Calculus
(Each video below will play on Windows Media Player and starts within 1-2 minutes)
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| Limits and The Derivative |
6A (click here)
24:07 mins. |
- Limits (introduction)
- Properties of Limits
- Right and Left hand Limits |
6B (click here)
26:21 mins. |
- Limits with Analytic Methods
- Limits and Graphs
- Limits, piecewise example
- Limits, 3 analytic techniques |
6C (click here)
23:01 mins. |
- Limits, analytic method and the GDC
- Limits and Asymptotes x ∞ |
6D (click here)
15:14 mins. |
- Asymptotes, Vertical and Horizontal |
6E (click here)
14:26 mins. |
- Rates of Change, Average and Instantaneous |
6F (click here)
14:48 mins. |
- Definition of the Derivative, Slopes of Tangents
|
6G (click here)
21:45 mins. |
- Apply Definition to Find Slopes of Tangents |
6H (click here)
15:50 mins. |
- Numerical Derivatives in the GDC
- Graphing Derivative Functions on the GDC
|
6I (click here)
14:00 mins. |
- Showing d/dx sin x = cos x in the GDC
- Exponential Functions d/dx ex and Showing in the GDC |
| Differentiation |
6J (click here
14:29 mins. |
- Derivatives of Polynomial Functions
|
6K (click here)
22:41 mins. |
- Rules of Differentiation
- The Product Rule
- The Quotient Rule |
6L (click here)
14:06 mins. |
- The Chain Rule |
6M (click here)
24:48 mins. |
- Higher-Order Derivatives
- Higher-Order Trig Derivatives, a pattern
- Quotient vs. Chain Rule, an example Deriving d/dx tan x = sec2 x
- The Natural Log and the Chain Rule
- The Exponential Function and the Chain Rule
|
| Optimization |
6N (click here)
31:50 mins. |
- Horizontal Tangents f ' (x) = 0
- Horizontal Tangent Lines, Global and Local Extrema
|
6O (click here)
13:27 mins. |
- Critical Points
- Increasing and Decreasing
- Functions, First Derivative
- Curvature and the Second Derivative
- Optimization Applications |
| Indefinite Integration |
6P (click here)
19:19 mins. |
- Anti-Differentiation
- More Anti-Differentiation |
6Q (click here)
15:54 mins. |
- Indefinite Integration
- Integration Technique: U-Substitutuon |
| Initial Value Problems; Definite integrals; Areas under curves; Volumes of Revolution |
6R (click here)
20:44 mins. |
- Example in Kinematics
|
6S (click here)
13:00 mins. |
- Area Under a Curve (including Riemann Sums)
- The Definite Integral
- Finding Area in the GDC |
6T (click here)
20:08 mins. |
- Properties of Definite Integrals
- Apply Properties of the Definite Integral |
6U (click here)
18:15 mins. |
- The Fundamental Theorem of Calculus
- Apply the Fundamental Theorem to Find Definite Integrals |
| Displacement, s, Velocity, v, and Acceleration, a3 |
6V (click here)
18:35 mins. |
- Kinematics (distance, velocity and acceleration)
- Distance-Velocity Example in the GDC |
6W (click here)
11:54 mins |
- The Second Derivative and Graphs
- Inflection Points |
6X (click here)
21:34 mins |
- Graphing Polynomial Functions using Analysis |
6Y (click here)
21:45 mins |
- Graphing Rational Functions using Analysis |
6Z (click here)
18:04 mins |
- Connecting Graphs of f , f’ and f’’
- A Thorough Example |
