Utkast
IB Mathematics HL
Innehåll
Limits and Continuity
Derivatives - definitions and visualizations
- Definition of a Derivative
- Average Velocity
- Average to Instantaneous (Intro)
- Derivatives (Intro)-1
- Derivatives (Intro)-2
- Workshop #3: Introducing Derivatives - The Slope Function
- Derivative of Sine Function (Intuitive Discovery)
- Derivative of Cosine Function (Intuitive Discovery)
- Sketch the Derivative (Warm Up)
- 3-Way Color-Changing Derivative Grapher
- Graphing The Derivative of a Function
Techniques of differentiation
Related Rates and Optimization
Integral Calculus
- Definite Integral Illustrator (I)
- Riemann Sums - Rectangular Approximation (LRAM, RRAM, MRAM)
- fundamental theorem of calculus
- The Fundamental Theorem of Calculus
- Definite Integrals: Sum
- Integral as area
- Rules of the Definite Integral
- Areas Between Curves (Intro)
- Area Between Curves
- Mean Value Theorem
- U-Substitution (Definite Integrals)
- Solids of Revolution (Discs)
- Parabola Around y-Axis
- Parabola Rotated Around y-Axis Wireframe
- Parabola Rotated Around x-Axis
- Solids Of Revolution: Disk Method
- Riemann Sums
Calculus Option
Series
- Taylor Polynomials
- Taylor Polynomial of f(x) centered at point a
- Convergent or Divergent Series
- Converging series
- Integral Test for Series Convergence
- Taylor Series
- Properties of Power Series
- Alternating Series
- Partial Sums and Series
- The Divergence and Integral Tests
- The Taylor and Maclaurin series.
- Power Series Representations of Functions
- Maclaurin series
Slope Fields