Description

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This ebook provides a comprehensive introduction to fundamental concepts in calculus and their applications, covering all of Calculus 1 and some of Calculus 2. The book starts with functions and limits, followed by differential calculus, and then moves on to integral calculus and a brief discussion of differential equations. It ends with the complete solution for a sample exam based on the AP Calculus AB course. Videos for the topics covered in the ebook, along with practice problems, exercises and quizzes, are available in the interactive Wolfram U course Introduction to Calculus. Contents

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What Is Calculus? · Functions · The Elementary Functions · The Limit of a Function · The Laws of Limits · Continuity · Derivatives and Rates of Change · The Derivative as a Function · Differentiation Formulas · Derivatives of Trigonometric Functions · The Chain Rule · Implicit Differentiation · Rates of Change in the Sciences · Related Rates · Linear Approximations · Maxima and Minima · The Mean Value Theorem · Derivatives and the Shape of Graphs · Asymptotes · Curve Sketching · Optimization · Antiderivatives · Riemann Sums · The Definite Integral · The Fundamental Theorem of Calculus · Indefinite Integrals · The Substitution Rule · Areas between Curves · Volumes of Solids · Volumes by Cylindrical Shells · Average Value of a Function · Approximate Integration · Exponential Functions · Logarithmic Functions · L'Hôpital's Rule · Slope Fields and Euler's Method · Separable Differential Equations · Calculus and Programming · Sample Calculus Exam, Part 1 · Sample Calculus Exam, Part 2 Related Topics

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Calculus and Analysis