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The Course 

In Advanced Functions and Modeling, I expect you to learn new mathematical techniques and to develop new ways to think about mathematics.  The themes of the course center on helping you develop power as a mathematician -- a person who approaches questions with self-confidence and with creative avenues of problem solving.  To achieve this power, you must make a serious commitment to this class.  You must be actively involved in class discussions as you share your ideas and learn from the ideas of others.  You must take good notes, review those notes each night, and make additions or clarifications while that day's ideas are still fresh in your mind.  Your questions may not always be answered in class.  You are expected to continue to work on those questions outside of class and to explore ideas with your classmates. You must do the reading and homework problems thoughtfully.  Working with your classmates to generate ideas, both in and out of class, is critical.  If you are confused, I expect you to take the initiative to find help.

Course Goals

It is my goal that by the end of the course, all students will be able to

  • recognize and utilize closed form functions and recursively defined functions
  • write mathematical functions to model situations described verbally and/or graphically.
  • determine a linear, power or exponential function to model a set of bivariate data and to evaluate the appropriateness of the fit by analyzing residual plots. 
  • describe the behavior of a function graphically and numerically given its equation.  These functions include transformations, compositions, products, and sums of toolkit functions.
  • interpret the coefficients in the equation and/or the behavior in the graph of a function within the context of a given problem.
  • perform algebraic manipulations to solve equations and inequalities.  The functions involved include exponential, trigonometric, logarithmic, and algebraic functions.
  • communicate their understanding of concepts both verbally and in writing.

Grading Policy
Trimester grades will be computed as follows:
Tests, Quizzes, and Projects:  60%
Graded Homework and Classwork: 30%
Participation and Effort: 10%

Course Final Grade will be computed as follows:
Trimesters 1, 2, and 3: 25% each
Midterm: 10%
Final Project: 15% 

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