Author: Justin Skycak

Publisher: Justin Skycak

Published: 2019-03-01

Total Pages: 258

ISBN-13: 1798447487

Justin Math: Calculus is the second book in a series that covers the foundations of high school and college math: Algebra, Calculus, and Linear Algebra (with Differential Equations baked into the latter two). It provides deep intuition for the core concepts and connections, along with plenty of practice exercises, while remaining as concise as possible. CONTENTS 1. LIMITS AND DERIVATIVES - Evaluating Limits; Limits by Logarithms, Squeeze Theorem, and Euler's Consant; Derivatives and the Difference Quotient, Power Rule, Chain Rule, Properties of Derivatives, Derivatives of Non-Polynomial Functions, Finding Local Extrema, Differentials and Approximation, L'Hôpital's Rule. 2. INTEGRALS - Antiderivatives, Finding Area, Substitution, Integration by Parts, Improper Integrals. 3. DIFFERENTIAL EQUATIONS - Separation of Variables, Slope Fields and Euler Approximation, Substitution, Characteristic Polynomial, Undetermined Coefficients, Integrating Factors, Variation of Parameters. 4. SERIES - Geometric Series, Tests for Convergence, Taylor Series, Manipulating Taylor Series, Solving Differential Equations with Taylor Series.