| Chapter 1 Chapter 2 Chapter 3 Chapter 4 |
Chapter 5 Chapter 6 Chapter 7 Chapter 8 |
Chapter 9 Chapter 10 Chapter 11 Chapter 12 |
Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 |
| 1.1 | Functions and the Analysis of Graphical Information Functions - create your own functions with this Mathematica notebook http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html |
| 1.2 | Properties of Functions Functions - create your own functions with this Mathematica notebook http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html |
| 1.3 | Graphing Functions on Calculators and Computers: Computer Algebra Systems Graphics - plotting functions in 2D and altering Mathematica-generated images http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html |
| 1.4 | New Functions from Old Reflections, Symmetry, and Inverses - TI-85/86 activity http://www.ti.com/calc/docs/act.85calc.htm Transformation of Functions - TI-85/86 activity http://www.ti.com/calc/docs/act.85calc.htm |
| 1.5 | Mathematical Models; Linear Models Calculating Velocities I and II - Mathematica notebook on spring-mass systems, equilibrium http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html |
| 1.6 | Families of Functions Power Functions - Mathematica notebook http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html |
Horizons Module Chapter 1 | |
Fractals and Chaos http://spanky.triumf.ca/ http://forum.swarthmore.edu/calcpow/solutions/solution.ehtml?puzzle=18 http://mathworld.wolfram.com/topics/ComplexSystems.html Iteration and Dynamical Systems http://www.geom.umn.edu/education/calc-init/population/ http://www.geom.umn.edu/education/calc-init/population/harvest.html http://mathworld.wolfram.com/topics/PopulationDynamics.html Recursion http://mathworld.wolfram.com/topics/Recursion.html http://www.ies.co.jp/math/java/ser_eq/ser_eq.html Deposition in a Bank, and Interest Formula http://mathworld.wolfram.com/topics/Accounting.html http://forum.swarthmore.edu/calcpow/solutions/solution.ehtml?puzzle=50 Fibonacci Sequence http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html | |
| 2.1 | Limits (An Intuitive Introduction) Intro to Limits - Graphically and Numerically - TI-85/86 activity http://www.ti.com/calc/docs/act.85calc.htm Continuity and Solving Equations - Maple worksheet http://www.math.gatech.edu/~bourbaki/c1program.html#week2 Limits - Maple worksheet uses a variety of graphical and numeric methods to study multi-dimensional limits http://mathlab.cit.cornell.edu/local_maple/mvc/lecguide.html |
| 2.2 | Limits (Computational Techniques) Alternate Intro to Limits - Geometrically, Numerically, Graphically, and Algebraically - TI-85/86 activity http://www.ti.com/calc/docs/act.85calc.htm |
| 2.4 | Continuity Root-Finding by Intermediate Values Applet - Java applet http://www.wiley.com/college/mat/anton243310/mod2/applets.html Continuity and Solving Equations - Maple worksheet http://www.math.gatech.edu/~bourbaki/c1program.html#week2 |
Horizons Module Chapter 2: No Module | |
| 3.1 | Tangent Lines and Rates of Change Role and Computation of Tangent Lines - Maple worksheet http://www.math.gatech.edu/~bourbaki/c1program.html#week3 |
| 3.2 | The Derivative The Derivative Function - Mathematica notebook on the relationship between a graph of a function and the graph of its derivative http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html Discovering the Derivative by Exploration - TI-82/83 activity http://www.ti.com/calc/docs/act.83calc.htm |
| 3.3 | Techniques of Differentiation Symbolic Derivatives - Mathematica notebook on the product rule and the chain rule http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html |
| 3.4 | Derivatives of Trigonometric Functions Differentiation - Maple worksheet http://www.math.gatech.edu/~bourbaki/c1program.html#week3 |
| 3.5 | The Chain Rule Symbolic Derivatives - Mathematica notebook on the product rule and the chain rule http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html Numerically Discovering a Formula for Derivatives - TI-85/86 activity http://www.ti.com/calc/docs/act.85calc.htm |
| 3.6 | Local Linear Approximation; Differentials Intro to Derivatives - Smooth Curves DonÕt When You Zoom In - TI-85/86 activity http://www.ti.com/calc/docs/act.85calc.htm |
Horizons Module Chapter 3 | |
Calculus of Robotics (Kinematics Equations) http://www.scas.bcit.bc.ca/scas/math/examples/ary_16_5/ary_16_5.htm http://mathworld.wolfram.com/topics/DynamicsandKinematics.html Cosine, and Sine http://forum.swa0rthmore.edu/calcpow/solutions/solution.ehtml?puzzle=44 http://www.seresc.k12.nh.us/alvirne/gues972.html http://mathworld.wolfram.com/topics/TrigonometricFunctions.html Derivative http://mathworld.wolfram.com/topics/MaximaandMinima.html http://www.mnsinc.com/hylton/dept/math/calculus/page4.htm http://forum.swarthmore.edu/calcpow/solutions/solution.ehtml?puzzle=35 http://www.seresc.k12.nh.us/alvirne/ap99p10.html | |
| 4.2 | Logarithmic and Exponential Functions The Natural Logarithm and Exponential Functions - TI-85/86 activity http://www.ti.com/calc/docs/act.85calc.htm |
| 4.3 | Implicit Differentiation Implicit Differentiation Problems and Plots - Maple worksheet http://www.math.gatech.edu/~bourbaki/c1program.html#week4 |
| 4.6 | Related Rates Related Average Rates PDF file - - TI-89/92 activity http://www.ti.com/calc/docs/act.89calc.htm Related Average Rates PDF file - - TI-92 activity http://www.ti.com/calc/docs/act.92calc.htm Related Rates - Maple worksheet http://www.math.gatech.edu/~bourbaki/c1program.html#week6 |
Horizons Module Chapter 4: No Module | |
| 5.2 | Analysis of Functions II: Relative Extrema; First and Second Derivative Tests The First Derivatives and Graphing: Extrema - Mathematica notebook on local and global extrema http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html |
| 5.3 | Analysis of Functions III: Applying Technology and the Tools of Calculus Little Red Corvette - analyzing functions with graphing calculators PDF file - - TI-89/92 activity http://www.ti.com/calc/docs/act.89calc.htm Graphing and Interpreting Graphs - Maple worksheet http://www.math.gatech.edu/~bourbaki/c1program.html#week6 Horizons Module: Functions from Data Least-Squares Data Fitting - TI-85/86 activity http://www.ti.com/calc/docs/act.85calc.htm Curve Fitting Applet - Java applet http://www.wiley.com/college/mat/anton243310/mod2/applets.html Least Squares Maple http://mathlab.cit.cornell.edu/local_maple/mvc/lecguide.html |
Horizons Module Chapter 5 | |
|
Interpolation http://grandmac.calpoly.edu/docs/math/diffcalc/wobegon.html http://mathworld.wolfram.com/topics/Interpolation.html Fitting curves to data http://www.geocities.com/SiliconValley/2902/curve-fi.htm Least Squares http://mathworld.wolfram.com/LeastSquaresFitting.html Regression Line http://mathworld.wolfram.com/LinearRegression.html Correlation Coefficient http://mathworld.wolfram.com/CorrelationCoefficient.html Linear Model/Nonlinear http://grandmac.calpoly.edu/docs/math/diffcalc/rentalcar.html Exponential Models http://www.sosmath.com/algebra/logs/log5/log53/log53.html Logarithmic Models http://www.scas.bcit.bc.ca/scas/math/examples/ary_9_4/ary_9_4.htm http://math.ucdavis.edu/~kouba/CalcOneDIRECTORY/logdiffdirectory/LogDiff.html Newton’s law of Cooling http://www.math.duke.edu/education/ccp/materials/diffcalc/ozone/ozone1.html http://forum.swarthmore.edu/calcpow/solutions/solution.ehtml?puzzle=48 | |
| 6.2 | Applied Maximum and Minimum Problems Fermat's Principle - Maple worksheet http://www.math.gatech.edu/~bourbaki/c1program.html#week5 Finding Maxima - Maple worksheet http://www.math.gatech.edu/~bourbaki/c1program.html#week5 Finding Maxima with Finite Points - Maple worksheet http://www.math.gatech.edu/~bourbaki/c1program.html#week5 |
| 6.4 | Newton's Method Newton's Method - Mathematica notebook http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html Newton's Method Applet - Java applet http://www.wiley.com/college/mat/anton243310/mod2/applets.html Solving Equations by Newton's Method - Maple worksheet http://www.math.gatech.edu/~bourbaki/c1program.html#week7 |
Horizons Module Chapter 6: No Module | |
Although there is no Module for this Horizons Module Chapter, these are two good links that relate to the Horizons Module Chapter. http://www.ies.co.jp/math/java/rolhei/rolhei.html http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/approx/newton.html | |
| 7.2 | The Indefinite Integral; Integral Curves and Directions Fields How Do You Graph Derivatives and Antiderivatives? PDF file - TI-85/86 activity http://www.ti.com/calc/docs/act.85calc.htm How Do You Graph Derivatives and Antiderivatives? PDF file - - TI-82/83 activity http://www.ti.com/calc/docs/act.83calc.htm Comparing Graphs - Maple worksheet http://www.math.gatech.edu/~bourbaki/c2program.html#week1 |
| 7.5 | The Definite Integral Riemann Sum Pictures and Calculating Riemann Sums - Mathematica notebooks on making pictures of left and right rectangle estimates of area, and calculating values of Riemann sums http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html Area Functions - Riemann sums and area TI-85/86 activity http://www.ti.com/calc/docs/act.85calc.htm Area by Chance - Maple worksheet http://www.math.gatech.edu/~bourbaki/c2program.html#week2 |
Horizons Module Chapter 7 | |
Elevation Angle http://www.seresc.k12.nh.us/alvirne/ap99p9.html http://www.kent.wednet.edu/pcpow/questions/calc/museum0/index.html Equations of Motion http://grandmac.calpoly.edu/docs/science/physics/wind_surf.html http://www.seresc.k12.nh.us/alvirne/gues994.html http://www.seresc.k12.nh.us/alvirne/ap98p9.html Trajectory http://www.netsrq.com/~hahn/pr8_2-4.html | |
| 8.1 | Area Between Two Curves Rotations - Maple worksheet http://www.math.gatech.edu/~bourbaki/c2program.html#week3 |
| 8.3 | Volumes by Cylindrical Shells Circular Cylinder and Planes- An introductory worksheet using the 3D Region Plot Package and other Maple tools http://mathlab.cit.cornell.edu/local_maple/mvc/lecguide.html |
| 8.4 | Length of a Plane Curve Length and Speed Along a Curve - Maple worksheet http://www.math.gatech.edu/~bourbaki/c2program.html#week4 |
Horizons Module Chapter 8: No Module | |
| 9.7 | Numerical Integration; Simpson's Rule Intro to Integration - Numerically and Statistically - TI-85/86 activity http://www.ti.com/calc/docs/act.85calc.htm Numerical Integration Applet - Java applet http://www.wiley.com/college/mat/anton243310/mod2/applets.html Approximating Definite Integrals Numerically - - Maple worksheet http://www.math.gatech.edu/~bourbaki/c2program.html#week8 Approximation Errors and Simpson's Rule - Maple worksheet http://www.math.gatech.edu/~bourbaki/c2program.html#week1 |
| Horizons Module Chapter 9 | |
| Railroad Design (Integration)
Surveying http://www.scas.bcit.bc.ca/scas/math/examples/ary_17_6/ary_17_6.htm Simpson’s Rule http://www.geocities.com/SiliconValley/2902/simpson.htm Volume http://www.seresc.k12.nh.us/alvirne/ap98p17.html http://www.seresc.k12.nh.us/alvirne/ap98p20.html Riemann Sums http://mathworld.wolfram.com/RiemannSum.html | |
| 10.1 | First-Order Differential Equations and Applications Understanding Differential Equations - TI-85/86 activity http://www.ti.com/calc/docs/act.85calc.htm |
| 10.3 | Modeling with Differential Equations Growth, Decay, and Exponential Functions - Maple worksheet http://www.math.gatech.edu/~bourbaki/c2program.html#week6 |
| Horizons Module Chapter 10: No Module | |
| http://grandmac.calpoly.edu/docs/science/chem/kinetics.html A real-life example based on First and Second Order Chemical Kinetics applied to radio- active decay | |
| 11.5 | Taylor and Maclaurin Series Taylor and Maclaurin Series Approximations - TI-85/86 activity http://www.ti.com/calc/docs/act.85calc.htm Taylor Series - Maple worksheet explores multivariate Taylor series. Compares graphically various Taylor polynomials to the original function. http://mathlab.cit.cornell.edu/local_maple/mvc/lecguide.html |
| Horizons Module Chapter 11: No Module | |
| 12.3 | Area in Polar Coordinates Polar Coordinates - Maple worksheet http://www.math.gatech.edu/~bourbaki/c2program.html#week5 |
| 12.4 | Conic Sections in Calculus Hyperbolae and Loran C Navigation - Maple worksheet http://www.math.gatech.edu/~bourbaki/c1program.html#week9 |
| Horizons Module Chapter 12 | |
Arc Length http://archives.math.utk.edu/visual.calculus/5/arclength.1/index.html Orbital http://www.seresc.k12.nh.us/alvirne/gues9814.html http://www.kent.wednet.edu/pcpow/questions/calc/colony2/index.html Ellipses http://mathworld.wolfram.com/Ellipse.html Polar Co- ordinate Systems http://mathworld.wolfram.com/PolarCoordinates.html http://archives.math.utk.edu/visual.calculus/5/polar.1/index.html http://www.ping.be/math/polar.htm Kepler’s Law II http://SunSITE.UBC.CA/LivingMathematics/V001N01/UBCExamples/Kepler/kepler.html Conic Sections http://mathworld.wolfram.com/ConicSection.html http://www.best.com/~xah/SpecialPlaneCurves_dir/ConicSections_dir/conicSections.html | |
| 13.1 | Rectangular Coordinates in 3-space; Spheres; Cylindrical Surfaces Three-Dimensional Graphics - Maple worksheet http://www.math.gatech.edu/~bourbaki/c3program.html |
| 13.2 | Vectors Learning About Vectors and Vector Operations - Java applet http://www.frontiernet.net/~imaging/vector_calculator.html Vectors - using Maple to computer addition of vectors, magnitudes, angles http://omega.albany.edu:8008/calc3/vectors-maple-dir/vector-maple.html Lines and planes with Maple http://omega.albany.edu:8008/calc3/Lines-Planes-dir/lines-plans-maple.html The distance from a point to a plane Maple routine http://omega.albany.edu:8008/calc3/intro2-ga-toc.html |
| 13.3 | Dot Products; Projections Projections Onto Lines and Planes - Maple worksheet http://www.math.gatech.edu/~bourbaki/c3program.html |
| 13.4 | Cross Product The Volume of a Parallelepiped - Maple worksheet http://www.math.gatech.edu/~bourbaki/c3program.html |
| 13.5 | Parametric Equations of Lines The distance from a point to a line, and the equation of the plane containing two given lines - Maple routines http://omega.albany.edu:8008/calc3/intro2-ga-toc.html |
| 13.6 | Planes in 3-space The plane through 3 points - Maple routine http://omega.albany.edu:8008/calc3/intro2-ga-toc.html |
| 13.8 | Cylindrical and Spherical Coordinates A Water Whirl (revolution of a cylinder) - Maple worksheet http://www.math.gatech.edu/~bourbaki/c3program.html Finding points and the distance from a point to a line with Maple http://omega.albany.edu:8008/calc3/intro2-ga-toc.html |
| Horizons Module Chapter 13: No Module | |
| 14.1 | Introduction to Vector-Valued Functions Limits and Continuity - introducing vector functions with Maple http://omega.albany.edu:8008/calc3/vector-funcs-toc.html |
| 14.2 | Calculus of Vector-Valued Functions The derivative of a vector function with Maple http://omega.albany.edu:8008/calc3/vector-funcs-toc.html |
| 14.3 | Change of Parameter; Arc Length Arc length and curvature with Maple http://omega.albany.edu:8008/calc3/vector-funcs-toc.html |
| 14.4 | Unit Tangent, Normal, and Binormal Vectors Unit tangent and Unit normal - what they are, how to with Maple http://omega.albany.edu:8008/calc3/vector-funcs-toc.html |
| 14.5 | Curvature Arc length and curvature with Maple http://omega.albany.edu:8008/calc3/vector-funcs-toc.html |
| 14.6 | Motion Along a Curve Length and Speed Along a Curve - Maple worksheet http://www.math.gatech.edu/~bourbaki/c2program.html#week4 |
| Horizons Module Chapter 14: No Module | |
| 15.1 | Functions of Two or More Variables Contour lines -Java Applet http://www.math.gatech.edu/~bourbaki/c3program.html Functions of several variables in Maple http://omega.albany.edu:8008/calc3/funcs-severalvars-toc.html |
| 15.2 | Limits and Continuity Computing limits with Maple http://omega.albany.edu:8008/calc3/funcs-severalvars-toc.html |
| 15.3 | Partial Derivatives Computing partial derivatives with Maple http://omega.albany.edu:8008/calc3/funcs-severalvars-toc.html |
| 15.4 | Differentiability and Chain Rules The Chain rule - Maple routine http://omega.albany.edu:8008/calc3/funcs-severalvars-toc.html |
| 15.5 | Tangent Planes; Total Differentials for Functions of Two Variables Tangent Planes and Normal Lines - Maple worksheet http://www.math.gatech.edu/~bourbaki/c3program.html Tangent planes with Maple http://omega.albany.edu:8008/calc3/funcs-severalvars-toc.html |
| 15.8 | Maxima and Minima of Functions of Two Variables Finding extrema with Maple http://omega.albany.edu:8008/calc3/funcs-severalvars-toc.html |
| 15.9 | Lagrange Multipliers Maximization with Constraints - Maple worksheet http://www.math.gatech.edu/~bourbaki/c3program.html Lagrange Multiplier Maple routine http://omega.albany.edu:8008/calc3/funcs-severalvars-toc.html Lagrange multipliers - The geometry of Lagrange multipliers is explored with Maple http://mathlab.cit.cornell.edu/local_maple/mvc/lecguide.html Constrained maxima and minima with LagrangeÕs Method - Mathematica lecture http://www.math.gatech.edu/~carlen/newton/html/c4program.html |
| Horizons Module Chapter 15: No Module | |
| 16.1 | Double Integrals Double integrals, approximating Riemann sums with Maple. http://omega.albany.edu:8008/calc3/int-severalvar-toc.html Computing volumes of solids with Maple http://omega.albany.edu:8008/calc3/int-severalvar-toc.html Random Riemann sums with Maple - shows how such can be computed for double integrals. http://mathlab.cit.cornell.edu/local_maple/mvc/lecguide.html |
| 16.2 | Double Integrals over Nonrectangular Regions Double integrals over general regions Maple routine http://omega.albany.edu:8008/calc3/int-severalvar-toc.html |
| 16.3 | Double Integrals in Polar Coordinates Transformation to polar coordinates with Maple http://omega.albany.edu:8008/calc3/int-severalvar-toc.html Integration in Polar Coordinates - Maple lecture http://www.math.gatech.edu/~carlen/newton/html/c4program.html |
| 16.4 | Parametric Surfaces; Surface Area Examples of surface areas computations with Maple http://omega.albany.edu:8008/calc3/surface-area-dir/examples-m2h.html Surface area of the intersection of 2 cylinders with Maple http://omega.albany.edu:8008/calc3/surface-area-dir/two-cyls-m2h.html |
| 16.6 | Centroid, Center of Gravity; Theorem of Pappus Distribution of Weights - Maple worksheet http://www.math.gatech.edu/~bourbaki/c2program.html#week4 Moments and Centroids - Java Applet http://www.math.gatech.edu/~bourbaki/c2program.html#week4 Centroids and Averages - Maple lecture http://www.math.gatech.edu/~carlen/newton/html/c4program.html The Theorem of Pappus - Maple lecture http://www.math.gatech.edu/~carlen/newton/html/c4program.html |
| 16.7 | Triple Integrals in Cylindrical and Spherical Coordinates Integration in cylindrical and spherical coordinates - Mathematica lecture http://www.math.gatech.edu/~carlen/newton/html/c4program.html Integration in 3 dimensions - Maple lecture http://www.math.gatech.edu/~carlen/newton/html/c4program.html |
| Horizons Module Chapter 16: No Module | |
| 17.2 | Line Integrals Numerical Evaluation of Line Integrals - PDF file TI-85/86 activity http://www.ti.com/calc/docs/act.85calc.htm Definition of a line integral with Maple http://omega.albany.edu:8008/calc3/vector-calculus-toc.html Computing line integrals with Maple http://omega.albany.edu:8008/calc3/vector-calculus-toc.html |
| 17.3 | Independence of Path; Conservative Vector Fields A Potential for Being Conservative - Maple lecture http://www.math.gatech.edu/~carlen/newton/html/c4program.html |
| 17.4 | Green's Theorem Green's Theorem for a Triangle - Maple worksheet does a variety of things related to Green's theorem for an infinitesimal triangle. http://mathlab.cit.cornell.edu/local_maple/mvc/lecguide.html Vector fields, line integrals, and the theorems of Green and Gauss - Mathematica lecture http://www.math.gatech.edu/~carlen/newton/html/c4program.html Green's Theorem - Maple lecture http://www.math.gatech.edu/~carlen/newton/html/c4program.html |
| 17.5 | Surface Integrals Surface integrals - Mathematica lecture http://www.math.gatech.edu/~carlen/newton/html/c4program.html Sample surface integrals - Maple lecture http://www.math.gatech.edu/~carlen/newton/html/c4program.html |
| 17.6 | Applications of Surface Integrals; Flux Flux and Circulation in Two Dimensions - Maple lecture http://www.math.gatech.edu/~carlen/newton/html/c4program.html |
| 17.7 | The Divergence Theorem The Divergence Theorem - Maple lecture http://www.math.gatech.edu/~carlen/newton/html/c4program.html |
| Horizons Module Chapter 17 | |
Hurricane Modeling Fluid dynamics http://mathworld.wolfram.com/VectorField.html Superposition principle http://mathworld.wolfram.com/SuperpositionPrinciple.html Uniform sink flow http://SunSITE.UBC.CA/LivingMathematics/V001N01/UBCExamples/Flow/flow.html Stream lines http://www.frontiernet.net/~imaging/vector_calculator.html Radial Unit Vector http://mathworld.wolfram.com/RadialCurve.html | |