I. Sequences, Differences, Difference Equations, and Sums

Week

Topic

Estimated

DDS

P&P

Module

# of Periods

Sections

Sections

1

Intro: Modeling Change with DDS

1

1.1 - 1.4

1.1 &1.4

Numerical Solution of a DDS on EXCEL

Numerical Solutions of a DDS

1

1.1 - 1.4

1.1 & 1.4

dds.doc (Word file)

Charge Cards and Drug Dosages

1

1.1 - 1.4

Worksheet

Long-term Behavior of Solutions: Equilibrium and Stability

1

1.1 - 1.4

Worksheet

2

Analytical Solutions and the Method of Conjecture

2

2.1

1.5

Retirement Planning or Deer and Cougars

First-Order, Linear, Homogeneous Difference Equations

2

2.2

1.5

or Newton's Law of Cooling (TI-CBL)

retirement.doc (Word file)
deer_cougars.doc (Word file)

3

Nonhomogeneous Diff Eq's: Constant Functions

1

2.3

1.6

Retirement Planning or Deer and Cougars

Nonhomogeneous Diff Eq's: Exponential Functions

1

2.4

suppl.

or Newton's Law of Cooling (TI-CBL)

Nonhomogeneous Diff Eq's: Polynomial Functions

1

2.5

suppl.

retirement.doc (Word file)
deer_cougars.doc (Word file)

Exam No. 1

1

-

-

4

Various Applications of 1st-Order, Linear, Diff Eq's

1

2.6 & 2.7

throughout

Lake Pollution ILAP and/or Deer and Cougars

Modeling Change with Systems of Diff Eq's

1

3.1

1.8

and/or Heat in a Bar or Spread of a Disease ILAP

Numerical Solutions of Systems of Diff Eq's

2

3.2

1.8

and/or Boat/Car Rental

deer_cougars.doc (Word file)
heat_bar.nb
car_rentals.doc (Word file)

5

Cobwebs for Linear and Nonlinear Diff Eq's

1

7.3

1.7

Exploration of Equilibrium and Stability of

Stability and Long-term Behavior via Cobwebs

1

7.4

1.7

Linear Difference Equations using Cobwebs

Nonlinear Systems, Equilibria, and Phase Plane Orbits

1

8.1 & 8.2

suppl.

equilibrium.doc (Word file)

Sequences and Differences

1

9.1

1.2

webplots.doc (Word file)

6

Difference Tables and Graphs

1

9.2

1.3

Convergence of Secant Slopes on the

Sums and Series

2

9.3

1.9

Derivative Function

Exam No. 2

1

-

-

Ch2_sec.nb

7

Functions of a Continuous Independent Variable

1

9.4

1. 10

Using Riemann Sums to Estimate Areas,

Derivatives: Limit of a Difference Quotient

1

9.5

1. 10

Volumes, and Lengths of Arc

Sumarize DDS and Transition to Calculus

2

9.5 & 9.6

1. 10

Ch4_avl.nb

II. Calculus

Week

Topic

Estimated

Thomas

Module

# of Periods

Sections

8

Limits and Rates of Change

1

1.1

Take It To the Limit and/or Going to Infinity

Finding Limits and One-Sided Limits

2

1.2

and/or Typing Equations and Making

Limits Involving Infinity

1

1.3

Presentations (Power Point)

Ch1_lim.nb
Ch1_inf.nb

9

Continuity

1

1.4

Derivatives, Slopes, Tangent Lines and

Tangent Lines

1

1.5

Making Movies and/or Convergence of

The Derivative as a Function

1

2.1

Secant Slopes on the Derivative Function

Exam No. 3

1

-

Ch3_lin.nb
Ch2_sec.nb

10

The Derivative as a Rate of Change

1

2.2

Overview of Mathematica/Maple

Derivatives of Powers, Quotients, and Negative Powers

1

2.3

ChP_intr.nb

Derivatives of Trig Functions

1

2.4

The Chain Rule

1+

2.5

11

The Chain Rule

1+

2.5

Implicit Differentiation Program for TI-92(89),

Implicit Differentiation

2

2.6

Mathematica, or Maple

Related Rates

1+

2.7

implicit_diff_ti.doc (Word file)

12

Related Rates

1+

2.7

Plotting with a CAS 

Extreme Values of a Function

2

3.1

ChP_intr.nb

Exam No. 4

1

-

13

The Mean Value Theorem and Differential Equations

1

3.2

Motion Along a Straight Line: Part I

The Shape of a Graph

2

3.3

Ch2_mo1.nb

Graphical Solutions of Autonomous Differential Equations

1+

3.4

14

Graphical Solutions of Autonomous Differential Equations

1+

3.4

Student Presentations

Student Presentations

2

-

Review for Comprehensive Final Exam

1

-

15

Final Exam

2

-