MATH 242 – Videos – Rob Grondahl

This is the updated set that is compliant with Title II of ADA. Please let me know if anything needs to be added or edited [email protected]

(*) Indicates a video that was not re-recorded for ADA, as I felt it was already compliant.

Red indicates videos that need remediation and will be linked when complete.

Review

U-Substitution

- - Changing Limits of Integration
  - Linear U-Substitution

Hyperbolic Trig Functions

Applications of Integration

Area Between Curves

- - Development With Respect to X
    - Example
  - Development With Respect to Y
    - Example

Volume by Cross-Sections

- - - Development
- Volume by Cylindrical Shells
  - Development
- Arc Length
  - Development
- Surface Area
  - Development
    - Example
- Physics Application – Work
Integration Techniques
- Integration by Parts
  - Development (*)
    - Example (*)
    - Table Method Example (*)
    - Unorthodox Example (*)
- Trigonometric Integrals
  - Powers of Sine and Cosine (Odd) (*)
  - Powers of Sine and Cosine (Even) (*)
  - Powers of Tangent (*)
  - Powers of Secent (Even) (*)
  - Powers of Secant (Odd) (*)
  - Products of Sine and Cosine (*)
- Trigonometric Substitution (Redo These)
- Partial Fractions (Redo These)
  - Linear Factors
  - Linear Factors with Shortcut
  - Linear Repeated Factors
  - Simplifying Improper Fractions
  - Irreducible Quadratic Factors
  - Repeated Irreducible Quadratic Factors
Improper Integrals
- L’Hopital’s Rule
- Evaluating Improper Integrals
- Comparing Improper Integrals
  - Integral Comparison Tests
  - P-Integrals
  - Comparison for Ln(x)
  - DCT – Development
    - DCT Example (Convergent)
    - DCT Example (Divergent)
  - LCT – Development
    - LCT – Example
Sequences and Series
- Sequences
  - Sequences and Series
  - Convergence of Sequences
  - Sequence Divergence to Infinity
  - Limit Properties of Sequences
  - Sandwich Thm. (Squeeze Thm.)
  - Thm 4. (Continuous Function Thm. for Sequences)
  - Thm. 5 (Common Limits)
- Infinite Series
  - Series
  - Geometric Series
    - Example
  - Telescoping Series
  - Series Properties
  - Useful Facts for Series
- Integral Test & Divergence Theorem
  - Nth Term Test (Divergence Theorem)
  - Integral Test Development
    - Example
  - P-Series
  - Truncation Error – Development
    - Example
- Comparison Tests
  - Series – DCT – Development
    - Example
  - Series – LCT – Development
    - Example
- Alternating Series
  - AST Development and Example
  - AST – Fail
  - Alternating Series Error Estimation
  - Absolute Convergence – Definition
  - ACT – Development
    - Example
- Ratio & Root Test
  - Ratio Test – Development 1
  - Ratio Test – Development 2
    - Example
  - Root Test – Development
    - Example
- Power Series
  - Power Series – Introduction
  - Interval of Convergence – Finite Interval
  - Interval of Convergence – All Reals
  - Interval of Convergence – Single Point
  - Visualizing with Desmos
- Properties of Power Series
  - Term-By-Term Differentiation
  - Term-By-Term Integration
- Taylor Series
  - Taylor Series – Introduction
  - Taylor Series – Development
  - Taylor Series – Natural Exponential
  - Taylor Series – Sine
  - Taylor’s Theorem
  - Error Bounds for Taylor Polynomials
Parametric Equations
- Parametric Equations
  - Parametric Equations
  - Non-Uniqueness of Parametric Equations
  - (ADD) Analyzing a Parametric Equation using Its Component Graphs
  - Parametrizing Circles
  - Parametrizing Lines
- Calculus of Parametric Equations
  - Slope of Parametric Curves
  - Higher Order Derivatives
  - Length of Parametric Curves
  - Area Under Parametric Curves
  - Surface Area of Revolution of Parametric Curves
Polar Equations
- Polar Coordinates
  - Introduction
  - Polar Curve: $r = \sin \theta$
  - Polar Curve – Cardiod
  - Slope of Polar Curves
- Calculus of Polar Equations
  - Area in Polar
    - Ex 1
    - Ex 2
    - Ex 3
  - Length in Polar
    - Ex