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Calculus Calculus: A Complete Course by Adams and Essex

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  1. Jan 22, 2013 #1

    micromass

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    Staff Emeritus
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    2016 Award


    Table of Contents:
    Code (Text):

    [LIST]
    [*] Preface
    [*] To the Student
    [*] To the Instructor
    [*] Acknowledgments
    [*] What Is Calculus?
    [*] Preliminaries
    [LIST]
    [*] Real Numbers and the Real Line
    [LIST]
    [*] Intervals
    [*] The Absolute Value
    [*] Equations and Inequalities Involving Absolute Values
    [/LIST]
    [*] Cartesian Coordinates in the Plane
    [LIST]
    [*] Axis Scales
    [*] Increments and Distances
    [*] Graphs
    [*] Straight Lines
    [*] Equations of Lines
    [/LIST]
    [*] Graphs of Quadratic Equations
    [LIST]
    [*] Circles and Disks
    [*] Equations of Parabolas
    [*] Reflective Properties of Parabolas
    [*] Scaling a Graph
    [*] Shifting a Graph
    [*] Ellipses and Hyperbolas
    [/LIST]
    [*] Functions and Their Graphs
    [LIST]
    [*] The Domain Convention
    [*] Graphs of Functions
    [*] Even and Odd Functions; Symmetry and Reflections
    [*] Reflections in Straight Lines
    [*] Defining and Graphing Functions with Maple
    [/LIST]
    [*] Combining Functions to Make New Functions
    [LIST]
    [*] Sums, Differences, Products, Quotients, and Multiples
    [*] Composite Functions
    [*] Piecewise Defined Functions
    [/LIST]
    [*] Polynomials and Rational Functions
    [LIST]
    [*] Roots and Factors
    [*] Roots and Factors of Quadratic Polynomials
    [*] Miscellaneous Factorings
    [/LIST]
    [*] The Trigonometric Functions
    [LIST]
    [*] Some Useful Identities
    [*] Some Special Angles
    [*] The Addition Formulas
    [*] Other Trigonometric Functions
    [*] Maple Calculations
    [*] Trigonometry Review
    [/LIST]
    [/LIST]
    [*] Limits and Continuity
    [LIST]
    [*]  Examples of Velocity, Growth Rate, and Area
    [LIST]
    [*] Average Velocity and Instantaneous Velocity
    [*] The Growth of an Algal Culture
    [*] The Area of a Circle
    [/LIST]
    [*]  Limits of Functions
    [LIsT]
    [*] One-Sided Limits
    [*] Rules for Calculating Limits
    [*] The Squeeze Theorem
    [/LIST]
    [*]  Limits at Infinity and Infinite Limits
    [LIST]
    [*] Limits at Infinity
    [*] Limits at Infinity for Rational Functions
    [*] Infinite Limits
    [*] Using Maple to Calculate Limits
    [/LIST]
    [*]  Continuity
    [LIST]
    [*] Continuity at a Point
    [*] Continuity on an Interval
    [*] There Are Lots of Continuous Functions
    [*] Continuous Extensions and Removable Discontinuities
    [*] Continuous Functions on Closed, Finite Intervals
    [*] Finding Maxima and Minima Graphically
    [*] Finding Roots of Equations
    [/LIST]
    [*] The Formal Definition of Limit
    [LIST]
    [*] Using the Definition of Limit to Prove Theorems
    [*] Other Kinds of Limits
    [/LIST]
    [*] Chapter Review
    [/LIST]
    [*] Differentiation
    [LIST]
    [*]  Tangent Lines and Their Slopes
    [LIST]
    [*] Normals
    [/LIST]
    [*] The Derivative
    [LIST]
    [*] Some Important Derivatives
    [*] Leibniz Notation
    [*] Differentials
    [*] Derivatives Have the Intermediate-Value Property
    [/LIST]
    [*] Differentiation Rules
    [LIST]
    [*] Sums and Constant Multiples
    [*] The Product Rule
    [*] The Reciprocal Rule
    [*] The Quotient Rule
    [/LIST]
    [*] The Chain Rule
    [LIST]
    [*] Finding Derivatives with Maple
    [*] Building the Chain Rule into Differentiation Formulas
    [*] Proof of the Chain Rule (Theorem 6)
    [/LIST]
    [*]  Derivatives of Trigonometric Functions
    [LIST]
    [*] Some Special Limits
    [*] The Derivatives of Sine and Cosine
    [*] The Derivatives of the Other Trigonometric Functions
    [/LIST]
    [*]  The Mean-Value Theorem
    [LIST]
    [*] Increasing and Decreasing Functions
    [*] Proof of the Mean-Value Theorem
    [/LIST]
    [*] Using Derivatives
    [LIST]
    [*] Approximating Small Changes
    [*] Average and Instantaneous Rates of Change
    [*] Sensitivity to Change
    [*] Derivatives in Economics
    [/LIST]
    [*]  Higher-Order Derivatives
    [*]  Implicit Differentiation
    [LIST]
    [*] Higher-Order Derivatives
    [*] The General Power Rule
    [/LIST]
    [*]  Antiderivatives and Initial-Value Problems
    [LIST]
    [*] Antiderivatives
    [*] The Indefinite Integral
    [*] Differential Equations and Initial-Value Problems
    [/LIST]
    [*]  Velocity and Acceleration
    [LIST]
    [*] Velocity and Speed
    [*] Acceleration
    [*] Falling Under Gravity
    [/LIST]
    [*] Chapter Review
    [/LIST]
    [*] Transcendental Functions
    [LIST]
    [*] Inverse Functions
    [LIST]
    [*] Inverting Non-One-to-One Functions
    [*] Derivatives of Inverse Functions
    [/LIST]
    [*] Exponential and Logarithmic Functions
    [LIST]
    [*] Exponentials
    [*] Logarithms
    [/LIST]
    [*] The Natural Logarithm and Exponential
    [LIST]
    [*] The Natural Logarithm
    [*] The Exponential Function
    [*] General Exponentials and Logarithms
    [*] Logarithmic Differentiation
    [/LIST]
    [*] Growth and Decay
    [LIST]
    [*] The Growth of Exponentials and Logarithms
    [*] Exponential Growth and Decay Models
    [*] Interest on Investments
    [*] Logistic Growth
    [/LIST]
    [*] The Inverse Trigonometric Functions
    [LIST]
    [*] The Inverse Sine (or Arcsine) Function
    [*] The Inverse Tangent (or Arctangent) Function
    [*] Other Inverse Trigonometric Functions
    [/LIST]
    [*]  Hyperbolic Functions
    [LIST]
    [*] Inverse Hyperbolic Functions
    [/LIST]
    [*] Second-Order Linear DEs with Constant Coefficients
    [LIST]
    [*] Recipe for Solving ay" + by' + с у = 0
    [*] Simple Harmonic Motion
    [*] Damped Harmonic Motion
    [/LIST]
    [*] Chapter Review
    [/LIST]
    [*] Some Applications of Derivatives
    [LIST]
    [*] Related Rates
    [LIST]
    [*] Procedures for Related-Rates Problems
    [/LIST]
    [*] Extreme Values
    [LIST]
    [*] Maximum and Minimum Values
    [*] Critical Points, Singular Points, and Endpoints
    [*] Finding Absolute Extreme Values
    [*] The First Derivative Test
    [*] Functions Not Defined on Closed, Finite Intervals
    [/LIST]
    [*] Concavity and Inflections
    [LIST]
    [*] The Second Derivative Test
    [/LIST]
    [*] Sketching the Graph of a Function
    [LIST]
    [*] Asymptotes
    [*] Examples of Formal Curve Sketching
    [/LIST]
    [*] Extreme-Value Problems
    [LIST]
    [*] Procedure for Solving Extreme-Value Problems
    [/LIST]
    [*] Finding Roots of Equations
    [LIST]
    [*] Newton's Method
    [*] Fixed-Point Iteration
    [*] "Solve" Routines
    [/LIST]
    [*]  Linear Approximations
    [LIST]
    [*] Approximating Values of Functions
    [*] Error Analysis
    [/LIST]
    [*]  Taylor Polynomials
    [LIST]
    [*] Taylor's Formula
    [*] Big-O Notation
    [/LIST]
    [*]  Indeterminate Forms
    [LIST]
    [*] l'Hopital's Rules
    [/LIST]
    [*] Chapter Review
    [/LIST]
    [*] Integration
    [LIST]
    [*]  Sums and Sigma Notation
    [LIST]
    [*] Evaluating Sums
    [/LIST]
    [*] Areas as Limits of Sums
    [LIST]
    [*] The Basic Area Problem
    [*] Some Area Calculations
    [/LIST]
    [*]  The Definite Integral
    [LIST]
    [*] Partitions and Riemann Sums
    [*] The Definite Integral
    [*] General Riemann Sums
    [/LIST]
    [*]  Properties of the Definite Integral
    [LIST]
    [*] A Mean-Value Theorem for Integrals
    [*] Definite Integrals of Piecewise Continuous Functions
    [/LIST]
    [*] The Fundamental Theorem of Calculus
    [*] The Method of Substitution
    [LIST]
    [*] Trigonometric Integrals
    [/LIST]
    [*] Areas of Plane Regions
    [LIST]
    [*] Areas Between Two Curves
    [/LIST]
    [*] Chapter Review
    [/LIST]
    [*] Techniques of Integration
    [LIST]
    [*] Integration by Parts
    [LIST]
    [*] Reduction Formulas
    [/LIST]
    [*] Inverse Substitutions
    [LIST]
    [*] The Inverse Trigonometric Substitutions
    [*] Completing the Square
    [*] Other Inverse Substitutions
    [*] The tan(theta/2) Substitution
    [/LIST]
    [*] Integrals of Rational Functions
    [LIST]
    [*] Linear and Quadratic Denominators
    [*] Partial Fractions
    [/LIST]
    [*] Integration Using Computer Algebra or Tables
    [LIST]
    [*] Using Maple for Integration
    [*] Using Integral Tables
    [/LIST]
    [*] Improper Integrals
    [LIST]
    [*] Improper Integrals of Type I
    [*] Improper Integrals of Type II
    [*] Estimating Convergence and Divergence
    [/LIST]
    6.6 The Trapezoid and Midpoint Rules
    [LIST]
    [*] The Trapezoid Rule
    [*] The Midpoint Rule
    [*] Error Estimates
    [/LIST]
    [*] Simpson's Rule
    [*] Other Aspects of Approximate Integration
    [LIST]
    [*] Approximating Improper Integrals
    [*] Using Taylor's Formula
    [*] Romberg Integration
    [*] Other Methods
    [/LIST]
    [*] Chapter Review
    [/LIST]
    [*] Applications of Integration
    [LIST]
    [*] Volumes by Slicing — Solids of Revolution
    [LIST]  
    [*] Volumes by Slicing
    [*] Solids of Revolution
    [*] Cylindrical Shells
    [/LIST]
    [*] More Volumes by Slicing
    [*] Arc Length and Surface Area
    [LIST]
    [*] Arc Length
    [*] The Arc Length of the Graph of a Function
    [*] Areas of Surfaces of Revolution
    [/LIST]
    [*] Mass, Moments, and Centre of Mass
    [LIST]  
    [*] Mass and Density
    [*] Moments and Centres of Mass
    [*] Two- and Three-Dimensional Examples
    [/LIST]
    [*] Centroids
    [LIST]
    [*] Pappus's Theorem
    [/LIST]
    [*] Other Physical Applications
    [LIST]
    [*] Hydrostatic Pressure
    [*] Work
    [*] Potential Energy and Kinetic Energy
    [/LIST]
    [*] Applications in Business, Finance, and Ecology
    [LIST]  
    [*] The Present Value of a Stream of Payments
    [*] The Economics of Exploiting Renewable Resources
    [/LIST]
    [*] Probability
    [LIST]
    [*] Discrete Random Variables
    [*] Expectation, Mean, Variance, and Standard Deviation
    [*] Continuous Random Variables
    [*] The Normal Distribution
    [/LIST]
    [*] First-Order Differential Equations
    [LIST]
    [*] Separable Equations
    [*] First-Order Linear Equations
    [/LIST]
    [*] Chapter Review
    [/LIST]
    [*] Conics, Parametric Curves, and Polar Curves
    [LIST]  
    [*] Conics
    [LIST]  
    [*] Parabolas
    [*] The Focal Property of a Parabola
    [*] Ellipses
    [*] The Focal Property of an Ellipse
    [*] The Directrices of an Ellipse
    [*] Hyperbolas
    [*] The Focal Property of a Hyperbola
    [*] Classifying General Conies
    [/LIST]
    [*] Parametric Curves
    [LIST]
    [*] General Plane Curves and Parametrizations
    [*] Some Interesting Plane Curves
    [/LIST]
    [*] Smooth Parametric Curves and Their Slopes
    [LIST]  
    [*] The Slope of a Parametric Curve
    [*] Sketching Parametric Curves
    [/LIST]
    [*] Arc Lengths and Areas for Parametric Curves
    [LIST]
    [*] Arc Lengths and Surface Areas
    [*] Areas Bounded by Parametric Curves
    [/LIST]
    [*] Polar Coordinates and Polar Curves
    [LIST]
    [*] Some Polar Curves
    [*] Intersections of Polar Curves
    [*] Polar Conics
    [/LIST]
    [*] Slopes, Areas, and Arc Lengths for Polar Curves
    [LIST]
    [*] Areas Bounded by Polar Curves
    [*] Arc Lengths for Polar Curves
    [/LIST]
    [*] Chapter Review
    [/LIST]
    [*] Sequences, Series, and Power Series
    [LIST]  
    [*] Sequences and Convergence
    [LIST]
    [*] Convergence of Sequences
    [/LIST]
    [*] Infinite Series
    [LIST]
    [*] Geometric Series
    [*] Telescoping Series and Harmonic Series
    [*] Some Theorems About Series
    [/LIST]
    [*] Convergence Tests for Positive Series
    [LIST]
    [*] The Integral Test
    [*] Using Integral Bounds to Estimate the Sum of a Series
    [*] Comparison Tests
    [*] The Ratio and Root Tests
    [*] Using Geometric Bounds to Estimate the Sum of a Series
    [/LIST]
    [*] Absolute and Conditional Convergence
    [LIST]  
    [*] The Alternating Series Test
    [*] Rearranging the Terms in a Series
    [/LIST]
    [*] Power Series
    [LIST]
    [*] Algebraic Operations on Power Series
    [*] Differentiation and Integration of Power Series
    [*] Maple Calculations
    [/LIST]
    [*] Taylor and Maclaurin Series
    [LIST]  
    [*] Maclaurin Series for Some Elementary Functions
    [*] Other Maclaurin and Taylor Series
    [*] Taylor's Formula Revisited
    [/LIST]
    [*] Applications of Taylor and Maclaurin Series
    [LIST]  
    [*] Approximating the Values of Functions
    [*] Functions Defined by Integrals
    [*] Indeterminate Forms
    [/LIST]
    [*] The Binomial Theorem and Binomial Series
    [LIST]
    [*] The Binomial Series
    [/LIST]
    [*] Fourier Series
    [LIST]
    [*] Periodic Functions
    [*] Fourier Series
    [*] Convergence of Fourier Series
    [*] Fourier Cosine and Sine Series
    [/LIST]
    [*] Chapter Review
    [/LIST]
    [*] Vectors and Coordinate Geometry in 3-Space
    [LIST]
    [*] Analytic Geometry in Three Dimensions
    [LIST]
    [*] Euclidean n-Space
    [*] Describing Sets in the Plane, 3-Space, and n-Space
    [/LIST]
    [*] Vectors
    [LIST]
    [*] Vectors in 3-Space
    [*] Hanging Cables and Chains
    [*] The Dot Product and Projections
    [*] Vectors in n-Space
    [/LIST]
    [*] The Cross Product in 3-Space
    [LIST]
    [*] Determinants
    [*] The Cross Product as a Determinant
    [*] Applications of Cross Products
    [/LIST]
    [*] Planes and Lines
    [LIST]
    [*] Planes in 3-Space
    [*] Lines in 3-Space
    [*] Distances
    [/LIST]
    [*] Quadric Surfaces
    [*] A Little Linear Algebra
    [LIST]  
    [*] Matrices
    [*] Determinants and Matrix Inverses
    [*] Linear Transformations
    [*] Linear Equations
    [*] Quadratic Forms, Eigenvalues, and Eigenvectors
    [/LIST]
    [*] Using Maple for Vector and Matrix Calculations
    [LIST]
    [*] Vectors
    [*] Matrices
    [*] Linear Equations
    [*] Eigenvectors and Eigenfunctions
    [/LIST]
    [*] Chapter Review
    [/LIST]
    [*] Vector Functions and Curves
    [LIST]
    [*] Vector Functions of One Variable
    [LIST]
    [*] Differentiating Combinations of Vectors
    [/LIST]
    [*] Some Applications of Vector Differentiation
    [LIST]  
    [*] Motion Involving Varying Mass
    [*] Circular Motion
    [*] Rotating Frames and the Coriolis Effect
    [/LIST]
    [*] Curves and Parametrizations
    [LIST]
    [*] Parametrizing the Curve of Intersection of Two Surfaces
    [*] Arc Length
    [*] Piecewise Smooth Curves
    [*] The Arc-Length Parametrization
    [/LIST]
    [*] Curvature, Torsion, and the Frenet Frame
    [LIST]  
    [*] The Unit Tangent Vector
    [*] Curvature and the Unit Normal
    [*] Torsion and Binormal, the Frenet-Serret Formulas
    [/LIST]
    [*] Curvature and Torsion for General Parametrizations
    [LIST]  
    [*] Tangential and Normal Acceleration
    [*] Evolutes
    [*] An Application to Track (or Road) Design
    [*] Maple Calculations
    [/LIST]
    [*] Kepler's Laws of Planetary Motion
    [LIST]  
    [*] Ellipses in Polar Coordinates
    [*] Polar Components of Velocity and Acceleration
    [*] Central Forces and Kepler's Second Law
    [*] Derivation of Kepler's First and Third Laws
    [*] Conservation of Energy
    [/LIST]
    [*] Chapter Review
    [/LIST]
    [*] Partial Differentiation
    [LIST]
    [*] Functions of Several Variables
    [LIST]
    [*] Graphical Representations
    [*] Using Maple Graphics
    [/LIST]
    [*] Limits and Continuity
    [*] Partial Derivatives
    [LIST]
    [*] Tangent Planes and Normal Lines
    [*] Distance from a Point to a Surface: A Geometric Example
    [/LIST]
    [*] Higher-Order Derivatives
    [LIST]
    [*] The Laplace and Wave Equations
    [/LIST]
    [*] The Chain Rule
    [LIST]
    [*] Homogeneous Functions
    [*] Higher-Order Derivatives
    [/LIST]
    [*] Linear Approximations, Differentiability, and Differentials
    [LIST]  
    [*] Proof of the Chain Rule
    [*] Differentials
    [*] Functions from n-space to m-space
    [/LIST]
    [*] Gradients and Directional Derivatives
    [LIST]
    [*] Directional Derivatives
    [*] Rates Perceived by a Moving Observer
    [*] The Gradient in Three and More Dimensions
    [/LIST]
    [*] Implicit Functions
    [LIST]
    [*] Systems of Equations
    [*] Jacobian Determinants
    [*] The Implicit Function Theorem
    [/LIST]
    [*] Taylor Series and Approximations
    [LIST]
    [*] Approximating Implicit Functions
    [/LIST]
    [*] Chapter Review
    [/LIST]
    [*] Applications of Partial Derivatives
    [LIST]  
    [*] Extreme Values
    [LIST]
    [*] Classifying Critical Points
    [/LIST]
    [*] Extreme Values of Functions Defined on Restricted Domains
    [LIST]
    [*] Linear Programming
    [/LIST]
    [*] Lagrange Multipliers
    [LIST]
    [*] The Method of Lagrange Multipliers
    [*] Problems with More than One Constraint
    [*] Nonlinear Programming
    [/LIST]
    [*] The Method of Least Squares
    [LIST]
    [*] Linear Regression
    [*] Applications of the Least Squares Method to Integrals
    [/LIST]
    [*] Parametric Problems
    [LIST]
    [*] Differentiating Integrals with Parameters
    [*] Envelopes
    [*] Equations with Perturbations
    [/LIST]
    [*] Newton's Method
    [LIST]
    [*] Implementing Newton's Method Using a Spreadsheet
    [/LIST]
    [*] Calculations with Maple
    [LIST]
    [*] Solving Systems of Equations
    [*] Finding and Classifying Critical Points
    [/LIST]
    [*] Chapter Review
    [/LIST]
    [*] Multiple Integration
    [LIST]
    Double Integrals
    [LIST]
    [*] Double Integrals over More General Domains
    [*] Properties of the Double Integral
    [*] Double Integrals by Inspection
    [/LIST]
    [*] Iteration of Double Integrals in Cartesian Coordinates
    [*] Improper Integrals and a Mean-Value Theorem
    [LIST]
    [*] Improper Integrals of Positive Functions
    [*] A Mean-Value Theorem for Double Integrals
    [/LIST]
    [*] Double Integrals in Polar Coordinates
    [LIST]  
    [*] Change of Variables in Double Integrals
    [/LIST]
    [*] Triple Integrals
    [*] Change of Variables in Triple Integrals
    [LIST]
    [*] Cylindrical Coordinates
    [*] Spherical Coordinates
    [/LIST]
    [*] Applications of Multiple Integrals
    [LIST]
    [*] The Surface Area of a Graph
    [*] The Gravitational Attraction of a Disk
    [*] Moments and Centres of Mass
    [*] Moment of Inertia
    [/LIST]
    [*] Chapter Review
    [/LIST]
    [*] Vector Fields
    [LIST]
    [*] Vector and Scalar Fields
    [LIST]  
    [*] Field Lines (Integral Curves)
    [*] Vector Fields in Polar Coordinates
    [/LIST]
    [*] Conservative Fields
    [LIST]  
    [*] Equipotential Surfaces and Curves
    [*] Sources, Sinks, and Dipoles
    [/LIST]
    [*] Line Integrals
    [LIST]
    [*] Evaluating Line Integrals
    [/LIST]
    [*] Line Integrals of Vector Fields
    [LIST]  
    [*] Connected and Simply Connected Domains
    [*] Independence of Path
    [/LIST]
    [*] Surfaces and Surface Integrals
    [LIST]  
    [*] Parametric Surfaces
    [*] Composite Surfaces
    [*] Surface Integrals
    [*] Smooth Surfaces, Normals, and Area Elements
    [*] Evaluating Surface Integrals
    [*] The Attraction of a Spherical Shell
    [/LIST]
    [*] Oriented Surfaces and Flux Integrals
    [LIST]  
    [*] Oriented Surfaces
    [*] The Flux of a Vector Field Across a Surface
    [/LIST]
    [*] Chapter Review
    [/LIST]
    [*] Vector Calculus
    [LIST]  
    [*] Gradient, Divergence, and Curl
    [LIST]
    [*] Interpretation of the Divergence
    [*] Distributions and Delta Functions
    [*] Interpretation of the Curl
    [/LIST]
    [*] Some Identities Involving Grad, Div, and Curl
    [LIST]  
    [*] Scalar and Vector Potentials
    [*] Maple Calculations
    [/LIST]
    [*] Green's Theorem in the Plane
    [LIST]
    [*] The Two-Dimensional Divergence Theorem
    [/LIST]
    [*] The Divergence Theorem in 3-Space
    [LIST]  
    [*] Variants of the Divergence Theorem
    [/LIST]
    [*] Stokes's Theorem
    [*] Some Physical Applications of Vector Calculus
    [LIST]  
    [*] Fluid Dynamics
    [*] Electromagnetism
    [*] Electrostatics
    [*] Magnetostatics
    [*] Maxwell's Equations
    [/LIST]
    [*] Orthogonal Curvilinear Coordinates
    [LIST]  
    [*] Coordinate Surfaces and Coordinate Curves
    [*] Scale Factors and Differential Elements
    [*] Grad, Div, and Curl in Orthogonal Curvilinear Coordinates
    [/LIST]
    [*] Chapter Review
    [/LIST]
    [*] Ordinary Differential Equations
    [LIST]  
    [*] Classifying Differential Equations
    [*] Solving First-Order Equations
    [LIST]
    [*] Separable Equations
    [*] First-Order Homogeneous Equations
    [*] Exact Equations
    [*] Integrating Factors
    [*] First-Order Linear Equations
    [/LIST]
    [*] Existence, Uniqueness, and Numerical Methods
    [LIST]
    [*] Existence and Uniqueness of Solutions
    [*] Numerical Methods
    [/LIST]
    [*] Differential Equations of Second Order
    [LIST]
    [*] Equations Reducible to First Order
    [*] Second-Order Linear Equations
    [/LIST]
    [*] Linear Differential Equations with Constant Coefficients
    [LIST]
    [*] Constant-Coefficient Equations of Higher Order
    [*] Euler (Equidimensional) Equations
    [/LIST]
    [*] Nonhomogeneous Linear Equations
    [LIST]  
    [*] Resonance
    [*] Variation of Parameters
    [*] Maple Calculations
    [/LIST]
    [*] Series Solutions of Differential Equations
    [*] Chapter Review
    [/LIST]
    [*] Appendix: Complex Numbers
    [LIST]  
    [*] Definition of Complex Numbers
    [*] Graphical Representation of Complex
    [*] Numbers
    [*] Complex Arithmetic
    [*] Roots of Complex Numbers
    [/LIST]
    [*] Appendix: Complex Functions
    [LIST]
    [*] Limits and Continuity
    [*] The Complex Derivative
    [*] The Exponential Function
    [*] The Fundamental Theorem of Algebra
    [/LIST]
    [*] Appendix: Continuous Functions
    [LIST]
    [*] Limits of Functions
    [*] Continuous Functions
    [*] Completeness and Sequential Limits
    [*] Continuous Functions on a Closed, Finite Interval
    [/LIST]
    [*] Appendix: The Riemann Integral
    [LIST]
    [*] Uniform Continuity
    [/LIST]
    [*] Appendix: Doing Calculus with Maple
    [LIST]
    [*] List of Maple Examples and Discussion
    [/LIST]
    [*] Answers to Odd-Numbered
    [*] Exercises
    [*] Index
    [/LIST]
     
     
    Last edited by a moderator: May 6, 2017
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