Outline
Calculus
- Author:
- Tim Brzezinski
- Topic:
- Calculus
Table of Contents
Preliminary Review Topics
Limits & Continuity
Derivatives: Introduction & Intuition
- Average Velocity
- Average to Instantaneous (Intro)
- Sketch the Derivative (Warm Up)
- Intuitive Derivative Graphing Exercise
- Intuitive Derivative Graphing Exercise: REVAMPED!!!
- Drawing Derivatives
- Constructing Graphs of Derivative Functions (Intuitively)
- Average Rate of Change Intervals
- Average Rate of Change of a Function: Dynamic Illustration
- Average to Instantaneous (Rate of Change)
- Average Rate of Change vs. Instantaneous Rate of Change
- Derivative Function: Without Words
- Derivatives (Intro)-1
- Derivatives (Intro)-2
- Graphing The Derivative of a Function
- 3-Way Color-Changing Derivative Grapher
- When does f'(x) = f(x)?
- Mean Value Theorem
- Mean Value Theorem (Without Words)
- Mean Value Theorem: Quick Intuitive Tests
- Which is f, f', f'' ?
- Which is f, f', f''? Part 2 !!!
- Create a Function: Calculus
- Descartes' View of Tangents: Quick Overview
- Fermat Calculus Insight
- Sketching Derivatives of Freehand Drawn Functions
- Blank Templates: Sketch Your Own Function and Derivative Graphs
- Derivatives of Freehand Drawn Functions (via Locus Tool)
- Open Middle: Circle Tangent to Line (1)
Derivatives of Special Functions & Differentiation Techniques
- Derivative of a Product
- Important Trig Limits
- Derivative of Sine & Cosine Functions (Quick Investigation)
- Derivative of Tangent Function (Investigation)
- Implicit Differentiation: Intro
- Folium of Descartes
- Implicit Differentiation (Quick Check)
- Derivative of Arcsine Function
- Derivative of Arccosine Function
- Derivative of Arctangent Function
- Derivatives of Inverse Functions
- Derivative of Natural Log Function
- Open Middle Calculus Problem
- Tangent to Cubic: Open Middle Problem
Related Rates & Linearization of Functions
- Related Rates (1)
- Related Rates (2)
- Falling Ladder !!!
- Related Rates (3)
- Related Rates: Adjustable Cone with dh/dt Constant
- Filling a Cone: dV/dt Constant versus dh/dt Constant
- Related Rates (Rolling Carts Problem)
- Linearization Illustrator (Calculus)
- Linearization Checker (Calculus)
- Newton's Method: Illustrated
Closed Interval Method & Optimization Problems
- Critical Numbers & Critical Points of Functions (Intro)
- The Closed Interval Method (Application Problem)
- Norman Window: Modifiable Explorer
- Optimization: Area of a Rectangle
- Distance From Point to Graph
- Marginal Revenue, Cost, Profit: Analysis Problem 1
- Minimizing the Area of a Triangle
- Optimization Problem: Isosceles Triangle Circumscribed about a Circle
- Optimization - Box
- Maximizing Trapezoid Area
- Optimization Challenge 1
- Optimization: Maximizing Area of a Rectangle Inside a Right Triangle
- Honeybee Population (Growth Rate Question)
- Oil Pipeline Optimization Problem
- Cylinder Inscribed Inside Sphere
- Cylinder Inscribed In Cone
- Sphere Inscribed Inside a Right Circular Cone
- Circle Optimization Challenge!
Riemann Sums; Indefinite and Definite Integrals
- Definite Integral Illustrator (I)
- Trapezoid: Area (I)
- Trapezoid: Area (2)
- Definite Integral Illustrator (II)
- Definite Integrals: Sum
- Open Middle: Definite Integral Problem
- Open Middle: Definite Integral Problem (2)
- Even Functions!
- Odd Functions!
- Odd Functions: Another Look (Take 2)!
- Parabolic Segment: Archimedes Insight
- Accumulations
- All Sums (Riemann Sums)
Areas and Volumes; Solids of Revolution & Non-Revolution
- U-Substitution (Definite Integrals)
- Areas Between Curves (Intro)
- Area Between Curves
- Area Between 2 Curves
- Rotating Function Graphs about the xAxis within GeoGebra AR
- Surface of Revolution: GeoGebra Augmented Reality Template
- Visualizing Volumes of Rotation
- Volume of Solid of Revolution about x-axis
- Disc Action!!!
- Disc Method: REVAMPED!
- Solids of Revolution (Discs)
- Custom Made Solid of Revolution
- Washer Action!!! (1)
- Washer Action !!! (2) - Calculus
- Washer Method: REVAMPED!
- Cylindrical Shells: REVAMPED!
- Cylindrical Shell Action!!! (1)
- Cylindrical Shell Action!!! (2)
- Calculus: Surface of Revolution formed by Rotating Area Between 2 Functions
- Arc Length to Surface of Revolution: Calculus
- Gabriel's Horn: Virtual Exploration in GeoGebra Augmented Reality
- Modifiable Solid: Isosceles Right Triangle Cross Sections Parallel to yAxis (VA)
- Modifiable Solid: Isosceles Right Triangle Cross Sections Parallel to yAxis (VB)
- Modifiable Solid: Equilateral Triangle Cross Sections Parallel to yAxis
- Toblerone Warm Up Modeling Question for Algebra, Geometry, AND Calculus!
- Building Surfaces with Cross Sections and Function Modeling
- Modifiable Solid: Isosceles Triangle (Modifiable) Cross Sections Parallel to yAxis
- Modifiable Solid: Square Cross Sections Parallel to yAxis
- Modifiable Solid: Rectangular Cross Sections Parallel to yAxis
- Custom Solid: Changeable Rhombus Cross Section Parallel to yAxis
- Modifiable Solid: Isosceles Trapezoid Cross Sections Parallel to yAxis
- Modifiable Solid: Regular Pentagon Cross Sections Parallel to yAxis
- Modifiable Solid: Regular Hexagon Cross Sections Parallel to yAxis
- Modifiable Solid: Regular Heptagon Cross Sections Parallel to yAxis
- Modifiable Solid: Regular Octagonal Cross Sections Parallel to yAxis
- Modifiable Solid: Regular Nonagon Cross Sections Parallel to yAxis
- Modifiable Solid: Regular Decagon Cross Sections Parallel to yAxis
- Modifiable Solid: Semicircular Cross Sections Parallel to yAxis
- Modifiable Solid: Parabolic Cross Sections Parallel to yAxis
- Custom Solid: Elliptical Cross Sections Parallel to yAxis
- Solids Formed From Certain Cross Sections
- Parabola Around y-Axis
- Parabola Rotated Around y-Axis Wireframe
- Parabola Rotated Around x-Axis
- Parabola Rotated Around x-Axis
- Solids of Revolution: Around the x-Axis
- Solids of Revolution: Around the y-Axis
- Solids of Revolution: Around y=6
- Calculus Solids
- V. of Solid NOT of Revolution
- Cross-Sections Perpendicular to x-Axis: Squares
- Cross-Sections Perpendicular to x-Axis: Equilateral Triangle
- Cross-Sections Perpendicular to x-Axis: Right Triangles
- Cross-Sections Perpendicular to x-Axis: Rectangles
- Areas & Volumes: Culminating Activity
- Custom Solid: Cross Sections Parallel to yAxis are Quadrilaterals Always Similar to the Base
- Surface with Square Cross Sections
Average Value and Arc Length
Integration Techniques
Differential Equations
Sequences & Series
Parametric Equations
Polar Coordinates
- Trig Function Values (30 Degrees)
- Trig Function Values (45 Degrees)
- Trig Function Values (60 Degrees)
- Special Angles in Standard Position: Intro (V1)
- Special Angles in Standard Position: Intro (V2)
- Special Angles in Standard Position: Intro (V3)
- Polar Coordinates: Introduction
- Writing Equivalent Polar Coordinates: Quiz
- Polar Function Grapher
- Derivatives in Polar Coordintes
- Areas with Polar Coordinates
- Area Between 2 Polar Graphs
- Arc Length in Polar Coordintes
Multivariable Calculus Topics
- Plotting Points in 3D: Dynamic Illustrator
- Plotting Points in 3 Space
- Writing Ordered Triples
- 3D BATTLESHIP !!!
- Cylindrical Coordinates: Dynamic Illustrator
- Spherical Coordinates: Dynamic Illustrator
- Partial Derivatives: Graphical Illustrator
- Sphere Investigation
- Circular Paraboloid of Revolution
- Animation 111
- Special Spheroid Action: Locus Illustration
- Animation 112
- Special Hyperboloid of 1 Sheet as a Locus
- Special Hyperboloid of 2 Sheets as a Locus
- Catenoid
- Crazy Slide!