Precalculus

In order to remove confusion of issues, I will be posting the material for trigonometry on a separate web page from the material on precalculus.

Here is the material and lecture slides that accompany my first four discussions.

Week 1


Here is a copy of the syllabus to the course

course syllabus

Here is a link to the current version of the Demana text updated to reflect the various different levels at which the information is to be classified.

Precalculus by Demana & Waits TEXTBOOK

Here is the link to the text by Larson which emphasizes the limit concept.

Larson Precalculus with Limits 3rd c2014 txtbk


Week 2


Here are the powerpoints used in Lecture 3, Tuesday July 28 — Transformations of Graphs dwp08_0601 and Inroduction to Vectors

And here are a couple of practice sheets to review the material from last week.

Precalculus 1 Worksheet on Functions

This week we started on our journey through the realm of vector geometry. We introduced the concept of a vector and discussed the relationship that vectors have with the analysis of physical problems. We also introduced the somewhat arbitrary notion of the “inner” product of two vectors. Here is link to the slides I used with Lecture 4 — dot products

Here are some exercises to help you get proficiency at using dot products and relating them to the geometry of vector relationships in the plane. Dot Products


Week 3


This week we will continue our study of vectors in the plane by looking parametric equations for lines and and other graphical representations of relations.

Here are the slides we will be using this week in our unit on parametric functions and vectors.

Parametric equations and motion Polar coordinates and graphs Polar form of complex numbers Polar representations

Here is the practice sheet we worked through during class.

Projections and operations

 

Here is the midterm which will be due on Tuesday July 12, 2016 at the start of class.

PreCalcMT Test Sheet


Week 4


Here are some practice problems working with parametric equations and polar graphs. You might find it useful to skim through the slides to get a review of the material we covered. They are posted in the Week 3 section of this webpage.

Parametrics and Polar Graphs


Week 5


This week we will wind up our study of complex numbers and tie them into ideas from trigonometry. We will cover De Moivre’s theorem which relates powers of complex numbers to their trigonometric representations. Specifically it says that if z is a complex number represented as a + bi, then z^n = r^n (\cos n\theta + i\sin n\theta) where r = |z| and \theta is the angle z makes with the positive real axis.

Here is a worksheet to practice applying these ideas.

Complex Numbers and Trigonometry


Week 6

This week we conclude our study of representations of complex numbers and begin our coverage of the material on discrete mathematics. Here is the first worksheet on combinatorics and counting principles.

Counting Principles


Final Homework Project

Be sure to review your notes on the binomial theorem since there are a couple problems on this test that deal with that concept.

Final Homework Project Precalculus Worksheet