Cesar Lopez Perez, 2016. — 246 p. — ISBN: 152343905XMathematica is a platform for scientific computing that helps you to work in virtually all areas of the experimental sciences and engineering. In particular, this software presents quite extensive capabilities and implements a large number of commands enabling you to efficiently handle problems involving Differential Calculus. Using Mathematica you will be able to work with Limits, Numerical and power series, Taylor and MacLaurin series, continuity, derivability, differentiability in several variables, optimization and differential equations. Mathematica also implements numerical methods for the approximate solution of differential equations.Limits And Continuity. One And Several Variables: Limits Of Sequences Limits Of Functions. Lateral Limits Continuity Several Variables: Limits And Continuity. Characterization Theorems Iterated And Directional Limits Continuity In Several Variables Numerical Series And Power Series Series. Convergence Criteria Numerical Series With Non-Negative Terms Alternating Numerical Series Power Series Power Series Expansions And Functions Taylor And Laurent Expansions Derivatives And Applications. One And Several Variables The Concept Of The Derivative Calculating Derivatives Tangents, Asymptotes, Concavity, Convexity, Maxima And Minima, Inflection Points And Growth Applications To Practical Problems Partial Derivatives Implicit Differentiation Derivability In Several Variables Differentiation Of Functions Of Several Variables Maxima And Minima Of Functions Of Several Variables Conditional Minima And Maxima. The Method Of “Lagrange Multipliers” Some Applications Of Maxima And Minima In Several Variables Vector Differential Calculus And Theorems In Several Variables Concepts Of Vector Differential Calculus The Chain Rule The Implicit Function Theorem The Inverse Function Theorem The Change Of Variables Theorem Taylor’s Theorem With N Variables Vector Fields. Curl, Divergence And The Laplacian Coordinate Transformation Differential Equations Separation Of Variables Homogeneous Differential Equations Exact Differential Equations Linear Differential Equations Numerical Solutions To Differential Equations Of The First Order Ordinary High-Order Equations Higher-Order Linear Homogeneous Equations With Constant Coefficients Non-Homogeneous Equations With Constant Coefficients. Variation Of Parameters Non-Homogeneous Linear Equations With Variable Coefficients. Cauchy-Euler Equations The Laplace Transform Systems Of Linear Homogeneous Equations With Constant Coefficients Systems Of Linear Non-Homogeneous Equations With Constant Coefficients Higher Order Equations And Approximation Methods The Euler Method The Runge–Kutta Method Differential Equations Systems By Approximate Methods Differential Equations In Partial Derivatives Orthogonal Polynomials
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