I. Calculus - Continued

Week

Topic

Estimated

Thomas

Module

# of Periods

Sections

1

Exponential Functions and Their Derivatives

1

part of 2.9

Solving dy/dx = y and/or Recursion on Mathematica

Optimization

2

3.5

dydx_eq_y.doc (Word file)
Recursion.nb

Linearization and Differentials

1

3.6

2

Newton's Method

1

3.7

Rain Catchers, Elevators, and Rockets

Indefinite Integrals, Diff Eq's, and Modeling

1

4.1

and/or Bending of Beams

Indefinite Integrals: u - Substitutions

2

4.2

Ch4_rc.nb
Ch4_bb.nb

3

Estimating with Finite Sums

1

4.3

Summing It Up with Riemann, Definite

Riemann Sums & Definite Integrals w/o Properties

2

part of 4.4

Integrals and the FTOC and/or Motion Along a Straight Line, Part 2

Exam No. 1

1

-

Ch4_rs.nb
Ch4_mo2.nb

4

Fundamental Theorem and the Natural Log Function

2

2.9,4.5,6.1

Rain Catchers, Elevators, and Rockets

Properties of, and u - Substitutions for Definite Integrals

1

4.4 and 4.6

Ch4_rc.nb

First-Order Differential Equations and Slope Fields

1+

2.9 & 5.4

5

First-Order Differential Equations and Slope Fields

1+

2.9 & 5.4

First-Order Differential Equations and

Areas

1

4.6

Slope Fields and/or Drug Dosages

Numerical Integration

2

4.7

Ch6_sf.nb
Ch6_dd.nb

6

Volumes

2

5.1 & 5.2

Riemann, Trapezoids, and Simpson

Springs, Pumping, and Lifting

1+

5.5

Ch4_rts.nb

Exam No. 2

1

-

7

Springs, Pumping, and Lifting

1+

5.5

Bungee Cord Jumping Module (Ch5_bcj.nb) and/or

Growth and Decay: Linear 1st-Order Diff Eq's

2

6.3

Bungee Cord Experiment (bung_cord_exp.doc - Word file) and/or

Euler's Method

1+

6.4

Compound Bows and Arrows (bow_exp.doc - Word file)

8

Euler's Method

1+

6.4

Solving Differential Equations with a CAS

Inverse Functions and Their Derivatives

1

P.4 & 2.8

Ch6_dd.nb

Derivatives of Inverse Trig Functions; Integral Forms

1

2.8 & 4.1

Basic Integration Forms

1

7.1

9

Integration by Parts

1

7.2

Integration with a CAS

Vectors in a Plane, Dot Products, and Projections

2

9.1 & 9.2

Ch4_bb.nb

Exam No. 3

1

-

II. Systems of Linear Difference Equations and Linear Algebra

Week

Topic

Estimated

DDS

P&P

Module

# of Periods

Sections

Sections

10

Solutions of Systems of Algebraic Equations

1

4.1

3.1

Lake Pollution ILAP and/or Boat/Car Rentals

The Augmented Matrix and Reduced Echelon Form

2

4.2

3.4

eigenval_eigenvec.doc (Word file)

Matrix Properties and Operations

1+

4.3

3.2 & 3.3

11

Matrix Properties and Operations

1+

4.3

3.2 & 3.3

Inverses and Determinants of Matrices and

Square Matrices: Inverses and Determinants

2

4.4

3.5 & 3.6

Solutions of Matrix Equations with a CAS

Matrix Equations and Their Solutions: Singular & Non

1+

4.5

3.4 - 3.6

det_by_gauss.doc (Word file)

12

Matrix Equations and Their Solutions: Singular & Non

1+

4.5

3.4 - 3.6

Eigenvalues and Eigenvalues with a CAS

Linear DDS's of Several Variables: Notation & Iteration

2

5.1

3.1 & 3.7

eigen_by_gauss.nb

Exam No. 4

1

-

-

13

Eigenvalues and Eigenvectors of a Square Matrix

2

5.2

3.7

Using a CAS to Solve a DDS with

Solving a Linear DDS with Eigenvalues and Eigenvectors

2+

5.3

3.7

Eigenvalues and Eigenvectors: Lake

Pollution and/or Boat/Car Rentals

LP_by_eigen.nb

14

Solving a Linear DDS with Eigenvalues and Eigenvectors

1+

5.3

3.7

Student Presentations

Equilibrium Solutions and Long-Term Behavior

1

5.4

3.7

Student Presentations

2

-

-

15

Final Exam