Daily Online Requirements

Review the following, especially those of you who have been away from Calculus 1 for a few months...OR years. If you need to review any of these topics, make sure to DOWNLOAD each of these files and click on "Begin Slideshow" in order to view it with important transitions.

• Basic Differentiation Rules
• Product and Quotient Rules
• Derivatives of Trigonometric Functions
• Chain Rule
• Implicit Differentiation
• Derivatives of Exponential and Logarithmic Functions

• Antiderivatives
• Fundamental Theorem of Calculus
• Integration using u-substitution
• Substitution with Definite Integrals

You should be able to differentiate all of these functions prior to starting Calculus 2

• The problems are on page 1 and the unsimplified answers are on page 2

You should be able to integrate all of these functions using u-substitution prior to starting Calculus 2

• The problems are on page 1 and the answers are on page 2

Please visit this discussion board every few days to discuss particular questions on each of these worksheets

• You can post pictures of the work you've done or comments on particular places where you are struggling
• Please indicate which number you are referring to and post your comment/picture under the appropriate section (Derivatives or Integrals)

• Derivatives of Inverse Trigonometric Functions (3.7 from Calculus Volume 1)
  • 0:00-52:00 Review of Inverse Trig Functions (From Trigonometry)
  • 53:00-56:00 Formulas For Derivatives
  • 56:00-1:07:00 Proofs of Derivative Formulas
  • 1:07:00-1:32:00 Examples of Derivatives
• Integrals Resulting in Inverse Trigonometric Functions (1.7)
  • 1:32:00-1:35:00 Formulas for Integrals
  • 1:35:00-1:52:00 Examples of Integrals

• Integration by Parts
  • 0:00-12:00 Derivation of the Formula
  • 12:00-41:00 Examples of Integrals
  • 41:00-1:55:00 More Interesting (Difficult) Examples
• Integration by Parts Lecture Notes

• Review for Reducing Powers of Trigonometric Functions (From Trigonometry)
• Trigonometric Integrals
  • 0:00-1:11:00 Examples involving Sine and Cosine (even and odd powers)
  • 1:11:00-1:23:00 Example of Definite Integral involving Sine and Cosine
  • 1:24:00-2:08:00 Examples involving Tangent and Secant OR Cotangent and Cosecant

• Trigonometric Substitution
  • 0:00-18:00 Intuition of Using Trig Functions to Make Integrals Easier
  • 18:00-36:00 Derivation of General Formulas
  • 36:00-1:32:00 Examples of Applying Trig Substitutions
  • 1:33:00-1:53:00 Completing the Square to Force a Trig Substitution

• Partial Fraction Decomposition
  • 0:00-38:00 Integrating a Rational Functions when Denominator has Distinct Linear Factors
  • 38:00-44:00 Shortcut for Example Above
  • 44:00-1:05:00 Integrating a Rational Function when Degree of Numerator is Larger than Degree of Denominator
  • 1:05:00-1:31:00 Integrating a Rational Functions when Denominator has Repeated Linear Factors
  • 1:31:00-2:01:00 Integrating a Rational Functions when Denominator has an Irreducible Quadratic
  • 2:01:00-2:12:00 Explanation of Last Part of Prior Example
  • 2:12:00-2:55:00 Integrating a Rational Functions when Denominator has REPEATED Irreducible Quadratics (Challenging Example
  • Partial Fraction Decomposition Lecture Notes

• Derivation of Trapezoidal Rule (Lecture Notes)
  • Example of Trapezoidal Rule
• Derivation of Simpson's Rule
  • Example of Simpson's Rule

• L'Hopital's Rule
  • 0:00-12:00 Method of evaluating limits that result in indeterminate form
  • 12:00-41:00 Examples for applying L'Hopital's rule on limits resulting in 0/0 or inf/inf
  • 41:00-57:00 Examples with limits resulting in infinity - infinity
  • 58:00-1:40:00 Examples with limits resulting in 0^inf , 1^inf , or inf^0

• Improper Integrals Lecture Notes
• Improper Integrals
  • 0:00-23:00 Finding definite integrals (area) with upper or lower limits of infinity
  • 23:00-43:00 Finding integrals over an infinite interval of functions of the form 1/(x^n)
  • 44:00-1:16:00 Examples where the upper OR lower limit is negative infinity or infinity.
  • 1:16:00-1:33:00 Example where the upper AND lower limits are negative infinity and infinity.
  • 1:33:00-1:55:00 Intuition for finding integrals on an interval that includes a vertical asymptote
  • 1:56:00-2:27:00 Examples of definite integrals with an infinite discontinuity on the interval
  • 2:27:00-2:43:00 DON'T WATCH

• Volume: Disk and Washer Methods Lecture Notes
• Finding Volumes using cross sections
  • Introductory Animation of Cross Sectional Method
  • Cross sections are squares
  • Cross sections are semicircles
  • Cross sections are isosceles right triangles
• Finding Volumes using the Disk Method
  • Introductory Animation of the Disk Method
  • Example : around x-axis
  • Intuition of Disk method formula
  • Example : around y-axis
  • Example : around a horizontal line (not x-axis)
  • Example : around a vertical line (not y-axis)
• Finding Volumes using the Washer Method
  • Introductory Animation of the Washer Method
  • Example : Volume of revolution
  • Intuition of Washer method formula
  • Example : around a horizontal line (not-x-axis)
  • Example : around a vertical line (not y-axis)

Disk and Washer Activity

• Finding Volume Using the Shell Method
  • 0:00-24:00 Theory and Derivation of Formula
  • 24:00-35:00 Examples for revolving a region around the y-axis
  • 35:00-44:00 Example for revolving a region around the x-axis
  • 44:00-54:00 Why use the Shell Method instead of the Washer method

• Arc Length of a Curve - Derivation and Example
• Area for a surface of revolution - Derivation and Example

• What is a Differential Equation?
• Verifying that a function is a solution to a Differential Equation
• Intro to Separable Differential Equations
• Example of Solving a Separable Differential Equation
• Bonus : How Differential Equations can describe a model for the spread of COVID-19

• Introduction to Sequences
• Limits of Sequences
• Introduction to Series
• Geometric Series
• Telescoping Series
• The Harmonic Series (1/n) Diverges!
• The Harmonic Series and other p-series
• Preview of Various Tests for Convergence

• Test for Divergence
• The Integral Test
• The Direct Comparison Test
• The Limit Comparison Test
• Test for Divergence vs. Limit Comparison Test

• Ratio and Root Tests
• Ratio Test Examples
• Root Test Examples
• Which test should I use in various cases?

• Power Series and Intervals of Convergence
• Finding Interval of Convergence Example
• Representing Functions as Power Series
• 
  

• Study for Exam 3

• Constructing a Power Series
• Integrating Power Series
• Differentiating Power Series

• Taylor Polynomials and creating Taylor Series

• Introduction to Parametric Equations
  • Review of Parametric Equations
• Calculus of Parametric Equations
  • Arc Length of Parametric Curves
  • Tangents to Parametric Curves
  • Second Derivatives of Parametric Equations
  • Area Under Parametric Curves

• Introductory Material on Polar Curves
  • Review of Polar Coordinates
  • Graphing Polar Curves
• Calculus of Polar Curves
  • Derivatives of Polar Functions
  • Areas bounded by Polar Curves