Calculus Notes and Videos
(If you are looking for Zitur AP™ Calculus BC, click here)
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On this site, you can find note templates (usually titled by section and topic) and completed notes (include a date in the file name). You will also find the YouTube video that goes along with the notes. We use Larson, Hostetler and Edwards 8th Edition Calculus. The problems can be found here. http://tinyurl.com/SASCalc or
Or
http://www.calcchat.com/book/Calculus-ETF-4e/
Select the Topics on the left or below to suit your needs and inside you will find more specific topics that cover the majority of the AP curriculum basics.
Chapter 1
Chapter 4 The Integral
Section 4.1 Anti-derivatives
Section 1.2 Limits Graphically and Numerically
Section 1.3 Limits: Direct Substitution
Section 1.4 Continuity
Section 1.5/3.5 Limits to Infinity: 1.5 Vertical Asymptotes and 3.5 Horizontal Asymptotes/ End Behavior
Section 4.2, 4.3 and 4.6 Summation Notation, Riemann Sums (Left, right and Midpoint) and Trapezoidal method (No video)
Section 4.4 First and Second Fundamental Theorems of Calculus
Section 4.5 U-substitution
Other topics:
1) Displacement vs Total Distance Traveled
Chapter 2 The Derivative
2) Position of a function given a velocity with an unknown anti-derivative and an initial value.
Chapter 5 Inverse, Logarithmic and Exponential Functions
Section 5.1 The Derivative of ln(x)
Section 2.1 Derivative and Tangent Line Problem
Section 2.2 Basic Derivative Rules
Section 2.3 Product Rule/ Quotient Rule
Section 2.4 Chain Rule
Section 2.5 Implicit Differentiation
Section 5.2 Integral of 1/x is ln(x)
Section 5.3 Inverse functions
Section 5.4 Derivative and anti-derivative of e^x
Section 5.5 Bases other than e
We will may add Ch 6 to Ch 5 for a test. 5.6 and 5.7 are usually a take-home assignment
Additional
Section 5.6 Derivatives of inverse functions
Section 2.6 Related Rates (This is done with applications after Ch 3)
Chapter 3 Applications of Differentiation
Section 5.7 Integrals of inverse functions
Chapter 6 Slope Fields/Differential Equations
Section 3.1 Absolute Extrrema
Section 3.2 Mean Value Theorem/ Rolle's Theorem
Section 3.3 First Derivative Test
Section 3.4 Concavity
Section 3.5 (Done in the Limits Section)
Section 3.6 Curve Sketching
More Applications
Section 3.7 Optimization
Section 2.6 Related rates
Tangent Line Approximations
Section 6.1 Slope Fields
Section 6.2 Differential Equations
Section 6.3 Separable Differential Equations
Chapter 7
Section 7.1 Area Between 2 Curves
Section 7.2 Disk Method for Volumes of Revolution
Section 7.3 Shell Method for Volumes of Revolution (This is not part of the AP Curriculum, but may be done)