AHRENS' VIDEO INDEX

for Math 1630

Some videos also apply to DSPM 0800, 0850; and Math 1130, 1710, 1730, 2000

 

You must have Flash installed to view these videos

To view videos, click on the slides

 

1)    The Slope of a Line

        Definition, applications, applying slope formula, special cases, increasing/decreasing intervals

 

2)    What is a Function? 

  Definition and examples; function notation and terminology; vertical line test 

   

3)    Writing Linear Equations 

  Using point-slope form; standard form; special cases; summary of properties of linear

  equations.  

    

4)    Cost/Revenue/Profit Analysis

  An application illustrating the use of linear total cost, total revenue, and total profit

  functions; break-even point; uses the four-step method   

 

5)    Solving a Linear System: Using Elimination

  Using elimination method; checking answers by hand and on calculator

   

6)    Solving a Linear System: When Things Go Wrong 

  Inconsistent systems and dependent systems

   

7)    Elementary Row Operations    

          Using the three elementary row operations.

 

8)    Solving a Linear System: Gauss-Jordan Elimination

 Augmented matrix, Gauss-Jordan method described; step-by-step application

 

9)    Matrix Math

  Definition of a matrix, equal matrices, addition, subtraction, scalar multiplication,

  linear combination, transpose.

 

10)   Matrix Multiplication 

  Scalar multiplication, matrix multiplication

 

11)   Special Matrices    

        The zero and identity matrices; related properties

 

12)   Finding an Inverse Matrix    

        Existence, forming augmented matrix, using elementary row operations to find
        inverse matrix by hand

 

13)   Solving a Linear System: Using a Matrix Equation

         Writing a matrix equation; using the inverse of the coefficient matrix

 

14)    Finding the Determinant    

         Definition of a determinant, expansion by minors, relationship of determinant and

         inverse matrix

  

15)    Cramer's Rule with automation and audio

          Using Cramer's Rule to solve a system of linear equations

 

16)   Systems of Linear Inequalities

         Graphing systems of inequalities, finding feasible region, finding corner points        

   

17)   The Corner Point Theorem

        Optimization; applying the corner point theorem; a special case          

   
18)   Slack Variables and the Initial Simplex Tableau
         Introducing slack variables, initial Simplex tableau, basic variables, reading initial solution   

19)   Performing a Pivot    

  Finding the pivot element and performing the pivot operation, checking for optimization

 

20)  The Standard Maximization Problem with automation and audio  

 Analyzing problem/organizing information, writing constraints and objective function

    [You must have Flash installed to view this video]

 

21)   The Standard Minimization Problem

  The primal problem, writing the dual, solving the dual, interpreting the solution