MAT240-35289

• Syllabus
• Syllabus Acknowledgement Receipt
• Homework Portfolio Instructions
• Homework
        

TENTATIVE TEST DATES

February 8
March 7
April 4
April 25
      

POWERPOINT PRESENTATIONS

• Preliminaries
  • Wikipedia: Multivariable Calculus
• Distance Formula in 3-Dimensions
• Functions of Several Variables
• Planes
• Cylindrical Coordinates
  • Wikipedia: Polar Coordinates
  • Wikipedia: Cylindrical Coordinates
• Spherical Coordinates
  • Wikipedia: Spherical Coordinates
• Lines
• Circles
  • Wikipedia: Parametric Equation
• Putting it All Together
• Epsilon-Delta Definition of a Limit
• Properties of Vectors
  • Khan Academy: Introduction to Vectors
  • Khan Academy: Vector Examples
  • Khan Academy: Parametric Representations of Lines
  • Wikipedia: Euclidean Vector
  • Wikipedia: Position Vector
  • Wikipedia: Displacement Vector
  • Wikipedia: Null Vector
  • Wikipedia: Unit Vector
• The Dot Product and the Cross Product
  • Khan Academy: The Dot Product
  • Khan Academy: Vector Dot Product and Vector Length
  • Khan Academy: Defining the Angle Between Vectors
  • Khan Academy: Cross Product Introduction
  • Khan Academy: Proof: Relationship Between Cross Product and Sin of Angle
  • Khan Academy: Cross Product 1
  • Khan Academy: Cross Product 2
  • Khan Academy: Cross Product and Torque
  • Khan Academy: Calculating Dot and Cross Products with Unit Vector Notation
  • Khan Academy: Dot and Cross Product Comparison/Intuition
  • Khan Academy: Dot vs. Cross Product
  • Wikipedia: Dot Product
  • Wikipedia: Cross Product
• Properties of the Dot Product
  • Khan Academy: Proving Vector Dot Product Properties
• Properties of the Cross Product
• Work, Components, and Projections
  • Wikipedia: Vector Projection
• The Plane Truth
  • Khan Academy: Defining a Plane in R3 with a Point and Normal Vector
• Parametric Surfaces and Transformations
  • Khan Academy: Introduction to Parametrizing a Surace with Two Parameters
  • Khan Academy: Determing a Position Vector-Valued Function for a Parametrization of Two Parameters
• Derivatives of Vector Valued Functions
  • Khan Academy: Position Vector Valued Functions
  • Khan Adademy: Derivative of a Position Vector Valued Function
  • Khan Academy: Differential of a Vector Valued Function
  • Khan Academy: Vector Valued Function Derivative Example
• Integrals of Vector Valued Functions
• Properties of Derivatives of Vector Valued Functions
• Arc Length
  • Wikipedia: Arc Length
• Unit Tangents and Normals
• Curvature
  • Wikipedia: Curvature
• Differentiability
• Partial Derivatives
  • Khan Academy: Partial Derivatives
  • Khan Academy: Partial Derivatives 2
• Partial Derivatives and Tangent Planes
• The Total Differential
• The Chain Rule
• Chain Rule Examples
• The Gradient Vector
• The Gradient and Level Curves
  • Wikipedia: Gradient
• The Directional Derivative
  • Khan Academy: Gradient 1
  • Khan Adademy: Gradient of a Scalar Field
• Second Order Partial Derivatives
• The Second Partials Test
  • Wikipedia: Second Partial Derivative Test
• Proof of the Second Partials Test
• Taylor Polynomial Approximations
• Review
• Optimization
• Lagrange Multipliers
  • Wikipedia: Lagrange Multiplier
• Constrained Optimization
• Double Integrals
  • Khan Academy: Double Integrals 1
  • Khan Academy: Double Integrals 2
  • Wikipedia: Multiple Integrals
• Fubini's Theorem
  • Khan Academy: Double Integrals 3
  • Khan Academy: Double Integrals 4
  • Khan Academy: Double Integrals 5
  • Khan Academy: Double Integrals 6
  • Wikipedia: Fubini's Theorem
• Probability Density Functions
• Surface Area
• Surface Integrals
• Triple Integrals
  • Khan Academy: Triple Integrals 1
  • Khan Academy: Triple Integrals 2
  • Khan Academy: Triple Integrals 3
• Integrals in Polar and Cylindrical Coordinates
• Integrals in Spherical Coordinates
• Change of Variables in Multiple Integrals
  • Wikipedia: Jacobian Matrix and Determinant
• Vector Fields
  • Khan Academy: Divergence 1
  • Khan Academy: Divergence 2
  • Khan Academy: Divergence 3
  • Khan Academy: Curl 1
  • Khan Academy: Curl 2
  • Khan Academy: Curl 3
• Line Integrals
  • Khan Academy: Introduction to the Line Integral
  • Khan Academy: Line Integral Example 1
  • Khan Academy: Line Integral Example 2 (Part 1)
  • Khan Academy: Line Integral Example 2 (Part 2)
  • Khan Academy: Parametrization of a Reverse Path
  • Khan Academy: Scalar Field Line Integral Independent of Path Direction
  • Khan Academy: Line Integrals and Vector Fields
  • Khan Academy: Using a Line Integral to find Work Done by a Vector Field Example
  • Khan Academy: Vector Field Line Integral Dependent on Path Direction
• Independence of Path
  • Khan Academy: Path Independence for Line Integrals
  • Khan Academy :Closed Curve Line Integrals of Conservative Vector Fields
  • Khan Academy: Example of Closed Line Integral of Conservative Field
  • Khan Academy: Second Example of Line Integral of Conservative Vector Field
• Green's Theorem
  • Khan Academy: Green's Theorem Proof (Part 1)
  • Khan Academy: Green's Theorem Proof (Part 2)
  • Khan Academy: Green's Theorem Example 1
  • Khan Academy: Green's Theorem Example 2
  • Wikipedia: Green's Theorem
• Green's, Stokes', and Gauss' Theorems
• Stokes' Theorem in Higher Dimensions
  • Wikipedia: Stokes' Theorem
• Divergence Theorem in Higher Dimensions
  • Wikipedia: Divergence Theorem
• Extra Stokes
• Parametric Surface Area and Integrals
  • Khan Academy: Partial Derivatives of Vector-Valued Functions
  • Khan Academy: Introduction to the Surface Integral
  • Khan Academy: Example of Calculating a Surface Integral Part 1
  • Khan Academy: Example of Calculating a Surface Integral Part 2
  • Khan Academy: Example of Calculating a Surface Integral Part 3
  • Wikipedia: Surface Integral
• Secret Identities
  
       

SUPPLEMENTARY HOMEWORK 

• 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

• 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
• Chapter 7 Derivatives
• Chapter 8 Integrals
• Chapter 9 Vector Fields
• Chapter 10 Line Integrals
• Chapter 11 Green's Theorem

 MAPLE Assignments

• MAPLE-1 due before 2/1/2012
• MAPLE-2 due before 2/15/2012
• MAPLE-3
• MAPLE-4
• MAPLE-5
• MAPLE-6
• MAPLE-7
  

 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