Bach, Dan



Diablo Valley College

Department of Mathematics

Pleasant Hill, CA 94523



dbach@viking.dvc.edu



Mathematica Notebooks for Precalculus





0.      Navigating Mathematica Notebooks.   How to get around, open 

groups of cells, type, copy, bring down commands, how to do basic and 

not-so-basic arithmetic.



1.      The coordinate plane, linear dependence, slopes and equations 

of lines, scatter plots, regression lines.  The xy-plane and the idea 

of equations vs. pictures and graphs.  The computer generates random 

lines and scatter plots; the student must determine the equation of 

the line or regression line. 



2.      Functions and graphs.  The crucial concept of a function as a 

rule to generate outputs from given inputs.  Domain, range, defining 

functions in Mathematica, composition, inverse functions, vertical and 

horizontal line tests for graphs.  Students are given inputs and 

outputs and guess the rule. 



3.      Exponential and Log functions.  Nonlinear growth, proportional 

change, applications including compound interest, Richter scale, 

population explosion, spread of disease, radioactive decay, and other 

cheerful topics. 



4.      Factoring polynomials, special products, roots.  Less emphasis 

is placed on factorization techniques, more on the correspondence 

between roots and linear factors of  f(x).  Graphs of parabolas are 

introduced by comparing  y = x - a,  y = x - b,  and  y = (x - a)(x - 

b).  *Dan's Amazing Parabocalc* is included at no additional cost! 



5.      Trigonometry.  Sine waves, frequency and amplitude and 

relation to sounds.  Using MathematicaUs Play feature, students can 

hear the difference between  Sin[200 t], Sin[400 t], and 3 Sin[200 t].   

Trig functions using the unit circle and triangles, Other 

applications: periodic events, daily and yearly temperature cycles. 



6.      Complex numbers, roots of polynomials, the Fundamental Theorem 

of Algebra.  Basic arithmetic in the complex numbers, factorization of 

Gaussian integers, factoring rational primes and sums of squares, as 

in x^2 + y^2 = (x + iy)(x - iy).  Polar and exponential forms of 

complex numbers, roots of unity, basic cyclotomic polynomials. 



7.      Graphs of secant lines and tangent lines.  The graph of 

yJ=Jf(x) and the secant line joining two nearby points approaching the 

tangent line.  Derivatives are not discussed per se, instead the 

concepts of average and instantaneous rates of change (such as 

velocity) are treated.



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