AHRENS' VIDEO INDEX

for Math 1630

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

 

To view videos, click on the slides

 

1)    What is a Function? 

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

 

2)    The Slope of a Line

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

   

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 Linear Systems Using 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)   Systems of Linear Inequalities

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

   

14)   The Corner Point Theorem

        Optimization; applying the corner point theorem; a special case          

   
15)  
Slack Variables and the Initial Simplex Tableau
        
Introducing slack variables, initial Simplex tableau, basic variables, reading initial solution   

16)  
Performing a Pivot    

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

 

17)  The Standard Maximization Problem with automation and audio  

 Analyzing problem/organizing information, writing constraints and objective function

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18)   The Standard Minimization Problem

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

 

19)   Finding the Determinant    

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

       inverse matrix

  

20)   Cramer's Rule with automation and audio

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

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