BC Calculus

Table of Contents

• Chapter 1 - Limits

  • limit analyzer
  • Limits: Introductory Questions
  • Limits Example 1
  • Limits Example 2
  • Limits Example 3
  • Limits Example 4
  • Limits Example 5
  • Limits Example 6
  • Limits Example 7
  • Cont in uity
  • Continuity Questions
  • Vertical Asymptote (Defined as a Limit)
  • Horizontal Asymptote (Defined as a Limit)
  • One Special Limit

• Chapter 2 - The Derivative

  • Derivatives (Intro)-2
  • When does f'(x) = f(x)?
  • Important Trig Limits
  • Graphical relationship between a function and its derivative

• Chapter 3 - Derivatives of Elementary Functions

  • Derivatives of Inverse Functions
  • Graphing The Derivative of a Function
  • Derivative of Sine & Cosine Functions (Quick Investigation)
  • Derivative of a Product
  • Derivative of Tangent Function (Investigation)
  • Implicit Differentiation: Intro
  • Implicit Differentiation (Quick Check)
  • Derivative of Arcsine Function
  • Derivative of Arccosine Function
  • Derivative of Arctangent Function
  • Derivative of Natural Log Function

• Chapter4 Applications of the Derivative

  • Derivative Definition
  • tangent and derivative
  • Existence of Derivative
  • The rate of change of a shadow
  • Mean Value Theorem (Without Words)
  • Critical Points
  • Critical Points of a function -Example
  • Critical Numbers & Critical Points of Functions (Intro)
  • Maximum/Minimum Videos
  • Relative Extrema Illustrator
  • Extrema on a Closed Interval
  • Investigating the derivative at a cusp.
  • Constructing Graphs of Derivative Functions (Intuitively)
  • Sketch the Derivative (Warm Up)
  • Quiz: Writing Exponential Growth & Decay Functions
  • Exponential Growth vs. Decay (Intro)
  • Newton's Law of Cooling
  • Logistic Growth Function

• Chapter 5 The Integral

  • Riemann Sums
  • All Sums (Riemann Sums)
  • Area between curves
  • Area between curves
  • Definite Integral Illustrator (II)
  • Average Velocity
  • Areas Between Curves (Intro)
  • Area Between Curves
  • Area Between 2 Curves

• Chapters 6 Antiderivatives

  • Cross-Sections Perpendicular to x-Axis: Squares
  • Region between two quadratics rotated about y=-3
  • Definite Integrals: Sum
  • What Makes a Function Even?
  • What Makes a Function Odd?
  • Odd Functions: Another Look (Take 2)!
  • U-Substitution (Definite Integrals)

• Chapters 7 & 8 - Applications of Integral

  • Volume of Rotation - Disk Method Visual
  • Visualizing Volumes of Rotation
  • 3D volume by rotation of a function
  • Parabola Around y-Axis
  • Parabola Rotated Around y-Axis Wireframe
  • Parabola Rotated Around x-Axis
  • Parabola Rotated Around x-Axis
  • Cross sections are semi-circles.
  • Cross sections are squares with one side in base.
  • Volume: Circ base cross section isos rt triangle hyp in base
  • Volume of revolution, donut shape, cylindrical shell method.
  • Cylindrical Shell Action!!! (1)
  • Cylindrical Shell Action!!! (2)
  • Volume by Cylindrical Shells: Illustrated
  • Volume of a Solid - Washer Method
  • illustration of volume as a set of nested cylinders
  • Arc length: Quick Investigation
  • Disc Action!!!
  • Washer Action!!! (1)
  • Washer Action !!! (2) - Calculus
  • V. of Solid NOT of Revolution
  • Areas & Volumes: Culminating Activity

• Chapter 9 - Techniques of Integration

  • Sine & Cosine of a Sum: Discovery
  • Partial Fraction Decomposition Calculator
  • Section 4.5-Integration using substitution

• Chapter 10 - Improper Integrals

  • Gabriel's Horn

• Chapter 11 - Infinite Series

  • Sequences (Dynamic Illustrator)
  • lagrange error bound
  • Calculus - Taylor Inequality (LaGrange Error Bound)
  • Taylor Polynomials
  • Taylor Series

• Chapter 12 - Differential Equations

  • Slope Fields.
  • Euler's Method of Function Approximation
  • Euler's Method

• Chapter 13 - Polar

  • Polar Grapher
  • Section 10.4-Area in Polar Coordinates
  • Areas with Polar Coordinates
  • Arc Length in Polar Coordintes
  • Derivatives in Polar Coordintes
  • Area Between 2 Polar Graphs