SYLLABUS
- SPRING 2003
Texts: Elementary
Mathematical Models, Order Aplenty and a Glimpse of Chaos, Dan Kalman, The
Mathematical Association of America (Incorporated), 1997.
ISBN 0-88385-707-3
Calculus, Elliot C. Goodman,
Barron’s, 1997
ISBN 0-8120-9819-6
The Plan for Solving Linear Equations – Handout
Chapter 2, EMM Sequences and Difference
Equations
Numerical,
Graphical, and Theoretical Approaches
Sample
Difference Equations
Chapter 1, Calculus, Equations,
Functions, and Graphs
1.1 Equations
The
Plan for solving linear equations (Handout)
1.2 Functions
Chapter 3, EMM Arithmetic Growth
Numerical,
Graphical, and Theoretical Properties
Arithmetic
Growth Difference Equations
Proportional Reasoning
Continuous
Models
Applications
including Simple Interest
Chapter 1, Calculus, Equations,
Functions, and Graphs
1.3 Graphs
The
Vertical Line Test
The
Domain of a Function
1.4 Summary of Main Points
Chapter 4, EMM Linear Graphs, Functions,
and Equations
Continuous
Models
Algebra
and Solving Linear Equations
Fitting
a Line to Data (Average
Rate of Change)
Formulating
Linear Models
Proportional
Reasoning
Chapter 5, EMM Quadratic Growth Models
Quadratic
Growth Difference Equations
Properties
of Quadratic Growth Models
(Whole
Number Sums and S
Notation)
Chapter 6, EMM Quadratic Graphs,
Functions, and Equations
Quadratic
Functions and Equations
Algebraic
Considerations
Solving
Equations
Chapter 2, Calculus, Change, and the Idea
of the Derivative
2.1 Average Rate of Change
2.2 Instantaneous Rate of Change
Numerical
Approach
Algebraic
Approach
2.3 The Derivative
2.4 The Geometric Meaning of Derivatives
Chapter 3, Calculus, The Idea of Limits
3.1 The Basic Definition
3.2 Some Complications with the Definition of
Limits
3.3 The Problem of Division By Zero
Chapter 4, Calculus, Computing Some
Derivatives by definition
4.1 Powers of x
Chapter 7, EMM Polynomial and Rational
Functions
Graphing
Polynomials
Solving
Polynomial Equations
Applications
Chapter 5, Calculus Formulas for
Derivatives
5.1 Derivatives of Some Particular Functions
5.2 Derivatives of Combinations of Functions
5.3 The Chain Rule
5.4 Summary of Main Points
Chapter 9, EMM Geometric Growth
The
Geometric Growth Assumption
The
Geometric Growth Difference Equation
Functional
Equation
Exponential
Functions
Applications
including Compound Interest
Chapter 10, EMM Exponential Functions
Graphs
Algebraic
Properties
Solving
Equations
The
number e