MULTIVARIABLE CALCULUS TOOLS

• PowerPoint Presentations
• Skill Building Exercises
• Supplementary Reading
• Free Software Tools
           
        

POWERPOINT PRESENTATIONS

• Preliminaries
• Distance Formula in 3-Dimensions
• Functions of Several Variables
• Planes
• Cylindrical Coordinates
• Spherical Coordinates
• Lines
• Circles
• Putting it All Together
• Epsilon-Delta Definition of a Limit
• Properties of Vectors
• The Dot Product and the Cross Product
• Properties of the Dot Product
• Properties of the Cross Product
• Work, Components, and Projections
• The Plane Truth
• Parametric Surfaces and Transformations
• Derivatives of Vector Valued Functions
• Integrals of Vector Valued Functions
• Properties of Derivatives of Vector Valued Functions
• Arc Length
• Unit Tangents and Normals
• Curvature
• Differentiability
• Partial Derivatives
• Partial Derivatives and Tangent Planes
• The Total Differential
• The Chain Rule
• Chain Rule Examples
• The Gradient Vector
• The Gradient and Level Curves
• The Directional Derivative
• Second Order Partial Derivatives
• The Second Partials Test
• Proof of the Second Partials Test
• Taylor Polynomial Approximations
• Review
• Optimization
• Lagrange Multipliers
• Constrained Optimization
• Double Integrals
• Fubini's Theorem
• Probability Density Functions
• Surface Area
• Surface Integrals
• Triple Integrals
• Integrals in Polar and Cylindrical Coordinates
• Integrals in Spherical Coordinates
• Change of Variables in Multiple Integrals
• Vector Fields
• Line Integrals
• Independence of Path
• Green's Theorem
• Green's, Stokes', and Gauss' Theorems
• Stokes' Theorem in Higher Dimensions
• Divergence Theorem in Higher Dimensions
• Extra Stokes
• Parametric Surface Area and Integrals
• Secret Identities
       

SKILL BUILDING EXERCISES 

• Preliminaries
  • Preliminaries - Answers
• Table of Values
  • Table of Values - Answers
• Intersections and Tangents
  • Intersections and Tangents - Answers
• Level Curves 1
  • Level Curves 1 - Answers
• Level Curves 2
  • Level Curves 2 - Answers
• Level Curves 3
  • Level Curves 3 - Answers
• Graphs
  • Graphs - Answers
• Planes
  • Planes - Answers
• Cylindrical Coordinates
  • Cylindrical Coordinates - Answers
• Spherical Coordinates
  • Spherical Coordinates - Answers
• Cylindrical Graphs
  • Cylindrical Graphs - Answers
• Spherical Graphs
  • Spherical Graphs - Answers
• Circles
  • Circles - Answers
• Lines
  • Lines - Answers
• Parametric Equations in Two Dimensions
  • Parametric Equations in Two Dimensions - Answers
• Parmetric Equations in Three Dimensions
  • Parametric Equations in Three Dimensions - Answers
• Cross-Sections and Tangents
  • Cross-Sections and Tangents - Answers
• Displacement Vectors
  • Displacement Vectors - Answers
• Vector Arithmetic
  • Vector Arithmetic - Answers
• Length of a Vector
  • Length of a Vector - Answers
• Dot Product
  • Dot Product - Answers
• Angles Between Vectors
  • Angles Between Vectors - Answers
• Perpendicular and Parallel Vectors
  • Perpendicular and Parallel Vectors - Answers
• Components and Projections
  • Components and Projections - Answers
• Cross Products
  • Cross Products - Answers
• Vectors Perpendicular to Planes
  • Vectors Perpendicular to Planes - Answers
• Equations of Planes
  • Equations of Planes - Answers
• Area of a Parallelogram
  • Area of a Parallelogram - Answers
• Transformations of Spheres
  • Transformations of Spheres - Answers
• Parametric Equations of Planes
  • Parametric Equations of Planes - Answers
• Derivatives of Vector-Valued Functions
  • Derivatives of Vector-Valued Functions - Answers
• Integrals of Vector-Valued Functions
  • Integrals of Vector-Valued Functions - Answers
• Position, Velocity, and Acceleration
  • Position, Velocity, and Acceleration - Answers
• Arc Length
  • Arc Length - Answers
• Unit Tangents and Normals
  • Unit Tangents and Normals - Answers
• Curvature
  • Curvature - Answers
• First Partials
  • First Partials - Answers
• Total Differential
  • Total Differential - Answers
• Total Differential Approximations
  • Total Differential Approximations - Answers
• Chain Rule Diagrams
  • Chain Rule Diagrams - Answers
• Chain Rule
  • Chain Rule - Answers
• Gradient to a Level Curve
  • Gradient to a Level Curve - Answers
• Gradient to a Level Surface
  • Gradient to a Level Surface - Answers
• Gradients to Level Curves and Surfaces
  • Gradients to Level Curves and Surfaces - Answers
• Gradients and Tangent Planes
  • Gradients and Tangent Planes - Answers
• Directional Derivatives
  • Directional Derivatives - Answers
• Constructions
  • Constructions - Answers
• Second Partials
  • Second Partials - Answers
• Second Partials Test
  • Second Partials Test - Answers
• Lagrange Multipliers
  • Lagrange Multipliers - Answers
• Double Integrals
  • Double Integrals - Answers
• Order of Integration
  • Order of Integration - Answers
• Joint Density Functions
  • Joint Density Functions - Answers
• Surface Area
  • Surface Area - Answers
• Surface Integrals
  • Surface Integrals - Answers
• Triple Integrals
  • Triple Integrals - Answers
• Polar Integrals
  • Polar Integrals - Answers
• Cylindrical Integrals
  • Cylindrical Integrals - Answers
• Spherical Integrals
  • Spherical Integrals - Answers
• Change of Variables
  • Change of Variables - Answers
• Vector Fields
  • Vector Fields - Answers
• Curl and Divergence
  • Curl and Divergence - Answers
• Line Integrals
  • Line Integrals - Answers
• Work
  • Work - Answers
• Circulation
  • Circulation - Answers
• Gradient Fields
  • Gradient Fields - Answers
• Independence of Path
  • Independence of Path - Answers
• Green's Theorem and Stokes' Theorem
  • Green's Theorem and Stokes' Theorem - Answers
• Divergence Theorem
  • Divergence Theorem - Answers
• Stokes' Theorem in Three Dimensions
  • Stokes' Theorem in Three Dimensions - Answers
• Divergence Theorem in Three Dimensions
  • Divergence Theorem in Three Dimensions - Answers
    

Supplementary Reading

• Front Cover
• Chapter 1 Functions of Several Variables
• Chapter 2 Cylindrical and Spherical Coordinates
• Chapter 3 Parametric Equations for Curves in Space
• Chapter 4 Vectors
• Chapter 5 Vector Transformations
• Chapter 6 Vector Calculus
• Front Cover-2
• Chapter 7 Derivatives
• Chapter 8 Integrals
• Chapter 9 Vector Fields
• Chapter 10 Line Integrals
• Chapter 11 Green's Theorem
• Back Cover
     
  

 Free Software Tools

Click here to go to the download page for the free LiveMath Viewer. Right-click to download the files below.
  

• Functions of Several Variables
  • pointplot.the
  • graphimplicit.the
  • graph2d.the
  • graph3d.the
  • planes.the
  • graphcrosssections.the
  • graphlevelcurve.the
  • animatedlevelcurve.the
       
• Epsilon Delta
  • epsilondelta.the
           
• Cylindrical and Spherical Coordinates
  • graphpolar.the
  • polaranimation.the
  • cylindrical.the
  • spherical.the
          
• Parametric Equations for Curves in Space
  • circles.the
  • lines.the
  • parametric2d.the
  • parametric3d.the
  • graphseveral.the
           
• Vectors
  • vectorarithmetic.the
  • length.the
  • dotproduct.the
  • angles.the
  • perpparallel.the
  • crossproduct.the
  • vectorcalculations.the
  • vectorsperpendiculartoplanes.the
  • equationsofplanes.the
  • area.the
  • volume.the
          
• Vector Transformations
  • graphparametric3d.the
  • twovariableparam.the
  • bizarreparametric.the
           
• Vector Calculus
  • derivatives.the
  • integrals.the
  • arclength.the
  • unitangentsandnormals.the
  • curvature.the
         
• Derivatives
  • firstpartials.the
  • totaldifferential.the
  • gradient.the
  • gradienttoalevelcurve.the
  • gradienttoalevelsurface.the
  • directionalderivatives.the
  • constructions.the
  • secondpartials.the
         
• Integrals
  • doubleintegrals.the
  • polarintegrals.the
  • cylindricalintegrals.the
  • sphericalintegrals.the
  • tripleintegrals.the
  • jacobiancalculator.the
          
• Vector Fields
  • 2dvectorfield.the
  • 3dvectorfield.the
  • gradientfield.the
  • flowline.the
  • curlanddivergence.the
           
• Line Integrals
  • lineintegrals.the
  • gradientfields.the
             
• Green's Theorem
  • greenstheorem.the
  • divergencetheorem.the