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# Lopez C.P. Differential Calculus using Mathematica

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Cesar Lopez Perez, 2016. — 246 p. — ISBN: 152343905X
Mathematica 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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