Math 115 Fall, 2010
 Tentative  Lecture Content Schedule [Subject to change and correction-9-20-10] 
Tuesday Wednesday

I. Introduction: Backgrounds and Key concepts 8-24
 Introduction : How to succeed in this course.
Sensible Precalc Ch 1.A

8-25 Pre-Test
What are Numbers? 
Comparing Numbers:=,< 

II. More Backgrounds:
Beginning Functions-Linear functions and key concepts. 
Number Operations, equation, inequality properties. Types of Numbers
Visualizing: numbers- intervals.
Rational numbers and decimals. See Moodle for worksheet.
9-2 The Pythagorean theorem. [Over 30 proofs !]
[Many Java Applets proofs ]
Sqr(2) is not a rational #. 
Solving linear inequalities
Applications of linear inequalities
Simplifying and Rationalizing
Visualizing variables and plane coordinate geometry.
Plane Coordinates.
Similar triangles.
Introduction to Winplot. Points, Animation..

III.Functions and lines
More Algebra review.
Review Polynomials.  (Factoring)
Introduction to Excel.
Linear and quadratic "Functions" and Visualization of data.
What's a function?
More on functions.

9-8  Linear functions.
Linear Functions and Visualization of data.

9-9 Lines.
Slopes and equations of lines.
Y and X intercepts.
Midpoints with coordinates.

IV. Start Trigonometry

9-14 Circles
Equations for circles.
Inequalities and absolute values.
MORE on functions!
Graphs and mapping figures.

9-15 Quiz #1
Quadratic Functions and Visualization of data.
9-16 Quadratic Functions
Other function qualities.
Winplot:Demonstation: Lines as equations and "functions".
Exploring functions with Winplot:
Primary Descriptive features of functions. (Increasing/decreasing/max/min)
Overview of Core functions...elementary functions.
Review of Key Triangles.

V. Triangle Trig
9-21 Modeling with quadratic functions.
Secant line slopes.
[Using winplot to graph and find key function feature and solve equations graphically for zeros.?]
Start trig. Trigonometric functions for Right Triangles
Solving Right triangles.
Triangle trig: Inverse sine, cosine, tangent for acute triangles.
Inverse trig
9-22 Law of sines 
sine for obtuse angles.
Law of Sines.
9-23 More on Solving triangles/ applications.
More Inverse trig (sine obtuse).
Graph piecewise functions.
Visualize triangle trig and unit circle.

VI.Finish Triangle Trig- Trig function graphs 9-28
More on Law of Sines.
Radian measure and circles in general.
9-29 Quiz #2
9- 30
Start Law of cosines.

Trig functions for all angles - with radian measure.(sine and cosine)(tan)

VII Trig Equations 
Trig Identities
More on law of cosines.
A visual proof for "The Law of Cosines" 
Dynamic proof :The Law of Cosines
Applications of triangle trig
Begin Trig Identities 
10-6 Quiz #3
10-7 Begin Graphs of trig functions. Sine and cosine.
Begin trig equations and review of  inverse trig functions(Asin and Acos)
Simple use of identities: relating trig function values on unit circle.
Solving Simple Trig Equations

VIII. More trig identities.:) 10-12 More on graphs of trig functions, identities and equations.
Graphs for tangent and secant.  Graphically solving trig equations.
Identity games..
10-13 Quiz #4
Addition formulae
double angles!

IX More trig identities, equations, and graphs!
More Trig functions and equations:
Addition formulae.
Double and half angles
10-20 10-21
Other Trig identities: Product to sum trig.
Applications of Sum to slopes and trig function graphs for sine and cosine..
Identities and Equations
Phase Shift - trig and linear compositions.

X  End of trig!
graphs and elementary functions
More on graphs and basic properties of trig functions.

Phase shifts.
Periodic functions
.Phase Shift - trig and linear compositions. Continued!
graph SinAX
graph A sin(BX+C)


XI Begin Exponential and logs

Misc. Trig.
Inverse trig functions.
More on inverse trig functions(Asin and Acos):
Graphs for inverse trig. (esp'lly Inverse tangent function)
More on inverse and trig functions.
graphs of combining trig functions.
Exponential Functions.
Compound interest? What is e?
Applications of Exponential functions
Solving simple exponential equations.exponential functions and graphs.
Graphs of exponential functions.
More on Exponential Applications- compound interest and growth.Exponential graphs

XII.Finish exponents and Logarithmic functions.
What are elementary functions?
Logarithms: Introduction and definition.
Basic properties of logs...  and applications and exponents-solving equations
Models using Exponential Functions
Continuously compounded interest: Pert.
11-10 11-11 No Class

XIII. Begin Polynomial and Rational Functions 11-16More exponential models (Growth/Decay)
Logs and Graphs of logs, exps with graphs of trig functions
Logarithmic calculations in equations and computations. "Transforming equations."
More applications of logs/exponential functions.

11-17 11-18
Logarithmic scales
log scales (simple)
Log scales

11-23 Fall Break

11-24 Fall Break 11-25 Fall Break
XIV More on rational functions.
11-28  Long division and factors of polys.
The remainder Theorem.
The Factor theorem
Roots and more on Polynomials.Functions The big picture on functions: Core functions and elementary functions
Symmetry [wrt origin....(axes).]
Quadratics and 1/x.

Rational functions.Asymptotes.
Translation, symmetry and scales for quadratics 
Difference quotients-Slopes of secant lines-
for Polynomials.
  Polynomial analysis
roots and  positive and negative values.
Roots of polynomials in general - inequalities.

XV Pre-Calculus! 12-4 Inequalities. Linear. Quadratic. Polynomial.
Absolute value functions and inequalities
Intermediate value theorem.
Complex numbers,
The fundamental theorem of algebra
Composition & Inverse functions
Quiz #8!

Final comments on elementary functions- algebraic, logrithmic exponential, and trignometric.
Some of my "favorite functions."
A pre-calculus view of some calculus problems.
Extremes, tangents,areas.

Final Exam
Review Session Sunday  and Room BSS  TBA

Tuesday, December 14 @ 10:20 am.

Inventory of topics and materials

Worksheet on log scales
Music and log scales
Earthquake Magnitude and logs.
Slide rules
On-line java sliderule
More Slide rules
More applications of logs
Trisection of angles, trig and algebra!

Complex numbers?
Complex arithmetic and trig
Properties of roots and exponents.
More on Complex Numbers, trig and roots??

TentativeAssignments on Webassisgn and Recommended Problems
[Work in Progress: Subject to change and correction] 
*Early or Just in time: When two due dates are given,
the first date is for preparation and/or starting problems,
the second date is for completion of problem work.

Last updated: 9-20-10
Reading Textbook
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

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