This playlist starts with sequences and series, Chapter 12, since SAGE is based on Python and Python has a great list data structure for displaying sequences and summing series. We explore Arithmetic, Geometric and Recursive series very nicely with SAGE. We even do a little probability when we get to the Binomial Expansion Series.
Then we spend about 8 weeks on everything you ever wanted to know about trig! Chapter 6 is about Right Triangle Trig, SOHCAHTOA and the Unit Circle. Chapter 7 is about proving Trig Identities and solving Trig Equations. Chapter 8 is about solving non Right Triangles using the Law Of Sines and the Law Of Cosines. Chapter 9 is about Vector and Polar Notation, Operations On Vectors and CIS(theta) notation.
Chapter 10 is about conic sections. Rotated Conics, aka Twisted Conics, are easier to graph when converted to Polar Notation, so a little Trig background helps here too!
Chapter 11 is about Matrices and solving Systems Of Equations.
Then we work on Exponential and Logarithmic functions in Chapter 5 and Polynomial functions in Chapter 4.
Through out the course we emphasize the concepts of Domain, Range, Graphs and Transformations whenever we talk about a new class of function!
We finish the year with an 8 week intro to Calculus: Chapter 3 on Rational Functions with Limits, UNIT02 on the Difference Quotient, UNIT03 on Derivatives and UNIT05 on AntiDerivatives. HTH, AJG