Math 115 Summer 2012
Tentative Schedule [Subject to change and correction-6-12-2012]
Week\Day
Monday
Tuesday
Wednesday
Thursday
I. Introduction: Backgrounds and Key concepts

5-21 Introduction : How to succeed in this course.
5-22 Finish course info?
What are Numbers?
Sensible Precalc Ch 1.A
R.1
Comparing Numbers:=,<
Operations.
5-23 R.1, R.2, R.5, 1.5
Number Operations, equation, inequality properties.
Types of Numbers
Rational numbers and decimals. See Moodle for worksheet.
Sqr(2) is not a rational #.
Visualizing: numbers- intervals.
5-24

Solving Linear Equations
Solving linear inequalities
Simplifying and Rationalizing
II. More Backgrounds:
Beginning Functions-Linear functions and key concepts.
Begin Right Triangle Trig
5-28
No Class Mem'l Day
5-29 Practice Quiz #1
Applications of linear inequalities
Abs. value inequalities
R.7 , (1.5), 1.6.
The Pythagorean theorem. [Over 30 proofs !]
[Many Java Applets proofs ]
Similar triangles.
Algebra review.
Review Polynomials.  (Factoring)
5-30 Quiz #1
Introduction to Winplot. Points, Animation.
Tables.
Visualizing variables and plane coordinate geometry.
Plane Coordinates.

5-31 R.4, 1.1, 1.2-

What's a function?
Linear Functions and Visualization of data
.Sensible Precalc Ch 1.B.1 (Firefox Preferred)
III. Triangle Trig 6-4 More Geometry review: Midpoints.
Circles
Graphs and mapping figures.
Other function qualities.

6-5 Review of Key Triangles.
Overview of Core: trigonometric for Right Triangles

Overview of Core: More on functions.
Linear functions.
6-6 Practice Quiz #2
Introduction to Excel.

Primary Linear "Functions" and Visualization of data.
Lines.
Slopes and equations of lines.
6-7 Quiz #2
Solving Right triangles.

6-11
Secant lines and Linear Interpolation

More Inverse trig.
Triangle trig: Inverse trig acute
6-12  Primary Linear and quadratic "Functions"
Descriptive features of functions. (Increasing/decreasing/max/min)

6-13 Practice Quiz #3

Areas of Parallelograms and triangles.
sine for obtuse angles.
Start  Law of Sines.

6-14 Quiz #3
Exponential Functions. Solving simple exponential equations
More on Exponential Applications- compound interest and growth.

Trig for obtuse angles
A visual proof for "The Law of sines" and More.

Trig functions for all angles (sine and cosine)(tan)
V. More Triangle Trig & Begin Exponential functions and Logarithmic functions

6-18
Applications of triangle trig
More law of sines
Law of cosines
Piecewise functions
6-19 More on law of cosines.
Properties of roots and exponents.

Basic properties of logs...  and applications and exponents-solving equations.
6-20 Practice Quiz #4
A visual proof for "The Law of Cosines"
Dynamic proof :The Law of Sines
Graphs of exponential,
Compound interest?
Applications of Exponential functions
More exponential functions and graphs.
What is e?
Composed Mapping figures.

6-21 Quiz #4
Logarithms: Introduction and definition.
logarithmic general. Graphs of logs, exps, sin and cos

Properties of logs and exponents-
The big picture on functions: Core functions and elementary functions
Symmetry [wrt axes.]

# Below this line is currently under development

VI.Trig function graphs [LAB? ] 6-25
More on graphs of trig functions.
Graphs of tan and sec.
Inverse tangent function.
Models using Exponential Functions
Logarithmic calculations in equations and computations.

More on graphs of trig functions.

graph SinAX
graph A sin(BX+C)
Graphs of tan and sec.
More on graphs and basic properties of trig functions.
More applications of logs
Logarithmic scales.Slide rules ?
7-2
Begin Trig Identities
Begin trig equations and review of
inverse trig functions
Log scales and graphs.
More exponential models Slide rules
On-line java sliderule
VII.Trig Equations
Trig Identities
***LAB ***?]
7-2
Trig Identities

Translation, symmetry and scales for quadratics . NO Class July 4 Holiday  Trig equations and review of
inverse trig functions (Asin and Acos)
More on graphs of trig functions, identities and equations.
VIII.Lab: Graphing Functions with Winplot.?
Lab: Graphing and Trig Applets.?
tfigs.wp2
7-9
Graphs for inverse trig.

More on Trig Identities: double angles! Double and half angles
Product to sum trig.Other Trig identities.
Begin Rational functions
Long division and factors of polys.
Complex numbers and trig
IX.Polynomial and Rational Functions 7-16
Roots and more on Polynomials.
More Trig functions and equations:
graphs and elementary functions
Complex arithmetic and trig!
Graphs of polynomials and rational functions. More on Complex Numbers, trig and roots.

Quiz # 8 will cover material from the following sections covered in assignments for TBA

Brief  look at The Logistic
Difference quotients.?
MORE Polynomials- rational, real and complex roots!   Intermediate value theorem.
Inequalities.
Bisection and Secant methods for estimating roots.
Rational functions.Asymptotes.
Putting functions together?
X. Pre-Calculus! 7-23
More on rational functions.
Combining trig Functions- lines review.
Composition & Inverse functions

Final comments on functions- algebraic and trignometric.
"Tangents to graphs for logs and exponential functions. "?? A precalculus view.
7-25
Final Exam Part I

(40 minutes on Log and exponential functions.)

7-26
Final Exam Part II (80 minutes with very little from Part I)

TentativeAssignments are on MyMathLab
Recommended Problems will be posted there as well.

[Work in Progress: Subject to change and correction]
Last updated: 5-23-12
SECTION
or in SC on line.
Special Instructions & Interesting but Optional
Sensible Precalc Ch 1.A
Sensible Precalc Ch 1.B.1 (Firefox Preferred)
Extra help from Purple Math on Converting between Decimals, Fractions,
and Percents
Sensible Precalc Ch 1.B.2 Read!(Firefox preferred)
Similar triangles.
More on Similar triangles.

Dynamic Geometry® Exploration SimilarTriangles

Ch 1.B.1:  1c, 2, 16

Law of Sines.

A visual proof for "The Law of Cosines"
Demonstrations of the laws of sines and cosines

History of Pi

sin(A+B) proof illustrated.

Summary of trig identities

History of Trigonometric functions

graph SinAX         graph A sin(BX+C)

Trisection of angles, trig and algebra!
Complex Numbers,

History of the number e

How and Why a Slide Rule Works
On-line java sliderule

History of the Function concept