Calculus

Dr. Jack L. Jackson II, Prapaporn Nongharnpituk, 6 paź 2022

Currently this book is under construction. It will be expanding greatly over the course of the next semester or two. This book contains GeoGebra Activities written to help understand the Calculus I, II, III sequence. This collection includes all of the Calculus GeoGebra activities written by Jack L. Jackson II, Ph.D.. Dr. Jackson's YouTube channel contains lecture videos using these activities and many other lectures over mathematical concepts. https://www.youtube.com/c/DrJackLJacksonII This collection also contains some of the best GeoGebra calculus activities written by other mathematics educators.

Spis treści

  1. 1 Limits and Continuity
    1. Introducing Limits Informally Graph and Table
    2. Limits: Introductory Questions (2)
    3. Introduction to Limits
    4. Graphical Limits
    5. Limit Quiz
    6. Formal Epsilon-Delta Definition of a Limit
    7. A tool to explore delta-epsilon understandings.
    8. Formal Limits for Vertical Asymptotes
    9. Formal Limit as x appoaches +- infinity
    10. One CRAZY Limit !!!
    11. Limit Laws
    12. Cont in uity
    13. Continuity Questions
    14. IVT Dynamic Illustrator
    15. One Special Limit
    16. Optimization Water & Land Travel Snell's Law
  2. 2 Derivative Concepts, Definitions, Approximations
    1. Slope (Quiz) I
    2. Slope (Quiz) II
    3. Finding Slope Given 2 Points: Question Generator
    4. Slope: Quick Intuitive Quiz Questions
    5. Quick Quiz: Graphing Slope Types
    6. Average Velocity
    7. Average Rate of Change of a Function: Dynamic Illustration
    8. Quiz: Average Rate of Change of a Function (3)
    9. Average to Instantaneous Rate of Change
    10. Defining the Derivative at a Point
    11. Estimating the Derivative at a Point from Graph
    12. Does Differentiability Imply Continuity?
    13. Does Continuity Imply Differentiability?
    14. Introducing the Derivative Function 1
    15. Estimating the Graph of the Derivative Function
    16. Intuitive Derivative Graphing Exercise: REVAMPED!!!
    17. Constructing Graphs of Derivative Functions (Intuitively)
    18. Derivative Function: Without Words
    19. 3-Way Color-Changing Derivative Grapher
    20. Graphs of Higher Order Derivative Functions
    21. Which is f, f', f'' ?
    22. Which is f, f', f''? Part 2 !!!
    23. Building a Function with Conditions on f, f', f"
    24. Linearization Checker (Calculus)
    25. Linearization Illustrator (Calculus)
    26. Implicit Differentiation: Intro
  3. 3 Integral: Concepts, Definitions, Approximations
    1. Definite Integral Introduction & Approximation
    2. Approximating a Definite Integral from Graph
    3. Definite Integral Calculator
    4. Regular Polygons
    5. Second Fundamental Theorem of Calculus
    6. First Fundamental Theorem of Calculus
    7. First Fundamental Theorem of Calculus 2
    8. fundamental theorem of calculus
  4. 4 Derivative: Algebraic Formulas
    1. Derivative of a Constant Function
    2. Derivative of a Linear Function
    3. Derivatives of Quadratic Functions
    4. Derivative of a Cubic Polynomial Function
    5. Polynomial Quiz
    6. Derivative of a Power Function
    7. Derivative Sum Rule
    8. Constant Multiple Derivative Rule
    9. Graphs of Higher Order Derivative Functions
    10. Vertical Shifts and Derivatives
    11. Chain Rule with Lines
    12. Derivative Chain Rule
    13. Chain Rule
    14. chain rule demonstration
    15. Chain Rule With One Inner Function
    16. Differentiation with Chain Rule Self Practice Sheet
    17. Derivatives of Exponential Functions
    18. When does f'(x) = f(x)?
    19. Derivative Product Rule 1
    20. Derivative Product Rule Practice
    21. Derivative Quotient Rule Practice
    22. Product and Quotient Rules Derivatives Drill
    23. f(x) = a(1-e^(-bx))+c
    24. Derivative Inverse Function Rule
    25. Derivative of Natural Log Function
    26. Derivative of Sine & Cosine Functions (Quick Investigation)
    27. Important Trigonometric Limits
    28. Derivatives of Basic Trig Functions
    29. f(x)=e^(ax)sin(bx)
    30. Derivative of Inverse Trig Functions
    31. Derivatives of Hyperbolic Trig Functions
    32. Derivatives of Inverse Hyperbolic Trig Functions
    33. Implicit Differentiation: Intro
  5. 5 Integral: Algebraic Formulas
    1. Definite Integral Calculator
    2. Definite Integrals: Sum
    3. U-Substitution (Definite Integrals)
    4. U-Substitution demonstration
    5. Integration by Substitution
  6. 6 Derivative Applications
    1. IVT Dynamic Illustrator
    2. Mean Value Theorem (Without Words)
    3. Lagrange Mean Value Theorem
    4. Mean Value Theorem
    5. Mean Value Theorem: Quick Intuitive Tests
    6. Newton's Method
    7. Newton Raphson Iteration (failure cases)
    8. f(x) = a(1-e^(-bx))+c
    9. f(x)=e^(ax)sin(bx)
    10. Related Rates (1)
    11. Related Rates (2)
    12. Filling a Cone: dV/dt Constant versus dh/dt Constant
    13. Related Rates: Adjustable Cone with dh/dt Constant
    14. Related Rates (3)
    15. Related Rates: Filling/Draining Cone
    16. Related Rates (Rolling Carts Problem)
    17. Falling Ladder !!!
    18. Tarzan Related Rates Problem
    19. Volcano - Related Rate
    20. Mathematical optimization: Building a rectangular pen
    21. Optimization Problem: Isosceles Triangle Circumscribed about a Circle
    22. Box with Open Top
    23. Optimization - Box
    24. Maximizing Trapezoid Area
    25. Optimization: Area of a Rectangle
    26. Optimization: Maximizing Area of a Rectangle Inside a Right Triangle
    27. Cylinder Inscribed In Cone
    28. Distance From Point to Graph
    29. Campbell's Test: Maximizing Volume
    30. Optimization Water & Land Travel Snell's Law
    31. Oil Pipeline Optimization Problem
    32. Two Pole Optimization Problem
    33. Optimization - Art Gallery
    34. Simple Harmonic Motion: Mass on a Spring
    35. Unwrapping a Cylinder
  7. 7 Integral Applications
    1. Definite Integral Calculator
    2. Area Between Two Curves
    3. Area Between Curves
    4. Area Between 2 Curves
  8. 8 Techniques of Integration
    1. Definite Integral Calculator
    2. Integration Drill Applet
    3. Completing the Square (1)
    4. Completing the Square (2)
    5. Completing the Square (3)
    6. Completing the Square
    7. Completing the Square
  9. 9. More Integral Applications
    1. Modifiable Solid: Square Cross Sections Parallel to yAxis
    2. Modifiable Solid: Rectangular Cross Sections Parallel to yAxis
    3. Surface with Square Cross Sections
    4. Building Surfaces with Cross Sections and Function Modeling
    5. Modifiable Solid: Isosceles Right Triangle Cross Sections Parallel to yAxis (VA)
    6. Modifiable Solid: Isosceles Trapezoid Cross Sections Parallel to yAxis
    7. Custom Solid: Cross Sections Parallel to yAxis are Quadrilaterals Always Similar to the Base
    8. Modifiable Solid: Semicircular Cross Sections Parallel to yAxis
    9. Solids with Various Cross Sections: AR Templates
    10. Volume of intersecting cylinders
    11. Disc Action!!!
    12. Volume of Solid of Revolution about x-axis
    13. Washer Action!!! (1)
    14. Washer Action !!! (2) - Calculus
    15. Washer Method: REVAMPED!
    16. Cylindrical Shell Action!!! (1)
    17. Cylindrical Shell Action!!! (2)
    18. Cylindrical Shells: REVAMPED!
    19. Volume by Cylindrical Shells: Illustrated
    20. illustration of volume as a set of nested cylinders
    21. Solid of Revolution
    22. Volume of Revolution
    23. Arclength
    24. Arc Length to Surface of Revolution: Calculus
    25. Gabriel's Horn
    26. Elastic PE
    27. Fluid Pressure in a Reservoir
  10. 10. Sequences and Series
    1. Sequence and Series
    2. Sequences (Dynamic Illustrator)
    3. Sequences of real numbers
    4. Formal Limit of a Sequence
    5. Graphs of arithmetic sequence on a coordinate plane
    6. AQR Section 21: Arithmetic or Geometric?
    7. Arithmetic Sequence Find the missing number
    8. Infinite Geometric Series
    9. Infinite Geometric Series
    10. Tower of Hanoi
    11. Integral Test for Series
    12. Comparison Test
    13. Convergent or Divergent Series
    14. Partial Sums Alternating Series
    15. Infinite Series
    16. Taylor Polynomials
    17. Binomial Series Expansion
  11. 11. Parametric and Polar Functions
    1. 2D Parametric Curves
    2. Parametric Equations Grapher
    3. Parametric Equations (I)
    4. Cycloid Animation!
    5. Parametric Curves Explorer in 3D
    6. Parametric curve - Superman Logo
    7. Parametric curve - Batman Begins
    8. Parametric curve - Batman Dark Knight
    9. Parametric curve - Spiderman logo
    10. Polar Coordinates: Introduction
    11. Polar Coordinates
    12. Writing Equivalent Polar Coordinates: Quiz
    13. Polar and Rectangular
    14. Polar Function Grapher
    15. Morphing Cartesian Graphs to Polar Graphs
    16. Derivatives in Polar Coordintes
    17. Areas with Polar Coordinates
    18. Area Between 2 Polar Graphs
    19. Area Between 2 Polar Graphs
    20. Arc Length in Polar Coordintes
    21. Conic Sections
    22. Conic sections
    23. Circle Equation: Center (h,k)
    24. Conic Sections, Standard Form
    25. Section 10.6-Conics in Polar Coordinates
  12. 12. Multivariable Functions, Partial Derivatives
    1. Plotting Points in 3D: Dynamic Illustrator
    2. Cylindrical Coordinates: Dynamic Illustrator
    3. Spherical Coordinates: Dynamic Illustrator
    4. Quadric Surfaces
    5. Tracing Out Surfaces in 3D
    6. Exploring functions of 2 variables
    7. Partial Derivatives: Graphical Illustrator
    8. Partial Derivatives
    9. Directional derivatives and Gradient
    10. Directional derivative
    11. Sphere Investigation
    12. Traces
  13. 13. Muiltivariable Functions, Multiple Integration
    1. Definition of the double integral
    2. Iterated Double Integrals
    3. Double integral over a rectangle
    4. Visualizing Riemann Sums of a Double Iterated Integral
    5. General Region Double Integral
  14. 14. Vector Functions
    1. Vectors: Introduction (1)
    2. Vectors: Magnitude & Direction (I)
    3. 2D Vector Introduction, Form Conversion
    4. Vector Addition
    5. Adding Vectors Geometrically
    6. Quiz: Adding Vectors Geometrically
    7. 2D Scalar times Vector
    8. Scaling Vectors
    9. 2D Vector Sum, Scalar Multiple, Linear Combination
    10. 3. The Dot Product and Projections
    11. Unit Coordinate Vectors
    12. Dot Product Insight
    13. 2D Dot Product
    14. Vector Projections (1)
    15. Dot Product: Basic Synthesis Questions
    16. Cross Product: Introduction
    17. Visualizing Magnitude of Dot and Cross Products
    18. 3D Dot and Cross Product
    19. Computing Cross-Product
    20. Line Integral Over Vector Field Intro
    21. Vector Fields
    22. Vector field 3D
    23. Slope field plotter
    24. Line integrals: Arc length & Area of fence
    25. Graph the Line

1.

1 Limits and Continuity

  • 1. Introducing Limits Informally Graph and Table
  • 2. Limits: Introductory Questions (2)
  • 3. Introduction to Limits
  • 4. Graphical Limits
  • 5. Limit Quiz
  • 6. Formal Epsilon-Delta Definition of a Limit
  • 7. A tool to explore delta-epsilon understandings.
  • 8. Formal Limits for Vertical Asymptotes
  • 9. Formal Limit as x appoaches +- infinity
  • 10. One CRAZY Limit !!!
  • 11. Limit Laws
  • 12. Cont in uity
  • 13. Continuity Questions
  • 14. IVT Dynamic Illustrator
  • 15. One Special Limit
  • 16. Optimization Water & Land Travel Snell's Law

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2.

2 Derivative Concepts, Definitions, Approximations

  • 1. Slope (Quiz) I
  • 2. Slope (Quiz) II
  • 3. Finding Slope Given 2 Points: Question Generator
  • 4. Slope: Quick Intuitive Quiz Questions
  • 5. Quick Quiz: Graphing Slope Types
  • 6. Average Velocity
  • 7. Average Rate of Change of a Function: Dynamic Illustration
  • 8. Quiz: Average Rate of Change of a Function (3)
  • 9. Average to Instantaneous Rate of Change
  • 10. Defining the Derivative at a Point
  • 11. Estimating the Derivative at a Point from Graph
  • 12. Does Differentiability Imply Continuity?
  • 13. Does Continuity Imply Differentiability?
  • 14. Introducing the Derivative Function 1
  • 15. Estimating the Graph of the Derivative Function
  • 16. Intuitive Derivative Graphing Exercise: REVAMPED!!!
  • 17. Constructing Graphs of Derivative Functions (Intuitively)
  • 18. Derivative Function: Without Words
  • 19. 3-Way Color-Changing Derivative Grapher
  • 20. Graphs of Higher Order Derivative Functions
  • 21. Which is f, f', f'' ?
  • 22. Which is f, f', f''? Part 2 !!!
  • 23. Building a Function with Conditions on f, f', f"
  • 24. Linearization Checker (Calculus)
  • 25. Linearization Illustrator (Calculus)
  • 26. Implicit Differentiation: Intro

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3.

3 Integral: Concepts, Definitions, Approximations

  • 1. Definite Integral Introduction & Approximation
  • 2. Approximating a Definite Integral from Graph
  • 3. Definite Integral Calculator
  • 4. Regular Polygons
  • 5. Second Fundamental Theorem of Calculus
  • 6. First Fundamental Theorem of Calculus
  • 7. First Fundamental Theorem of Calculus 2
  • 8. fundamental theorem of calculus

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4.

4 Derivative: Algebraic Formulas

  • 1. Derivative of a Constant Function
  • 2. Derivative of a Linear Function
  • 3. Derivatives of Quadratic Functions
  • 4. Derivative of a Cubic Polynomial Function
  • 5. Polynomial Quiz
  • 6. Derivative of a Power Function
  • 7. Derivative Sum Rule
  • 8. Constant Multiple Derivative Rule
  • 9. Graphs of Higher Order Derivative Functions
  • 10. Vertical Shifts and Derivatives
  • 11. Chain Rule with Lines
  • 12. Derivative Chain Rule
  • 13. Chain Rule
  • 14. chain rule demonstration
  • 15. Chain Rule With One Inner Function
  • 16. Differentiation with Chain Rule Self Practice Sheet
  • 17. Derivatives of Exponential Functions
  • 18. When does f'(x) = f(x)?
  • 19. Derivative Product Rule 1
  • 20. Derivative Product Rule Practice
  • 21. Derivative Quotient Rule Practice
  • 22. Product and Quotient Rules Derivatives Drill
  • 23. f(x) = a(1-e^(-bx))+c
  • 24. Derivative Inverse Function Rule
  • 25. Derivative of Natural Log Function
  • 26. Derivative of Sine & Cosine Functions (Quick Investigation)
  • 27. Important Trigonometric Limits
  • 28. Derivatives of Basic Trig Functions
  • 29. f(x)=e^(ax)sin(bx)
  • 30. Derivative of Inverse Trig Functions
  • 31. Derivatives of Hyperbolic Trig Functions
  • 32. Derivatives of Inverse Hyperbolic Trig Functions
  • 33. Implicit Differentiation: Intro

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5.

5 Integral: Algebraic Formulas

  • 1. Definite Integral Calculator
  • 2. Definite Integrals: Sum
  • 3. U-Substitution (Definite Integrals)
  • 4. U-Substitution demonstration
  • 5. Integration by Substitution

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6.

6 Derivative Applications

  • 1. IVT Dynamic Illustrator
  • 2. Mean Value Theorem (Without Words)
  • 3. Lagrange Mean Value Theorem
  • 4. Mean Value Theorem
  • 5. Mean Value Theorem: Quick Intuitive Tests
  • 6. Newton's Method
  • 7. Newton Raphson Iteration (failure cases)
  • 8. f(x) = a(1-e^(-bx))+c
  • 9. f(x)=e^(ax)sin(bx)
  • 10. Related Rates (1)
  • 11. Related Rates (2)
  • 12. Filling a Cone: dV/dt Constant versus dh/dt Constant
  • 13. Related Rates: Adjustable Cone with dh/dt Constant
  • 14. Related Rates (3)
  • 15. Related Rates: Filling/Draining Cone
  • 16. Related Rates (Rolling Carts Problem)
  • 17. Falling Ladder !!!
  • 18. Tarzan Related Rates Problem
  • 19. Volcano - Related Rate
  • 20. Mathematical optimization: Building a rectangular pen
  • 21. Optimization Problem: Isosceles Triangle Circumscribed about a Circle
  • 22. Box with Open Top
  • 23. Optimization - Box
  • 24. Maximizing Trapezoid Area
  • 25. Optimization: Area of a Rectangle
  • 26. Optimization: Maximizing Area of a Rectangle Inside a Right Triangle
  • 27. Cylinder Inscribed In Cone
  • 28. Distance From Point to Graph
  • 29. Campbell's Test: Maximizing Volume
  • 30. Optimization Water & Land Travel Snell's Law
  • 31. Oil Pipeline Optimization Problem
  • 32. Two Pole Optimization Problem
  • 33. Optimization - Art Gallery
  • 34. Simple Harmonic Motion: Mass on a Spring
  • 35. Unwrapping a Cylinder

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7.

7 Integral Applications

  • 1. Definite Integral Calculator
  • 2. Area Between Two Curves
  • 3. Area Between Curves
  • 4. Area Between 2 Curves

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8.

8 Techniques of Integration

This unit continues Unit 5 with more advanced techniques of finding antiderivatives.

  • 1. Definite Integral Calculator
  • 2. Integration Drill Applet
  • 3. Completing the Square (1)
  • 4. Completing the Square (2)
  • 5. Completing the Square (3)
  • 6. Completing the Square
  • 7. Completing the Square

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9. More Integral Applications

  • 1. Modifiable Solid: Square Cross Sections Parallel to yAxis
  • 2. Modifiable Solid: Rectangular Cross Sections Parallel to yAxis
  • 3. Surface with Square Cross Sections
  • 4. Building Surfaces with Cross Sections and Function Modeling
  • 5. Modifiable Solid: Isosceles Right Triangle Cross Sections Parallel to yAxis (VA)
  • 6. Modifiable Solid: Isosceles Trapezoid Cross Sections Parallel to yAxis
  • 7. Custom Solid: Cross Sections Parallel to yAxis are Quadrilaterals Always Similar to the Base
  • 8. Modifiable Solid: Semicircular Cross Sections Parallel to yAxis
  • 9. Solids with Various Cross Sections: AR Templates
  • 10. Volume of intersecting cylinders
  • 11. Disc Action!!!
  • 12. Volume of Solid of Revolution about x-axis
  • 13. Washer Action!!! (1)
  • 14. Washer Action !!! (2) - Calculus
  • 15. Washer Method: REVAMPED!
  • 16. Cylindrical Shell Action!!! (1)
  • 17. Cylindrical Shell Action!!! (2)
  • 18. Cylindrical Shells: REVAMPED!
  • 19. Volume by Cylindrical Shells: Illustrated
  • 20. illustration of volume as a set of nested cylinders
  • 21. Solid of Revolution
  • 22. Volume of Revolution
  • 23. Arclength
  • 24. Arc Length to Surface of Revolution: Calculus
  • 25. Gabriel's Horn
  • 26. Elastic PE
  • 27. Fluid Pressure in a Reservoir

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10.

10. Sequences and Series

  • 1. Sequence and Series
  • 2. Sequences (Dynamic Illustrator)
  • 3. Sequences of real numbers
  • 4. Formal Limit of a Sequence
  • 5. Graphs of arithmetic sequence on a coordinate plane
  • 6. AQR Section 21: Arithmetic or Geometric?
  • 7. Arithmetic Sequence Find the missing number
  • 8. Infinite Geometric Series
  • 9. Infinite Geometric Series
  • 10. Tower of Hanoi
  • 11. Integral Test for Series
  • 12. Comparison Test
  • 13. Convergent or Divergent Series
  • 14. Partial Sums Alternating Series
  • 15. Infinite Series
  • 16. Taylor Polynomials
  • 17. Binomial Series Expansion

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11.

11. Parametric and Polar Functions

  • 1. 2D Parametric Curves
  • 2. Parametric Equations Grapher
  • 3. Parametric Equations (I)
  • 4. Cycloid Animation!
  • 5. Parametric Curves Explorer in 3D
  • 6. Parametric curve - Superman Logo
  • 7. Parametric curve - Batman Begins
  • 8. Parametric curve - Batman Dark Knight
  • 9. Parametric curve - Spiderman logo
  • 10. Polar Coordinates: Introduction
  • 11. Polar Coordinates
  • 12. Writing Equivalent Polar Coordinates: Quiz
  • 13. Polar and Rectangular
  • 14. Polar Function Grapher
  • 15. Morphing Cartesian Graphs to Polar Graphs
  • 16. Derivatives in Polar Coordintes
  • 17. Areas with Polar Coordinates
  • 18. Area Between 2 Polar Graphs
  • 19. Area Between 2 Polar Graphs
  • 20. Arc Length in Polar Coordintes
  • 21. Conic Sections
  • 22. Conic sections
  • 23. Circle Equation: Center (h,k)
  • 24. Conic Sections, Standard Form
  • 25. Section 10.6-Conics in Polar Coordinates

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12.

12. Multivariable Functions, Partial Derivatives

  • 1. Plotting Points in 3D: Dynamic Illustrator
  • 2. Cylindrical Coordinates: Dynamic Illustrator
  • 3. Spherical Coordinates: Dynamic Illustrator
  • 4. Quadric Surfaces
  • 5. Tracing Out Surfaces in 3D
  • 6. Exploring functions of 2 variables
  • 7. Partial Derivatives: Graphical Illustrator
  • 8. Partial Derivatives
  • 9. Directional derivatives and Gradient
  • 10. Directional derivative
  • 11. Sphere Investigation
  • 12. Traces

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13.

13. Muiltivariable Functions, Multiple Integration

  • 1. Definition of the double integral
  • 2. Iterated Double Integrals
  • 3. Double integral over a rectangle
  • 4. Visualizing Riemann Sums of a Double Iterated Integral
  • 5. General Region Double Integral

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14.

14. Vector Functions

  • 1. Vectors: Introduction (1)
  • 2. Vectors: Magnitude & Direction (I)
  • 3. 2D Vector Introduction, Form Conversion
  • 4. Vector Addition
  • 5. Adding Vectors Geometrically
  • 6. Quiz: Adding Vectors Geometrically
  • 7. 2D Scalar times Vector
  • 8. Scaling Vectors
  • 9. 2D Vector Sum, Scalar Multiple, Linear Combination
  • 10. 3. The Dot Product and Projections
  • 11. Unit Coordinate Vectors
  • 12. Dot Product Insight
  • 13. 2D Dot Product
  • 14. Vector Projections (1)
  • 15. Dot Product: Basic Synthesis Questions
  • 16. Cross Product: Introduction
  • 17. Visualizing Magnitude of Dot and Cross Products
  • 18. 3D Dot and Cross Product
  • 19. Computing Cross-Product
  • 20. Line Integral Over Vector Field Intro
  • 21. Vector Fields
  • 22. Vector field 3D
  • 23. Slope field plotter
  • 24. Line integrals: Arc length & Area of fence
  • 25. Graph the Line

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14.20.

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14.21.

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14.22.

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14.23.

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14.24.

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14.25.

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Informacja