# MAT 151-04 Calendar. Fall 2017. Jennings.

Chapters and sections refer to our textbook, Intermediate Algebra, a Modeling Approach by Katherine Yoshiwara.

• 1st Week, Aug. 21-25. Chapter 1: Linear Models (models based on equations of lines e.g. $$y=mx+b$$, $$ax+by=c$$ ), Chapter 2 Applications of Linear Models
• 1.1 Linear Models
• 1.2 Intercepts
• 1.3 Graphs and Equations (of lines)
• 1.4 Slope
• 1.5 Equations of Lines
• 2.1 Linear Regression (estimating "best fit" line for given data by eye).
• Supplementary material: Using a spreadsheet and its "trendline" feature to graph the line then use the "linest" spreadsheet function to obtain its equation. I used the free web-based "Google Sheets" spreadsheet (just google it to find out how to use it). There's even a free phone app for Google Sheets. Microsoft Excel or any other spreadsheet program works pretty much the same way.
• 2nd Week, Aug. 28 - Sept. 1: Chapter 2 (cont.)
• 2.2 Linear Systems (two linear equations, two variables).
• Desmos https://www.desmos.com is a free, easy-to-use web-based calculator that solves these problems graphically. There's also a free phone app for it. Warning: I don't let people use Desmos on exams!!
• 2.3 Algebraic Solutions of Systems (solution must satisfy two linear equations).
• Wolfram Alpha http://www.wolframalpha.com is a free web-based program that solves these problems (and many others). There's also a very inexpensive phone app for it. Warning: I don't let people use Wolfram Alpha on exams!!
• 2.4 Gaussian Reduction (using elimination to solve large systems of linear equations equations). (Wolfram Alpha will solve these too, very handy!)
• 3rd Week, Sept. 4-8. Chapter 3 Quadratic Models: (models based on quadratic equations like $$y=ax^2+bx+c$$)
• Labor Day holiday, Monday Sept. 4
• 3.1 Extraction of Roots (solving "perfect square equations" like $$2(5x+3)^2=38$$, volume formulas, compound interest)
• 3.2 Intercepts, Solutions and Factors (of quadratic equations, problems involving gravity, area, etc.)
• 4th Week, Sept. 11-15. Chapter 3 (cont.)
• 3.2 (cont.)
• 3.3 Graphing Parabolas (vertex, finding maxima and minima)
• Start 3.4, 4.1 Quadratic formula, completing the square
• 5th Week, Sept. 18-22. Chapter 3 (cont.), Chapter 4 Applications of Quadratic Models
• 3.4 Completing the Square (prelude to the quadratic formula)
• 4.1 Quadratic Formula ($$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$ solves $$ax^2+bx+c=0$$)
• 4.2 The Vertex (highest or lowest point on a parabola)
• Supplementary discussion: how linear regression works (not in the text).
• 6th Week, Sept. 25-29. Chapter 4 (cont.)
• 4.4 Quadratic inequalities (solving $$ax^2+bx+c \geq 0$$, $$ax^2+bx+c \lt 0$$ etc.)
• Review: Chapters 1-4.
• First Midterm Exam Friday Sept. 29 (Date changed!!)
• (Skip this: 4.3 Curve Fitting -- fitting parabola to given data, quadratic regression.)
• 7th Week, Oct. 2-6. Chapter 4 (cont.), Chapter 5 Functions and Their Graphs
• 5.1 Functions
• 5.2 Graphs of Functions ("vertical line test")
• 8th Week, Oct. 9-13. Chapter 5 (cont.)
• 5.3 Some Basic Graphs ($$y = \lvert x \rvert$$, $$y=\sqrt{x}$$, $$y=\sqrt[3]{x}$$, $$y=1/x$$, $$y=1/x^2$$, etc.)
• 5.4 Variation (direct variation, inverse variation, scaling, etc.)
• 5.5 Functions as Models
• 9th Week, Oct. 16-20. Chapter 6 Powers and Roots
• 6.1 Integer Exponents ($$x^{-n}=1/x^n$$, $$x^0=1$$ -- when this makes sense)
• 6.2 Roots and Radicals ($$x=\sqrt[n]{y}$$ solves $$y=x^n$$ -- when this makes sense)
• 6.3 Rational Exponents ($$x^{1/n}=\sqrt[n]{x}$$ -- when this makes sense)
• 6.4 The Distance and Midpoint Formula (distance between two points in the plane, midpoint of a line segment)
• 10th Week, Oct. 23-27. Chapter 6 (cont.), Chapter 7 Exponential Functions (for example $$y=Ae^x$$ very important in science!)
• 6.6 Radical Equations (solving them)
• 7.1 Exponential Growth and Decay
• 11th Week, Oct. 30 - Nov. 3. Chapter 7 (cont.)
• Notes from Monday's lecture: Exponentials and Logs.
• 7.2 Exponential Functions
• 7.3 Logarithms
• 7.4 Properties of Logarithms (key fact: $$\log(A^x)=x\log(A)$$ no matter what the base of the logarithm is.)
• 12th Week, Nov. 6-10. Chapter 7 (cont.)
• 7.5 Applications of Exponential Functions and Logarithms (compound interest, growth, power laws, half-life, ... -- there are many more)
• Second Midterm Exam Wednesday Nov. 8 (Date changed!!) Solutions
• Veterans' Day Holiday Friday Nov. 10
• 13th Week, Nov. 13-17. Chapter 7 (cont.), Chapter 8 Polynomials and Rational Functions (fractions! rational functions are quotients of polynomials)
• 7.5 (cont.)
• 7.6 Logarithmic Scales (Richter scale, decibels, etc. log-log and semilog scales, log-linear regression)
• 8.1 Polynomial Functions
• Graphs of Polynomial Functions over Very Large and Very Small Intervals (not in the text)
• 14th Week, Nov. 20-24.
• 8.2 Algebraic Fractions (rational functions)
• Graphs of Rational Functions over Very Large and Very Small Intervals (not in the text)
• 8.3 Operations with Algebraic Fractions (addition, subtraction, multiplication, division, and so on)
• Thanksgiving Holiday Thursday, Friday Nov. 23-24
• 15th Week, Nov. 27 - Dec. 1. Graphs, Supplementary material, Review
• 8.4 More Operations with Algebraic Fractions (quotients of sums, quotients of differences, etc. of rational functions)
• 8.5 Equations with Fractions (equations with rational functions. In principle this is easy: clear fractions, solve a polynomial equation, check the results. But the calculations can be messy.)
• 9.1 Properties of Lines (parallel and perpendicular lines; back to the beginning!)
• 16th Week, Monday Dec. 4 only.
• Review
• Final Exam Wednesday Dec. 13 11:30am-1:30pm