Intermediate Calculus

S. Chen, Jan 22, 2021

Table of Contents

  1. Chapter 13 Vectors
    1. Vectors: Introduction (1)
    2. Scaling Vectors
    3. Parallel Vectors
    4. Vector Addition
    5. Definition of vector addition
    6. Vector Subtraction
    7. Adding Vectors Geometrically
    8. Vectors: Unit Vector & Component Form
    9. Force Vector
    10. Graph a 3D Surface by typing in an equation
    11. How are you doing?
  2. Chapter 14
    1. 14.1 Vector-Valued Functions in Space
    2. 14.1 Helix Graph of a Vector-Valued Function
    3. 14.2 Derivative of a Vector-valued Function
    4. 14.2 Derivatives of vector valued functions - tangent vector
    5. 14.4 Motion in space
    6. 14.5 Unit Tangent, Normal, and Binormal Vectors
  3. Chapter 15
    1. Level Curves
    2. 15.1 Level Curves (contour map)
    3. 15.3 Partial Derivatives: Graphical Illustrator
    4. Partial Derivatives
    5. 15.5 Directional derivatives and Gradient
    6. 15.6 Tangent Plane to a Surface
    7. 15.7 Max/Min (Cylinder Inscribed In Cone)
    8. absolute max & min
    9. mml_hmwk15.7.85
    10. 15.8 Lagrange Multiplier
  4. Chapter 16
    1. 16.1Notes Question1
    2. 16.1 Notes Question 2
    3. 16.1 Example 4
    4. 16.1 Example 6
    5. 16.1 Example 7
    6. Homework 16.2.83
    7. 16.3 Polar and Cartesian Coordinates
    8. 16.4 Triple Integral Visualizer
    9. 16.5 Cylindrical Coordinates
    10. 16.5 Spherical Coordinates
    11. 16.5 Spherical Coord Demonstration
    12. Triple Integral in Spherical Coordinates
    13. 16.5 Triple Integral in Spherical Coordinates Example
    14. 16.5 Triple Integral in Spherical Coordinates - Visualizer - can change bounds
    15. 16.6 Integrals for Mass 3D examples
  5. Chapter 17
    1. 17.1 Vector Fields
    2. 17.1 Vector field 3D
    3. 17.2 Geometric interpretation of the line integral
    4. 17.4 Green's Theorem (Circulation Form) in 2D
    5. 17.4 Illustration of the flux form of the Green's Theorem
    6. 17.5 Vector Fields, Divergence, Curl, and Line Integrals
    7. 17.5 Divergence and Curl of 3D vector field
    8. 17.6 Surface integral of a vector field over a surface
    9. 17.7 Stokes' Theorem - Line Integrals and Surface Integrals

1.

Chapter 13 Vectors

  • 1. Vectors: Introduction (1)
  • 2. Scaling Vectors
  • 3. Parallel Vectors
  • 4. Vector Addition
  • 5. Definition of vector addition
  • 6. Vector Subtraction
  • 7. Adding Vectors Geometrically
  • 8. Vectors: Unit Vector & Component Form
  • 9. Force Vector
  • 10. Graph a 3D Surface by typing in an equation
  • 11. How are you doing?

1.1.

Vectors: Introduction (1)

Recall a [b]VECTOR[/b] is a quantity with [b]both MAGNITUDE and DIRECTION. [/b][br][br]The applet below illustrates how we GEOMETRICALLY represent a vector.[br][br]Interact with this applet for a few minutes. [br]Then, complete the investigation questions you received at the beginning of class.
– Tim Brzezinski

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2.

Chapter 14

  • 1. 14.1 Vector-Valued Functions in Space
  • 2. 14.1 Helix Graph of a Vector-Valued Function
  • 3. 14.2 Derivative of a Vector-valued Function
  • 4. 14.2 Derivatives of vector valued functions - tangent vector
  • 5. 14.4 Motion in space
  • 6. 14.5 Unit Tangent, Normal, and Binormal Vectors

2.1.

14.1 Vector-Valued Functions in Space

– S. Chen, Mike Martinez

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3.

Chapter 15

  • 1. Level Curves
  • 2. 15.1 Level Curves (contour map)
  • 3. 15.3 Partial Derivatives: Graphical Illustrator
  • 4. Partial Derivatives
  • 5. 15.5 Directional derivatives and Gradient
  • 6. 15.6 Tangent Plane to a Surface
  • 7. 15.7 Max/Min (Cylinder Inscribed In Cone)
  • 8. absolute max & min
  • 9. mml_hmwk15.7.85
  • 10. 15.8 Lagrange Multiplier

3.1.

Level Curves

This worksheet illustrates the level curve [math]f(x,y)=c[/math].
Level Curves
– Kristen Beck

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4.

Chapter 16

  • 1. 16.1Notes Question1
  • 2. 16.1 Notes Question 2
  • 3. 16.1 Example 4
  • 4. 16.1 Example 6
  • 5. 16.1 Example 7
  • 6. Homework 16.2.83
  • 7. 16.3 Polar and Cartesian Coordinates
  • 8. 16.4 Triple Integral Visualizer
  • 9. 16.5 Cylindrical Coordinates
  • 10. 16.5 Spherical Coordinates
  • 11. 16.5 Spherical Coord Demonstration
  • 12. Triple Integral in Spherical Coordinates
  • 13. 16.5 Triple Integral in Spherical Coordinates Example
  • 14. 16.5 Triple Integral in Spherical Coordinates - Visualizer - can change bounds
  • 15. 16.6 Integrals for Mass 3D examples

4.1.

16.1Notes Question1

– S. Chen

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5.

Chapter 17

  • 1. 17.1 Vector Fields
  • 2. 17.1 Vector field 3D
  • 3. 17.2 Geometric interpretation of the line integral
  • 4. 17.4 Green's Theorem (Circulation Form) in 2D
  • 5. 17.4 Illustration of the flux form of the Green's Theorem
  • 6. 17.5 Vector Fields, Divergence, Curl, and Line Integrals
  • 7. 17.5 Divergence and Curl of 3D vector field
  • 8. 17.6 Surface integral of a vector field over a surface
  • 9. 17.7 Stokes' Theorem - Line Integrals and Surface Integrals

5.1.

17.1 Vector Fields

Change the components of the vector field.
This applet was done thanks to the work of Linda Fahlberg-Stojanovska: [url=https://www.geogebra.org/u/lfs-d]https://www.geogebra.org/u/lfs-d[/url]
– S. Chen, Juan Carlos Ponce Campuzano

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