of Various Limit Properties, Proof of Various Derivative Facts/Formulas/Properties, Proof of Trig Limits, Proofs of Derivative Applications Facts/Formulas, Proof of Various Integral Facts/Formulas/Properties, Area and Volume Formulas, Types of Infinity, Summation Notation, Constants of Integration

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