# Calculus: The Language of Change

## Homework solutions & more problems (as Mathematica NoteBooks)

 Introduction 1MapleWorkSheets.mws    2MapleNumerics.mws    3MapleSymbolics.mws    4MapleGraphics.mws    5MapleLists.mws Calculus with Computers         1.1 Previews of Coming Attractions         1.2 An Introduction to Computing         1.3 Linearity in Local Coordinates         1.4 Derivatives for Explicit Formulas         1.5 Review of High School Math         1.6 Free Advice Linear Functions with CAS    Derivatives as Limits by CAS LinearIntro.nb or .mws    DerivLimit.nb or .mws Using Calculus to Model Epidemics         2.1 The First Model         2.2 Shortening the Time Steps         2.3 The Continuous Variable Model         2.4 Analysis of Change         2.5 Long-Term Change         2.6 Calculus and the S-I-R Invariant         2.7 Chapter Summary         2.8 Projects The First S-I-R Epidemic Model    A Second Computation with Lists    Euler's Recursion vs. CAS's    CAS Solution of S-I-R Equations    Limits for S-I-R & the Invariant FirstSIR.nb or .mws    SecondSIR.nb or .mws    ThirdSIR.nb or .mws    SIRsolver.nb or .mws    EpidemicRoots.nb or .mws Linearity vs. Local Linearity         3.1 Approximation of Ox-bows         3.2 Graphical Increments         3.3 Algebra of Microscopes         3.4 Symbolic Increments         3.5 Projects Microscopic Zooming    Zooming into the Tangent Gap    Weierstrass' Function Zoom.nb or .mws    SecantGapZ.nb or .mws    Weierstrass.nb or .mws Chapter 4 Differential Equations and Derivatives         4.1 The Cool Canary         4.2 Instantaneous Rates of Change         4.3 Projects Euler's Approximation for IVPs EulerApprox.nb or .mws Chapter 5 Symbolic Increments         5.1 The Gap for Power Functions         5.2 Moving the Microscope         5.3 Trigonometric Derivatives         5.4 Derivatives of Log and Exp         5.5 Continuity and the Derivative         5.6 Projects and Theory The Symbolic Microscope in 1-D    Symbolic Increments of Functions    Function Limits for Derivatives    Exponentials and Percent Growth Micro1D.nb or .mws    SymbIncr.nb or .mws    DfctLimit.nb or .mws    PercentGth.nb or .mws Chapter 6 Symbolic Differentiation         6.1 Rules for Special Functions         6.2 The Superposition Rule         6.3 The Product Rule         6.4 The Chain Rule         6.5 General Exponentials         6.6 Derivative of the Natural Log         6.7 Combined Symbolic Rules         6.8 Review - Inside the Microscope         6.9 Projects Computing with Your Own Rules    Symbolic Differentiation with CAS    Check Differentiation with CAS    The Symbolic Microscope in 1-D    The Tangent to the Graph DiffRules.nb or .mws    DfDx.nb or .mws    HomeWkCk.nb or .mws    Micro1D.nb or .mws    Tangents.nb or .mws Chapter 7 Related Rates and Implicit Derivatives         7.1 Differentiation with Parameters         7.2 Implicit Differentiation         7.3 Implicit Tangents and Derivatives         7.4 Related Rates         7.5 Implicitly Linked Variables         7.6 Projects Symbolic Differentiation with CAS    Implicit Derivative and Tangent DfDx.nb or .mws    ImplicitDeriv.nb or .mws Chapter 8 The Natural Log and Exponential         8.1 The Official Natural Exponential         8.2 e as a "Natural" Base         8.3 Growth of Log, Exp, and Powers         8.4 Official Properties         8.5 Projects Exact Solution of y'=k y    Exponentials and Percentage    Orders of Infinity    Rapid Exponential Growth    Slow Logarithmic Growth ExpEquns.nb or .mws    PercentGth.nb or .mws    Infinities.nb or .mws    ExpGth.nb or .mws    LogGth.nb or .mws Chapter 9 Graphs and the Derivative         9.1 Graphs from Formulas         9.2 Graphs Without Formulas         9.3 Ups and Downs of the Derivative         9.4 Bending & the Second Derivative         9.5 Graphing Differential Equations         9.6 Projects Derivatives, Shape Tables, and Computer Plots Graph2D.nb or .mws Chapter 10 Velocity, Acceleration, and Calculus         10.1 Acceleration         10.2 Galileo's Law of Gravity         10.3 Projects Acceleration and Gravity Gravity.nb or .mws Chapter 11 Maxima and Minima in One Variable         11.1 A Graphical Minimum         11.2 Critical Points         11.3 Max - min with Endpoints         11.4 Max - min without Endpoints         11.5 Supply and Demand         11.6 Constrained Max-Min         11.7 Max-min with Parameters         11.8 Projects Proof of The Extreme Value Thm    Exact and Approximate Solution ExtremeValue.nb or .mws    SolveEqns.nb or .mws Basic Integration         12.1 Slice Approximations         12.2 Distance When Speed Varies         12.3 The Definite Integral         12.4 Computer Summation         12.5 The Algebra of Summation         12.6 The Algebra of Integration         12.7 Fundamental Theorem, Part 1         12.8 Fundamental Theorem, Part 2 Sums with CASs    The Disk Method    Numerical Approximation Sums.nb or .mws    ConeVol.nb or .mws    IntegrAprx.nb or .mws Chapter 13 Symbolic Integration         13.1 Indefinite Integrals         13.2 Specific Integral Formulas         13.3 Superposition of Antiderivatives         13.4 "Substitution" for Integrals         13.5 Change of Limits of Integration         13.6 Trig Substitutions         13.7 Integration by Parts         13.8 Impossible Integrals Symbolic Integration with CAS SymbolicIntegr.nb or .mws Chapter 14 Applications of Integration         14.1 The Length of a Curve         14.2 Duhamel's Principle         14.3 Geometric Integrals         14.4 Improper Integrals Arc Length of Curves    Surface Area of a Torus    Area Between Curves    Area of a Parabolic Antenna ArcLength.nb or .mws    DonutIcing.nb or .mws    AreaBetween.nb or .mws    AntennaArea.nb or .mws Chapter 15 Basic Vector Geometry         15.1 Cartesian Coordinates         15.2 Position Vectors         15.3 Geometry of Vector Addition         15.4 Scalar Multiplication         15.5 Differences and Displacements         15.6 Angles and Projections         15.7 Cross Product in 3 Dimensions         15.8 Geometry and Algebra Lexicon Position Vectors and Length    Vector Sums, Tips to Tails    Scalar Multiplication of Vectors    Free Vectors, Displacements    Angles, Lengths    The Vector Cross Product    An Algebraic-Geometric Lexicon PositVec.nb or .mws    VectSum.nb or .mws    ScalarMult.nb or .mws    DisplVect.nb or .mws    AnglPerp.nb or .mws    CrossProd.nb or .mws    AlgGeoLx.nb or .mws Chapter 16 Parametric Curves         16.1 The Vector Parametric Line         16.2 Parametric Circles         16.3 Polar Curves         16.4 3-D Parametric Curves         16.5 Tangents and Velocity Vectors         16.6 Projects Parametric Equations for a Line    Parametric Equations for a Circle    Classic Parametric Curves in 2-D    Curves in Polar Coordinates    Parametric Curves in 3-D    Velocity and Tangents ParamLine.nb or .mws    Circles.nb or .mws    ClassicCrvs.nb or .mws    PolarCrvs.nb or .mws    Param3D.nb or .mws    PrmVelTan.nb or .mws Chapter 17 Graphs in Several Variables         17.1 The Expicit Plane in 3-D         17.2 Vertical Slices and Chickenwire         17.3 Implicit Linear Equations         17.4 Gradients and Contour Plots         17.5 Horizontal Slices and Contours         17.6 Explicit, Implicit, Parametric         17.7 Lines, Curves, & Planes Slices of Surfaces    Basic Graphs in 3-D    Graphs of Surfaces by Slices    Explicit, Implicit Lines and Planes    Plane Through Three Points    Contour Plots of Linear Functions    Contours and Horizontal Slices    Explicit Plots for Problem 17.6    Contour Plots for Problem 17.6 SurfaceFlyBy.nb or .mws    BasicGrfs3D.nb or .mws    SurfSlices.nb or .mws    PlaneLines.nb or .mws    ThreePoints.nb or .mws    LinearContours.nb or .mws    ContourSlices.nb or .mws    ExplicitSurfaces.nb or .mws    ContourPlots.nb or .mws Chapter 18 Differentiation in Several Variables         18.1 Partial and Total Derivatives         18.2 Partial Differentiation Examples         18.3 Differential Approximations         18.4 Geometry of the Differential         18.5 The Meaning of the Gradient         18.6 Implicit Differentiation (Again)         18.7 Review Exercises A Microscope for 3D Graphs    Zooming to a Tangent    Partial and Total Derivatives    The Normal and Tangent    The Gradient of a Function    Review Uses of Partial Derivatives Micro3D.nb or .mws    Zoom3D.nb or .mws    PartialD.nb or .mws    SurfNorm.nb or .mws    Grad.nb or .mws    DiffReview.nb or .mws Several Variable Optimization         19.1 Critical Points to Investigate         19.2 Existence of Extreme Values         19.3 Compact Regions         19.4 Implicit Constraints         19.5 Noncompact Extrema in 2-D         19.6 Projects on Max - min Partial Information for Max-Min    Max-min Examples using CAS MxMnThy.nb or .mws    SvVarMxMn.nb or .mws Discrete Dynamical Systems         20.1 Models for Price Adjustment         20.2 Cobwebs         20.3 The Linear System         20.4 Logistic Growth         20.5 Calculus and Nonlinearity         20.6 Projects A First Look at Discrete Systems    Dynamical Systems and Cobwebs FstDscrDySy.nb or .mws    CobWeb.nb or .mws Chapter 21 Continuous Dynamical Systems in 1-D         21.1 Exponential Growth and Decay         21.2 Logistic Growth Laws         21.3 Some Helpful Theory         21.4 Separation of Variables         21.5 Projects Exact Solution of Percentage    Rapid Exponential Growth    Accurate Numerical Solution    One Dimensional Flow    Euler's Approximation    Euler's Approximation Compared ExpEquns.nb or .mws    ExpGth.nb or .mws    AccDEsol.nb or .mws    Flow1D.nb or .mws    EulerApprox.nb or .mws    EULERexact.nb or .mws Chapter 22 Continuous Dynamical Systems in 2-D         22.1 Basic Theory in 2-D         22.2 Geometric Solution in 2-D         22.3 Flows vs. Explicit Solutions         22.4 Flow Analysis of Models         22.5 Projects Direction Fields in 2-D    Flows in 2-D    Views of Solutions of 2-D ODEs    Accurate Numerical Solution    Flows in 3-D DirField.nb or .mws    Flow2D.nb or .mws    SolnViews.nb or .mws    AccDEsol.nb or .mws    Flow3D.nb or .mws Chapter 23 Linear Dynamical Systems         23.1 The Shock Absorber Equation         23.2 Constant Coefficient Systems         23.3 Symbolic Exponential Solutions         23.4 Rotation and Euler's Formula         23.5 Basic Solutions         23.6 Superposition and All Solutions         23.7 Second-Order IVPs         23.8 Projects Equilibria of Linear ODEs in 2-D    Computation of Local Stability    Linear Flows in 2-D LinearEquilibria.nb or .mws    LocalStability.nb or .mws    Flow2D.nb or .mws Chapter 25 Geometric Series         25.1 Geometric Series: Convergence         25.2 Convergence by Comparison         25.3 Compound Interest Basic Examples of Series    The Geometric Series    Series for the Classical Functions    Power, Fourier, and Other Series    Weierstrass' Function BasicSeries.nb or .mws    GeomSeries.nb or .mws    ClassicalSeries.nb or .mws    FourierSeries.nb or .mws    Weierstrass.nb or .mws Chapter 26 Power Series         26.1 Computation of Power Series         26.2 The Ratio Test         26.3 Integration of Series         26.4 Differentiation of Power Series Series for the Classical Functions    A Series for the Absolute Value    Formal Taylor Series    The Binomial Series    Specific Infinite Sums    Series for Hyperbolic Functions    Series for Bessel Functions ClassicalSeries.nb or .mws    AbsSeries.nb or .mws    FormalTSeries.nb or .mws    BinomialSeries.nb or .mws    SomeSums.nb or .mws    CoshSeries.nb or .mws    BesselSeries.nb or .mws Chapter 27 The Edge of Convergence         27.1 Alternating Series         27.2 Telescoping Series         27.3 Integrals Compared to Series         27.4 Limit Comparisons         27.5 Fourier Series Slowly Convergent Series SlowSeries.nb or .mws High School Review with Computing         28.1 Linear Functions         28.2 Polynomials         28.3 Functions from Formulas         28.4 Power Functions         28.5 Trig Functions         28.6 Logs and Exponentials         28.7 Chaining or Composition         28.8 Parameters         28.9 Functional Identities Polynomials with Mathematica    Defining Functions with CSAs    Laws of Exponents    Rapid Exponential Growth    Slow Logarithmic Growth    Translation and Scaling a Parabola Polynomials.nb or .mws    Functions.nb or .mws    ExpRules.nb or .mws    ExpGth.nb or .mws    LogGth.nb or .mws    SlideSquash.nb or .mws Complex Numbers         29.1 Algebra of Complex Numbers         29.2 Geometry of Numbers Complex Arithmetic with CASs CmplxNrs.nb or .mws

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