MAT375: Non-linear Exam....      This insight implements Newton's method as an InsightMaker model.       It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)      Fun to try a couple of different cases, so I have built four choices into this exa
MAT375: Non-linear Exam....

This insight implements Newton's method as an InsightMaker model.

It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)

Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.

Andy Long
Spring, 2020




    This insight implements integration as an InsightMaker model.       It is important to use Euler's method, with Simulation Length equal to n, in Seconds.       Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" o

This insight implements integration as an InsightMaker model.

It is important to use Euler's method, with Simulation Length equal to n, in Seconds.

Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.

Andy Long
Spring, 2020




 MAT375: Non-linear Exam....      This insight implements Newton's method as an InsightMaker model.       It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)      Fun to try a couple of different cases, so I have built four choices into this exa
MAT375: Non-linear Exam....

This insight implements Newton's method as an InsightMaker model.

It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)

Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.

Andy Long
Spring, 2020




 MAT375: Non-linear Exam....      This insight implements Newton's method as an InsightMaker model.       It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)      Fun to try a couple of different cases, so I have built four choices into this exa
MAT375: Non-linear Exam....

This insight implements Newton's method as an InsightMaker model.

It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)

Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.

Andy Long
Spring, 2020




 MAT375: Non-linear Exam....      This insight implements Newton's method as an InsightMaker model.       It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)      Fun to try a couple of different cases, so I have built four choices into this exa
MAT375: Non-linear Exam....

This insight implements Newton's method as an InsightMaker model.

It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)

Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.

Andy Long
Spring, 2020




 MAT375: Non-linear Exam....      This insight implements Newton's method as an InsightMaker model.       It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)      Fun to try a couple of different cases, so I have built four choices into this exa
MAT375: Non-linear Exam....

This insight implements Newton's method as an InsightMaker model.

It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)

Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.

Andy Long
Spring, 2020




 MAT375: Non-linear Exam....      This insight implements Newton's method as an InsightMaker model.       It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)      Fun to try a couple of different cases, so I have built four choices into this exa
MAT375: Non-linear Exam....

This insight implements Newton's method as an InsightMaker model.

It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)

Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.

Andy Long
Spring, 2020




An infinite number of mathematicians walk into a bar. The first one tells the bartender he wants a beer. The second one says he wants half a beer. The third one says he wants a fourth of a beer. The bartender puts two beers on the bar and says “You guys need to learn your limits.” From  Wild About M
An infinite number of mathematicians walk into a bar. The first one tells the bartender he wants a beer. The second one says he wants half a beer. The third one says he wants a fourth of a beer. The bartender puts two beers on the bar and says “You guys need to learn your limits.” From Wild About Math
 MAT375: Non-linear Exam....      This insight implements Newton's method as an InsightMaker model.       It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)      Fun to try a couple of different cases, so I have built four choices into this exa
MAT375: Non-linear Exam....

This insight implements Newton's method as an InsightMaker model.

It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)

Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.

Andy Long
Spring, 2020




 This is an example of a finite state machine (FSM), from Gersting's 7th edition (p. 730, Example 29).      It's the first time I've used vectors (for input); and there are a few interesting twists on models that are different for the Finite State Machine.       So it's been an interesting learning
This is an example of a finite state machine (FSM), from Gersting's 7th edition (p. 730, Example 29).

It's the first time I've used vectors (for input); and there are a few interesting twists on models that are different for the Finite State Machine.

So it's been an interesting learning experience for me....
 
It works!
Andy Long
Spring, 2020

Year of Covid-19​
 One of my favorite topics in Discrete Math is Finite State Machines (FSM). We study deterministic machines without feedback, which can be used to     * recognize certain types of strings   * perform certain tasks (e.g. binary addition).       This particular example of an FSM recognizes input that
One of my favorite topics in Discrete Math is Finite State Machines (FSM). We study deterministic machines without feedback, which can be used to
 * recognize certain types of strings
 * perform certain tasks (e.g. binary addition).

This particular example of an FSM recognizes input that include multiples of 3 0s (including none). If the nth input represents a complete multiple of 3 0s, then the output will be 1; otherwise 0.

Andy Long
Spring, 2020

Year of Covid-19​
7 months ago
Problem of the car slowing down under friction and drag
Problem of the car slowing down under friction and drag
 This is an example of a finite state machine (FSM), from Gersting's 7th edition (p. 730, Example 29).      It's the first time I've used vectors (for input); and there are a few interesting twists on models that are different for the Finite State Machine.       So it's been an interesting learning
This is an example of a finite state machine (FSM), from Gersting's 7th edition (p. 730, Example 29).

It's the first time I've used vectors (for input); and there are a few interesting twists on models that are different for the Finite State Machine.

So it's been an interesting learning experience for me....
 
It works!
Andy Long
Spring, 2020

Year of Covid-19​
 MAT375: Non-linear Exam....      This insight implements Newton's method as an InsightMaker model.       It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)      Fun to try a couple of different cases, so I have built four choices into this exa
MAT375: Non-linear Exam....

This insight implements Newton's method as an InsightMaker model.

It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)

Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.

Andy Long
Spring, 2020




 MAT375: Non-linear Exam....      This insight implements Newton's method as an InsightMaker model.       It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)      Fun to try a couple of different cases, so I have built four choices into this exa
MAT375: Non-linear Exam....

This insight implements Newton's method as an InsightMaker model.

It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)

Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.

Andy Long
Spring, 2020




 MAT375: Non-linear Exam....      This insight implements Newton's method as an InsightMaker model.       It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)      Fun to try a couple of different cases, so I have built four choices into this exa
MAT375: Non-linear Exam....

This insight implements Newton's method as an InsightMaker model.

It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)

Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.

Andy Long
Spring, 2020




 MAT375: Non-linear Exam....      This insight implements Newton's method as an InsightMaker model.       It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)      Fun to try a couple of different cases, so I have built four choices into this exa
MAT375: Non-linear Exam....

This insight implements Newton's method as an InsightMaker model.

It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)

Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.

Andy Long
Spring, 2020




 MAT375: Non-linear Exam....      This insight implements Newton's method as an InsightMaker model.       It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)      Fun to try a couple of different cases, so I have built four choices into this exa
MAT375: Non-linear Exam....

This insight implements Newton's method as an InsightMaker model.

It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)

Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.

Andy Long
Spring, 2020




THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES TURBULENT CHAOTIC DESTRUCTION  The existing global capitalistic growth paradigm is totally flawed  Growth in supply and productivity is a summation of variables as is demand ... when the link between them is broken by catastrophic failure in a compon
THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES TURBULENT CHAOTIC DESTRUCTION

The existing global capitalistic growth paradigm is totally flawed

Growth in supply and productivity is a summation of variables as is demand ... when the link between them is broken by catastrophic failure in a component the creation of unpredictable chaotic turbulence puts the controls ito a situation that will never return the system to its initial conditions as it is STIC system (Lorenz)

The chaotic turbulence is the result of the concept of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks

See Guy Lakeman Bubble Theory for more details on keeping systems within finite working containers (villages communities)

In  mathematics , a  Lissajous curve   /ˈlɪsəʒuː/ , also known as  Lissajous figure  or  Bowditch curve   /ˈbaʊdɪtʃ/ , is the graph of a system of  parametric equations {\displaystyle x=A\sin(at+\delta ),\quad y=B\sin(bt),} which describe  complex harmonic motion . This family of  curves  was invest
In mathematics, a Lissajous curve /ˈlɪsəʒuː/, also known as Lissajous figure or Bowditch curve /ˈbaʊdɪtʃ/, is the graph of a system of parametric equations{\displaystyle x=A\sin(at+\delta ),\quad y=B\sin(bt),}

which describe complex harmonic motion. This family of curves was investigated by Nathaniel Bowditch in 1815, and later in more detail by Jules Antoine Lissajous in 1857.

Simulation of MTBF with controls   F(t) = 1 - e ^ -λt   Where    • F(t) is the probability of failure    • λ is the failure rate in 1/time unit (1/h, for example)   • t is the observed service life (h, for example)  The inverse curve is the trust time On the right the increase in failures brings its
Simulation of MTBF with controls

F(t) = 1 - e ^ -λt 
Where  
• F(t) is the probability of failure  
• λ is the failure rate in 1/time unit (1/h, for example) 
• t is the observed service life (h, for example)

The inverse curve is the trust time
On the right the increase in failures brings its inverse which is loss of trust and move into suspicion and lack of confidence.
This can be seen in strategic social applications with those who put economy before providing the priorities of the basic living infrastructures for all.

This applies to policies and strategic decisions as well as physical equipment.
A) Equipment wears out through friction and preventive maintenance can increase the useful lifetime, 
B) Policies/working practices/guidelines have to be updated to reflect changes in the external environment and eventually be replaced when for instance a population rises too large (constitutional changes are required to keep pace with evolution, e.g. the concepts of the ancient Greeks, 3000 years ago, who based their thoughts on a small population cannot be applied in 2013 except where populations can be contained into productive working communities with balanced profit and loss centers to ensure sustainability)

Early Life
If we follow the slope from the leftmost start to where it begins to flatten out this can be considered the first period. The first period is characterized by a decreasing failure rate. It is what occurs during the “early life” of a population of units. The weaker units fail leaving a population that is more rigorous.

Useful Life
The next period is the flat bottom portion of the graph. It is called the “useful life” period. Failures occur more in a random sequence during this time. It is difficult to predict which failure mode will occur, but the rate of failures is predictable. Notice the constant slope.  

Wearout
The third period begins at the point where the slope begins to increase and extends to the rightmost end of the graph. This is what happens when units become old and begin to fail at an increasing rate. It is called the “wearout” period.