01 Videos: Intro & Terminology Noteguide 01
Book Sections 1.1-1.2

• Order, Prime & Leibniz Notation, Linearity (PDEs not needed on Noteguide)
• Examples: Verify Solutions & Intervals
  
  

02 Videos: Initial Value Problems (IVP) & Separation of Variables (SEP VAR) Noteguide 02
Book Sections 1.2 and 2.2

• Examples: SEP VAR & IVP
  
  

03 Videos: Modeling Examples Noteguide 03
Book Sections 1.3, 3.1, 3.3

• Newton's Law of Cooling
• Mixing Problems
  
  

04 Videos: Direction Fields AKA Slope Fields Noteguide 04
Book Section 2.1

• How to draw a direction field
• Existence & Uniqueness Theorem
  
  

Recommended Slope Field Generator

05 Videos: First Order Linear DEs (FOL) Noteguide 05
Book Section 2.3

• Example: FOL DE
  
  

06 Videos: Exact DEs Noteguide 06
Book Section 2.4

• What is an Exact DE? And an example
• (Optional Video) Systems of DEs (not included on Noteguide, we will cover this during class time)
  
  

Just For Fun !

07 Videos: Other DEs that transform into SEP or FOL Noteguide 07
Book Sections 2.5

• Bernoulli DEs (set u=y^(1-n), becomes linear)
  
  

08 Videos: Linear Homogeneous 2nd Order DEs Noteguide 08
Book Sections 4.1, 4.3

• Linear (In)dependence, Wronskian, and Examples
• RULES for Linear Homogeneous Constant Coefficient 2nd Order DEs
• A complex example
  
  

09 Videos: Linear NON-Homogeneous 2nd Order DEs Noteguide 09
Book Section 4.4

• Undetermined Coefficients - Part 1
• Undetermined Coefficients - Part 2
  
  

10 Videos: 2nd Method for Linear NON-Homogeneous 2nd Order DEsNoteguide 10
Book Section 4.6

• Variation of Parameters
  
  

11 Videos: Cauchy-Euler DEs Noteguide 11
Book Section 4.7

• RULES for Cauchy-Euler DEs and an example
  
  

12 Videos: Power Series Basics Noteguide 12
Book Section 6.1

• Review of Ratio Test & Interval of Convergence
• Review of Shifting Index for Power Series
• Handout: Series Convergence Chart
  
  

13 Videos: Solving DEs with Power Series Noteguide 13
Book Section 6.2

• Power Series Solutions to DEs
  
  

14 Videos: Intro to Laplace Transforms Noteguide 14
Book Sections 7.1-7.2

• Definition of Laplace Transform of f(t) = 1
• Definition of Laplace Transform of f(t) = t
• (Optional Video) Transforms of Derivatives (not included on Noteguide, we will cover this during class time)
  
  

15 Videos: Solving DEs with Laplace Transform Noteguide 15
Book Sections 7.2-7.3

• Example of Solving DE with Laplace Transform
  
  

16 Videos: Intro to Step Functions Noteguide 16
Book Section 7.3

• Intro Part 1
• Intro Part 2
• (Optional Video) Laplace Transform of Unit Step Functions (not included on Noteguide, we will cover this during class time)
  
  

17 Videos: Review of Eigenvalue & Eigenvectors Noteguide 17
Book Section 8.1

• What are Eigenvalues and Eigenvectors?
• How to find Eigenvalues and Eigenvectors, given a matrix A
  
  

18 Videos: Homogeneous Linear Systems Noteguide 18
Book Section 8.2

• Linear Systems: Distinct Eigenvalues Example
• Linear Systems: Complex Eigenvalues Example
  
  

19 Videos: Homogeneous Linear Systems Continued Noteguide 19
Book Section 8.2

• Linear Systems: Repeated Eigenvalues Example
  
  

20 Optional Video: Phase Portraits for Systems
Book Section 10.2

• Phase Portraits & Stability Examples