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