College Algebra is an introductory text for a college algebra survey course. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The authors describe their approach as "Functions First," believing introducing functions first will help students understand new concepts more completely. Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions are open-ended).
Derivation of Euler's formula from a Taylor series expansion of the expontential function for a complex argument.Derivation of the multiple angle trig identities for sine and cosine using the Binaomial theorem and Euler's formula.
Derive Euler's formula from the Taylor series of the exponential function with a complex argument.
Derive the multi-angle trigonometric identities using Euler's formula.
Derive the Binomial theorem by induction.
This Intermediate Algebra textbook was developed with consideration of neuroscience principles about learning. It is organized around the concepts of 'solving' and 'graphing'. The problem sets incorporate distributed and mixed practice to promote long term memory formation for the concepts and procedures involved in each section.