Mathematica® by Example

Preface1 Getting Started 1.1 Introduction to Mathematica 1.2 Getting Started with Mathematica 1.3 Loading Packages Two Words of Caution 1.4 Getting Help from Mathematica Help Commands Mathematica Help2 Mathematical Operations on Numbers, Expressions, and Functions 2.1 Numerical Calculations and Built-in Functions Numerical Calculations Built-In Constants Built-In Functions The Absolute Value, Exponential and Logarithmic Functions Trigonometric Functions Inverse Trigonometric Functions A Word of Caution 2.2 Expressions and Functions Basic Algebraic Operations on Expressions Naming and Evaluating Expressions A Word of Caution Defining and Evaluating Functions Additional Ways to Evaluate Functions and Expressions Composition of Functions A Word of Caution 2.3 Graphing Functions, Expressions, and Equations Graphing Functions of a Single Variable Graphing Several Functions Piecewise-Defined Functions Graphs of Parametric Functions in Two Dimensions Three-Dimensional Graphics Graphing Level Curves of Functions of Two Variables Graphing Parametric Curves and Surfaces in Space A Word of Caution 2.4 Exact and Approximate Solutions of Equations Exact Solutions of Equations Numerical Approximation of Solutions of Equations Application: Intersection Points of Graphs of Functions3 Calculus 3.1 Computing Limits Computing Limits One-Sided Limits A Word of Caution 3.2 Differential Calculus Calculating Derivatives of Functions and Expressions Tangent Lines Locating Critical Points and Inflection Points Using Derivatives to Graph Functions Graphing Functions and Derivatives Approximations with FindRoot Application: Rolle's Theorem and The Mean-Value Theorem Application: Graphing Functions and Tangent Lines Application: Maxima and Minima 3.3 Implicit Differentiation Computing Derivatives of Implicit Functions Other Methods to Compute Derivatives of Implicit Functions Other Methods to Graph Equations 3.4 Integral Calculus Estimating Areas Computing Definite and Indefinite Integrals Approximating Definite Integrals Application: Area Between Curves Application: Arc Length Application: Volume of Solids of Revolution Application: The Mean-Value Theorem for Integrals A Word of Caution 3.5 Series Introduction to Series Determining the Interval of Convergence of a Power Series Computing Power Series Application: Approximating the Remainder Application: Series Solutions to Differential Equations Other Series 3.6 Multivariable Calculus Limits of Functions of Two Variables Partial Differentiation Other Methods of Computing Derivatives Application: Classifying Critical Points Application: Tangent Planes Application: The Method of Lagrange Multipliers Double Integrals Application: Volume Triple Integrals Higher-Order Integrals4 Introduction to Lists and Tables 4.1 Defining Lists A Word of Caution 4.2 Operations on Lists Extracting Elements of Lists Graphing Lists of Points and Lists of Functions Evaluation of Lists by Functions Evaluation of Parts of Lists by Functions Other List Operations Alternative Way to Evaluate Lists by Functions 4.