Principles of Mathematical Modeling

Geogebra Cumbres, Feb 12, 2016

Construct and interpret mathematical models by applying arithmetic, algebraic, geometric and variational procedures, and argues problem solving with numerical, graphical, analytical and variational methods can be defined as the competencies of this course. Math 2nd Semester.

Table of Contents

  1. Arithmetic
    1. Order of operations
    2. Operations with fractions
    3. Percentages
  2. Algebra
    1. Law of exponents
    2. Factorization
  3. Concept of function
    1. Relation and Function
  4. Function, equation y and linear inequality and their transform actions
    1. Representations of Linear Functions
    2. Characteristics of Linear Functions
    3. X and Y intercepts
    4. Transformation of Linear Functions
    5. Linear inequalities
    6. Systems of Linear Equations
    7. Linear model
  5. Function, equation and quadratic inequalities and their transform actions
    1. Parabola Representations
    2. Characteristics of Quadratic Functions
    3. Finding the roots in a quadratic function
    4. Finding the vertex
    5. Transformation of Quadrati Functions
    6. Quadratic Inequalities
    7. Quadratic- Linear Systems
    8. Quadratic Models
  6. Polynomial Function and Equation from Degree 3-5 and their Transfomrations
    1. Roots of Polynomial Functions Degree 3
    2. Characteristics of Polynomial Function
    3. Cubic Models
  7. Mathematical Models (linear, quadratic and cubic)
    1. Mathematical Models

1.

Arithmetic

[list] 1.- Order of Operations 2.- Operations with Fractions 3.- Percentages [/list]

  • 1. Order of operations
  • 2. Operations with fractions
  • 3. Percentages

1.1.

Order of operations

1.1 Order of operations[br]1.2 Operations with Fractions[br]1.3 Percenteges
1.1 Order of operations
[br]Look at the table above and analyze how the operations are accommodated[br]depending the order of the signs.
– Geogebra Cumbres

1.2.

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1.3.

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2.

Algebra

[list] 1.- Laws of Exponents 2.- Factorization [/list]

  • 1. Law of exponents
  • 2. Factorization

2.1.

Law of exponents

In each problem, depending the multiply or dividing sign they are using, is how we can know by the law of exponents what to do with the exponents represented in each operation. Click on new problem to have the possibility to use another operation, and then in the option check anser to observe how it is execute. 
– Pratima Nayak, Geogebra Cumbres

2.2.

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3.

Concept of function

[list] 1.- Definition of Relation and Function [/list]

  • 1. Relation and Function

3.1.

Relation and Function

In this video is represented the explanation of what is relation and function.
– Geogebra Cumbres

4.

Function, equation y and linear inequality and their transform actions

[list] 1.- Representations of Linear Functions 2.- Characteristics of Linear Functions 3.- X and Y Intercepts 4.- Transformation of Linear Functions 5.- Linear Inequalities 6.- Systems of Linear Equations 7.- Linear Model [/list]

  • 1. Representations of Linear Functions
  • 2. Characteristics of Linear Functions
  • 3. X and Y intercepts
  • 4. Transformation of Linear Functions
  • 5. Linear inequalities
  • 6. Systems of Linear Equations
  • 7. Linear model

4.1.

Representations of Linear Functions

Observe the three different ways to reresent a Linear Function.
– Geogebra Cumbres

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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5.

Function, equation and quadratic inequalities and their transform actions

[list] 1.- Parabola Representations 2.- Characteristics of Quadratic Functions 3.- Finding the roots in a Quadratic Function 4.- Finding the Vertex 5.- Transformations of Quadratic Functions 6.- Quadratic Inequalities 7.- Quadratic-Linear Systems 8.- Quadratic Models [/list]

  • 1. Parabola Representations
  • 2. Characteristics of Quadratic Functions
  • 3. Finding the roots in a quadratic function
  • 4. Finding the vertex
  • 5. Transformation of Quadrati Functions
  • 6. Quadratic Inequalities
  • 7. Quadratic- Linear Systems
  • 8. Quadratic Models

5.1.

Parabola Representations

– Rick Hollenbeck, Geogebra Cumbres

5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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5.7.

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5.8.

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6.

Polynomial Function and Equation from Degree 3-5 and their Transfomrations

[list] 1.- Roots of Polynomial Functions Degree 3 2.- Characteristics of a Polynomial Function 3.- Cubic Models [/list]

  • 1. Roots of Polynomial Functions Degree 3
  • 2. Characteristics of Polynomial Function
  • 3. Cubic Models

6.1.

Roots of Polynomial Functions Degree 3

If you write a polynomial as the product of two or more polynomials, you have factored the polynomial. Here is an example:[br][br][img width=404,height=23]http://www.sosmath.com/algebra/factor/fac02/img1.gif[/img][br][br]The polynomials [i]x[/i]-3 and [img width=51,height=29]http://www.sosmath.com/algebra/factor/fac02/img2.gif[/img] are called factors of the polynomial [img width=149,height=33]http://www.sosmath.com/algebra/factor/fac02/img3.gif[/img] . Note that the degrees of the factors, 1 and 2, respectively, add up to the degree 3 of the polynomial we started with. Thus factoring breaks up a complicated polynomial into easier, lower degree pieces.[br][br]We are not completely done; we can do better: we can factor[br][br][img width=447,height=24]http://www.sosmath.com/algebra/factor/fac02/img4.gif[/img][br][br]We have now factored the polynomial into three linear (=degree 1) polynomials. Linear polynomials are the easiest polynomials. We can't do any better. Whenever we cannot factor any further, we say we have factored the polynomial completely.
– Geogebra Cumbres

6.2.

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6.3.

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7.

Mathematical Models (linear, quadratic and cubic)

[list] 1.- Mathematical Models [/list]

  • 1. Mathematical Models

7.1.

Mathematical Models

[list][*]A mathematical model is a description of a system using mathematical concepts and language. ...[/*][*]Mathematical models can take many forms, including dynamical systems, statistical models, differential equations, or game theoretic models. ...[/*][*]Mathematical models are usually composed of relationships and variables.[/*][/list]
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