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# Joy of Mathematica

Mathematica for Calculus, Differential equations and algebra

350 pages, parution le 15/10/2000 (2eme édition)

## Résumé

Preface
Installation
Part I An Introduction to The Joy of Mathematica
A Brief Tour of Joy
Starting Joy
Using Mathematica Directly
Working with Notebooks
Quitting Joy
Creating Expressions
Reopening Your Mathematica Notebooks
Changing Joy's Settings
On-line Help
Troubleshooting
Part II How to Use Joy for ...
Graphing in Two Dimensions
How to Graph y = f(x)
How to Graph Implicit Functions
How to Plot Points
How to Combine Graphs
How to Graph 2D Parameterized Curves
How to Find Coordinates in a Graph
How to Customize Graphs
How to Graph in Polar Coordinates
How to Animate Graphs
Manipulating Expressions
How to Substitute into an Expression
How to Tabulate an Expression
How to Name an Expression
How to Expand an Expression
How to Factor a Polynomial
How to Collect Terms
How to Find Partial Fractions
How to Find a Common Denominator
How to Simplify Expressions in General
How to Clear a Definition or Value
Solving Equations
How to Solve Equations Algebraically
How to Solve Equations Numerically
How to Find Roots of Polynomials Numerically
How to Visualize Newton's Method
Working with Functions of One Variable
How to Create a Function
How to Evaluate a Function
How to Tabulate a Function
How to Plot a Table of Values
How to Iterate a Function
Differentiating Functions of One Variable
How to Differentiate y = f(x)
How to Find f' (a)
How to Graph f' (x)
How to Find Higher-Order Derivatives of f(x)
How to Differentiate an Expression in One
Variable
How to Find the Derivative of an Expression at a Point
How to Graph the Derivative of an Expression
How to Find Higher-Order Derivatives of an Expression
How to Approximate a Derivative Numerically
How to Differentiate an Implicit Function
Integrating Functions of One Variable
How to Find an Antiderivative (Indefinite
Integral)
How to Find a Definite Integral
How to Integrate Numerically
Working with Sequences and Series
How to Create a Sequence
How to Find a Value in a Sequence
How to List the Values of a Sequence
How to Plot a Sequence
How to Create a Series
How to Find One Partial Sum of a Series
How to Tabulate the Partial Sums of a Series
How to Plot the Partial Sums of a Series
How to Estimate a Sum Numerically
How to Create a Taylor Series
Graphing in Three Dimensions
How to Graph a Surface
How to Change Your View of a Surface
How to Plot the Level Curves of a Surface (Contours)
How to Plot Level Surfaces (3D Contours)
How to Combine 3D Graphs
How to Graph a Curve in Space
How to Graph a Parameterized Surface
How to Change the Range in a 3D Graph
How to Animate 3D Graphs
Working with Functions of Several Variables
How to Create a Function of Several
Variables
How to Evaluate a Function of Several
Variables
How to Tabulate a Function of Several
Variables
How to Graph Functions of Several Variables
How to Create a Vector-Valued Function
Differentiating Functions of Several Variables
How to Find a Partial Derivative
How to Find a Partial Derivative at a Point
How to Find Second-and Higher-Order Partial
Derivatives
How to Find a Gradient
How to Find a Directional Derivative
Integrating with Several Variables
How to Calculate a Multiple Integral
How to Calculate Multiple Integrals Numerically
Working with Vector Fields
How to Graph a 2D Vector Field
How to Graph a 3D Vector Field
How to Create a Function That Describes a
Vector Field
How to Plot a Gradient Field in 2D
How to Plot a Gradient Field in 3D
Solving Differential Equations
How to Graph the Slope Field of a
First-Order DE
How to Solve a DE Symbolically
How to Solve a DE Numerically
How to Solve a DE Using Euler's Method
How to Solve a System of DE Symbolically
How to Plot the Direction Field of an Autonomous System
How to Animate Solutions
Working with Vectors and Matrices
How to Create a Vector
How to Find Linear Combinations of Vectors
How to Find the Dot (Scalar) Product of Two
Vectors
How to Create a Matrix
How to Find Linear Combinations of Matrices
How to Apply Elementary Row Operations
How to Row Reduce a Matrix in One Step
How to Multiply Matrices
How to Invert a Matrix
How to Solve a Matrix Equation
How to Find a Determinant
How to Transpose a Matrix
How to Find Powers of a Matrix
How to Find a Characteristic Polynomial
How to Find Eigenvalues and Eigenvectors
Part III Exercises and Labs
Functions
Visualizing and Finding Roots
Symmetry in Graphs
Transforming Graphs
Rates of Growth
Inverse Functions
Polar Coordinates
Fitting Cosines to Periodic Data (Hours
of Daylight)
Inverse Functions and Parametric Curves
Limits and Continuity
Conjecturing Limits
The Definition of Limit
Visualizing the Definition of Limit
Numerical Evidence and Limits
Derivatives in One Variable
Derivatives without Equations
Estimating Derivatives Numerically
Differentiation Practice
Derivatives, Tangents, and Graphs
Implicit Differentiation
Using Derivatives
Local Linearity and Derivatives
Optimization
Newton's Method for Estimating Roots
Iteration and Fixed Points
Integrals in One Variable
Areas
Accumulated Change and the Fundamental Theorem
Numerical Integration
The Fundamental Theorem of Calculus and
the Normal Curve
Animating the Fundamental Theorem of
Calculus
Numerical Integration with Left and Right Endpoint Approximations
Numerical Integration with Trapezoidal
and Midpoint Approximations
Numerical Integration with Simpson's Rule
Improper Integrals and Numerical
Integration
Sequences and Series
Conjecturing Limits of Sequences
The Definition of the Limit of a Sequence
Infinite Series
Convergence Tests
Taylor Series
Alternating Series
Definition of Convergence for a Series
The Error in the Taylor Approximation
Parameterized Curves
Curves in the Plane
Curves in Space
Parametric Curves, Gravity, and Motion
Two Parameterizations of an Ellipse
Numerical Integration and Halley's Comet
Surfaces and Level Sets
Surfaces
Level Curves
Level Surfaces
Animating Cross-Sections and Level Curves
Level Curves of Periodic Functions
Continuity in Three Dimensions
Derivatives in Several Variables
Visualizing Partial Derivatives
Estimating Partial Derivatives Numerically
Differentiation Practice
Directonal Derivatives and Gradients
Tangent Planes
Optimization
Local Linearity
Constrained Optimization: Lagrange
Multipliers
Directional Derivatives, Gradients, and
the Cobb--Douglas Function
Multiple Integrals
Riemann Sums
Volume and Cross-Section Area
Double Integrals on Nonrectangular Regions
Triple Integrals
Integrating in Polar Coordinates
Double Integrals and Riemann Sums
Double Integrals and Housing Prices
Differential Equations
Slope Fields and Visualizing Solutions
Euler's Method
Least Squares, Population, and the
Logistic Equation
Numerical Solution of Differential
Equations: Designing a Waterslide
Systems of Differential Equations
Linear Systems of First-Order Equations
Nonlinear Systems
Sharks vs Fish: A Predator--Prey

## L'auteur - Frederic W. Shultz

Frederic W. Shultz, Wellesley College

## Caractéristiques techniques

 PAPIER Éditeur(s) Apress Auteur(s) Alan Shuchat, Frederic W. Shultz Parution 15/10/2000 Édition 2eme édition Nb. de pages 350 Couverture Broché EAN13 9780126407303 ISBN13 978-0-12-640730-3

## Nouveautés "Mathematica"

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