Math Analysis

 

Course Syllabus and Description

 

Teacher:  Dan Appel               Phone: 644-4586                Email: dappel@berkeley.k12.ca.us

 

General Course Description: 

This course is designed to build upon many of the topics seen in Algebra 1 and Geometry and Algebra 2.  Students will formalize many of the concepts presented in these courses, as well as delving deeper into the topics.  These topics include but are not limited to:  functions, polynomials, exponential and logarithmic functions, trigonometric functions & identities, systems of equations, sequences & sums, limits, and derivatives.  Moreover, students will continue to grow as mathematicians by learning various problem solving strategies, learn to apply mathematical models to real world scenarios, and present their ideas clearly, both written and oral.

 

Goals/Objectives:

The main goals for students in this course are to understand the mathematical concepts presented, continue to build fluency with mathematical notation, and to see math as a tool which is applicable to their lives.  Students are expected to be active members of the classroom.  This includes:

1.      Discussion with group members and classmates.

2.      Doing the homework.

Students will learn how to evaluate their own progress and understanding of the material.  This will help students to become better problem solvers, ask better questions, and become better at formalizing their ideas. 

 

Course Content:

The course is divided into 13 chapters, each with a different theme.  The following provides a general outline of the topics presented during the course.  More detailed calendars will be given as the course progresses.

Chapter 1: Review

*         Reviews many topics/notation seen in previous courses

 

Chapter 2: Functions & Graphs

*         Functions, functional notation, graphs, and inverse functions

 

Chapter 3:  Linear & Quadratic Functions

*         Rates of change and quadratic functions

 

Chapter 4:  Polynomial & Rational Functions

*         Polynomials, roots, rational functions, complex numbers

 

Chapter 5:  Exponential & Logarithmic Functions

*         Exponential functions, Logarithms (common and natural)

 

Chapter 6:  Trigonometric Functions

*         Trigonometric functions, basic graphs and identities

 

Chapter 7:  Triangle Trigonometry

*         Right triangle trigonometry, law of sines/cosines

 

Chapter 8: Trigonometric Identities and Equations

*         Other identities & proofs, inverse functions

 

Chapter 9: Applications of Trigonometry

*         Complex plane, polar form, DeMoivre's Theorem, vectors, dot product

 

Chapter 10:  Analytic Geometry

*         Conic sections, polar coordinates

 

Chapter 11:  Systems of Equations

*         Systems of linear equations, matrices

 

Chapter 12:  Discrete Algebra

*         Sequences, sums, arithmetic/geometric sequences, mathematical induction

Supplement:  Limits, A preview to Calculus

*         Finding limits and derivatives

Grades/Credits:

Students' grades will be determined by a variety of assessments.  This ranges from homework assignments, portfolios and class participation to more formal assessments such as tests and quizzes.  Students will also complete various projects and Problems of the Week (POW's).  Weekly grade reports will be posted in the classroom and weekly individual progress reports can be requested.  Students' work will be divided into the following categories:

 

I.    Homework, Journals, Presentations, Participation and Classwork (20% of final grade)

 

II.   Tests, Quizzes, POW's and Projects (80% of final grade)

 

Materials:

We will be using Contemporary Precalculus: A Graphing Approach, Thomas Hungerford (1997, 2^nd Edition) as the primary text for the course.  There will be additional supplementary material distributed throughout the course. 

Students will be expected to come to class with the following each day: the text book, a three ring binder/notebook with paper, pencils, and a graphing calculator*

**If you do not already have a graphing calculator, I suggest that you purchase one.  I am most familiar with the Texas Instruments (TI-82 and above) graphing calculator, however any brand will be sufficient.  The model bought by most students is the TI-83 Plus (which is about $90) and is available at Office Depot, Target and other office supply stores.  A limited supply of graphing calculators will be available for use during class time, but will not be available for students to use on homework assignments.

 

Binder Expectations:

There should be sections for the following categories.  Binders will be evaluated during the year at various intervals.

1.      Notes (including blank binder paper)

2.      Graph Paper

3.      Homework

4.      Handouts

5.      Tests & Quizzes.