Number series

• Sequence and series
• Taylor series
• Binomial theory. Expanded details (from Lamar University). Pascal's triangle method. Animation of Pascal's triangle.
• Optional material - binomial theory expansion for non-integer powers. First derived by Isaac Newton!

Example calculations

• Taylor series of ln(x)
• Use of binomial expansion in acoustic wave derivation
• Online tool - Taylor series calculator (courtesy Wolfram Alpha)
• Online tool - Binomial theorem calculator (courtesy Kusachi)
• Online tool - Power Series calculator (courtesy Symbolab)

Spreadsheet examples

• Review - what is an array and its usage in computer languages
• Arrays in Excel
• a) Entering array formulas in Excel.  b) Spreadsheet example. c) Many examples from Duke University
• Taylor series application for exp(1) in a spreadsheet
  

Computer language examples

• Taylor series, MATLAB
  
• Taylor series, FORTRAN
  
• Taylor series, python
  
• Power series expansion, Mathematica
  
• Binomial expansion, Pascal's triangle, MATLAB
  
• Symbolic expansion of polynomials and elementary functions, MATLAB
  
• Pascal's triangle, many languages (Rosetta Stone website)
  

Recorded lecture

• Video
• Audio only