MareMathics

Maremathics, Apr 23, 2022

[color=#1551b5]Innovative Approach in Mathematical Education for Maritime Students 2019-1-HR01-KA203-061000[/color]

Table of Contents

  1. Complex Numbers
    1. Polar Form of a Complex Number
    2. Powers of Complex Numbers
    3. Application: Phase difference
    4. Application: Series RL Circuit
  2. Matrices
    1. Matrix Addition
    2. Matrix Multiplication
    3. Example: Matrix Operations
    4. Example: Martix multiplication
    5. Example: Determinant
  3. Trigonometry
    1. Bearing & Trigonometric Ratios
    2. Sine and cosine from rotating vector
    3. Unit circle and sine/cosine curve
    4. Submarine_solution
    5. Connections and maritime applications
    6. Trigonometry Application: Spring Motion
  4. Functions
    1. Vertical line test
    2. Vertical_line_test_2
    3. Quiz-The Vertical-Line Test
    4. Rovenska_Novalja
    5. Submarine
    6. Function values
    7. Increasing/decreasing
    8. Computing Limits: Graphically
    9. Function_Basis
  5. Calculus
    1. Derivation of elementary functions
    2. Differential Calculation
    3. Derivative of function
    4. Extrema of functions of one variable
    5. QUIZ.
    6. GAME: Properties of Calculus
    7. Area Between Curves2
    8. Related Rates - Pulling Boat
    9. Partial derivatives and the tangent plane
  6. Vectors
    1. Vectors
    2. Definitions
    3. Scalar or Vector? - Quiz
    4. Adding Vectors Geometrically
    5. Vector Application: Ship's Course
    6. Quiz
    7. Vector 3D
    8. Vector Application: Relative velocity of drones
  7. Statistics
    1. Relative frequencies of tossing 5 coins

1.

Complex Numbers

  • 1. Polar Form of a Complex Number
  • 2. Powers of Complex Numbers
  • 3. Application: Phase difference
  • 4. Application: Series RL Circuit

1.1.

Polar Form of a Complex Number

Polar Form Representation of a Complex Number
The [color=#ff0000][b]Polar Form[/b][/color] of a complex number is written in terms of its magnitude and angle. Thus, a polar form vector is presented as: [br] [size=100][b][color=#0000ff] z= r ∠±[/color][/b][math]\phi[/math][b][color=#0000ff], [/color][/b][/size][size=100]where: [b]z[/b] is the [b]complex [/b]number in polar form, [b]r[/b] is the [b]magnitude [/b]or [b]modulo [/b]of the vector and[b] [/b][math]\phi[/math][b] [/b]is its [b]angle [/b]or argument of r. T[br][br]In polar form the location of the point is represented in a “triangular form” as shown below.[/size]
Converting between Rectangular Form and Polar Form
We can use simple geometry of the triangle and especially trigonometry and Pythagoras’s Theorem on triangles to find both the magnitude and the angle of the complex number. As we remember from school, trigonometry deals with the relationship between the sides and the angles of triangles so we can describe the relationships between the sides as:
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1.2.

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1.3.

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1.4.

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2.

Matrices

  • 1. Matrix Addition
  • 2. Matrix Multiplication
  • 3. Example: Matrix Operations
  • 4. Example: Martix multiplication
  • 5. Example: Determinant

2.1.

Matrix Addition

Operations with matrices
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2.2.

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2.3.

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2.4.

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2.5.

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3.

Trigonometry

  • 1. Bearing & Trigonometric Ratios
  • 2. Sine and cosine from rotating vector
  • 3. Unit circle and sine/cosine curve
  • 4. Submarine_solution
  • 5. Connections and maritime applications
  • 6. Trigonometry Application: Spring Motion

3.1.

Bearing & Trigonometric Ratios

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3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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4.

Functions

  • 1. Vertical line test
  • 2. Vertical_line_test_2
  • 3. Quiz-The Vertical-Line Test
  • 4. Rovenska_Novalja
  • 5. Submarine
  • 6. Function values
  • 7. Increasing/decreasing
  • 8. Computing Limits: Graphically
  • 9. Function_Basis

4.1.

Vertical line test

The Vertical-Line Test
Let’s now determine how we can look at a graph and decide whether it is a graph of a function. [br][b][i]A function has exactly one output for every input, [/i][/b][br]This fact means that the graph represents a function [color=#0000ff]if a vertical line could intersect the graph in more than one place.[/color]
– Toni Milun

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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4.8.

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4.9.

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5.

Calculus

[color=#1551b5][/color][*][color=#1551b5][/color]MareMathics

  • 1. Derivation of elementary functions
  • 2. Differential Calculation
  • 3. Derivative of function
  • 4. Extrema of functions of one variable
  • 5. QUIZ.
  • 6. GAME: Properties of Calculus
  • 7. Area Between Curves2
  • 8. Related Rates - Pulling Boat
  • 9. Partial derivatives and the tangent plane

5.1.

Derivation of elementary functions

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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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5.9.

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6.

Vectors

  • 1. Vectors
  • 2. Definitions
  • 3. Scalar or Vector? - Quiz
  • 4. Adding Vectors Geometrically
  • 5. Vector Application: Ship's Course
  • 6. Quiz
  • 7. Vector 3D
  • 8. Vector Application: Relative velocity of drones

6.1.

Vectors

https://www.geogebra.org/m/aehmatkf
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6.2.

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6.3.

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6.4.

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6.5.

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6.6.

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6.7.

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6.8.

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7.

Statistics

  • 1. Relative frequencies of tossing 5 coins

7.1.

Relative frequencies of tossing 5 coins

Frequencies and relative frequencies
A table of frequencies and relative frequencies is one form of data viewing.[br]It is created for the selected variable.[br][br]The [b][color=#ff0000]frequency [/color][/b]of one category is the number of recorded values of a variable that belong to that category.[br]The [b][color=#ff0000]relative frequency[/color][/b] of a category is the frequency divided by the total number of data for that variable.[br][br]Common labels are:[br][br][list][*]frequency ⇒ [math]f[/math][/*][*]number of data of the selected variable ⇒ [math]n[/math][/*][*]relative frequency ⇒[math]\frac{f}{n}[/math][/*][/list][br]
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