Understanding Polynomial Addition: A Fundamental Operation in Algebra

 Introduction: Polynomial addition lies at the heart of algebraic manipulation, forming the basis for solving equations, graphing functions, and understanding complex mathematical relationships. In this article, we'll delve into the fundamentals of polynomial addition, exploring its significance, basic rules, and practical applications.

What are Polynomials? Before diving into polynomial addition, it's essential to understand what polynomials are. A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents. They often represent functions, equations, or mathematical models in various fields like physics, engineering, and economics.

The Basics of Polynomial Addition: Polynomial addition involves combining like terms to simplify expressions or solve equations. When adding polynomials, it's crucial to ensure that similar terms are grouped together and then added or subtracted accordingly. For instance, when adding $2x^2+3x-5$ and $4x^2-2x+7$, we group terms with the same exponent together: $2x^2+4x^2$ for the $x^2$ terms, $3x-2x$ for the $x$ terms, and constants separately. This process ensures clarity and accuracy in calculations.

The Rules of Polynomial Addition:

1. Like Terms: Only terms with the same variables and exponents can be added or subtracted.
2. Coefficients: When combining like terms, add or subtract their coefficients while keeping the variables and exponents unchanged.
3. Constants: Always combine constants separately.
4. Maintain Order: When adding or subtracting polynomials, maintain the order of terms to avoid errors.
5. Zero Coefficients: If a term is missing in one polynomial, treat its coefficient as zero during addition.

Examples of Polynomial Addition: Let's consider a few examples to illustrate polynomial addition:

1. Adding $3x^2+2x+5$ and $4x^2-3x+2$ yields $7x^2-x+7$.
2. Combining $2x^3+3x^2-2x$ and $5x^3-2x^2+4x$ results in $7x^3+x^2+2x$.

Applications of Polynomial Addition:

1. Solving Equations: Polynomial addition is crucial for solving equations involving algebraic expressions.
2. Graphing Functions: By adding or subtracting polynomials, one can graph functions to understand their behavior and characteristics.
3. Curve Fitting: Polynomial addition plays a vital role in curve fitting, where data points are approximated using polynomial functions.
4. Engineering and Physics: In engineering and physics, polynomial addition is used to model physical phenomena, analyze systems, and solve complex problems.

Conclusion: In summary, polynomial addition is a fundamental operation in algebra, enabling mathematicians, scientists, and engineers to manipulate expressions, solve equations, and analyze data effectively. By understanding its principles, rules, and applications, individuals can harness the power of polynomial addition to explore the depths of mathematics and its practical implications across various disciplines.

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stm32g030 read analog PA0 and PA3 code with STM32CubeID

To read analog values from pins PA0 and PA3 on the STM32G030 microcontroller using STM32CubeIDE, you can follow these steps:

1. Open STM32CubeIDE and create a new project.

2. Select the appropriate board or microcontroller model (STM32G030 in this case).

3. Configure the necessary settings for your project, such as clock configuration and GPIO pins.

4. Enable the ADC peripheral:

   • Go to the "Pinout & Configuration" tab.
   • Select the desired ADC channel(s) for PA0 and PA3 by clicking on the respective pins.
   • Assign the pins to the ADC peripheral.
   • Click on the "ADC" peripheral in the "Middlewares" section.
   • Enable the ADC and configure its settings, such as resolution, sampling time, and conversion mode.

5. In your code, include the necessary header files:

#include "stm32g0xx_hal.h"

1. Initialize the ADC and GPIO:

ADC_HandleTypeDef hadc;
GPIO_InitTypeDef GPIO_InitStruct;

void SystemClock_Config(void);
void Error_Handler(void);

void MX_GPIO_Init(void)
{
  /* GPIO Ports Clock Enable */
  __HAL_RCC_GPIOA_CLK_ENABLE();

  /*Configure GPIO pin : PA0 */
  GPIO_InitStruct.Pin = GPIO_PIN_0;
  GPIO_InitStruct.Mode = GPIO_MODE_ANALOG;
  GPIO_InitStruct.Pull = GPIO_NOPULL;
  HAL_GPIO_Init(GPIOA, &GPIO_InitStruct);

  /*Configure GPIO pin : PA3 */
  GPIO_InitStruct.Pin = GPIO_PIN_3;
  GPIO_InitStruct.Mode = GPIO_MODE_ANALOG;
  GPIO_InitStruct.Pull = GPIO_NOPULL;
  HAL_GPIO_Init(GPIOA, &GPIO_InitStruct);
}

void MX_ADC_Init(void)
{
  ADC_ChannelConfTypeDef sConfig;

  /* ADC Initialization */
  hadc.Instance = ADC1;
  hadc.Init.ClockPrescaler = ADC_CLOCK_ASYNC_DIV1;
  hadc.Init.Resolution = ADC_RESOLUTION_12B;
  hadc.Init.DataAlign = ADC_DATAALIGN_RIGHT;
  hadc.Init.ScanConvMode = ADC_SCAN_DISABLE;
  hadc.Init.EOCSelection = ADC_EOC_SINGLE_CONV;
  hadc.Init.LowPowerAutoWait = DISABLE;
  hadc.Init.LowPowerAutoPowerOff = DISABLE;
  hadc.Init.ContinuousConvMode = DISABLE;
  hadc.Init.DiscontinuousConvMode = DISABLE;
  hadc.Init.ExternalTrigConv = ADC_SOFTWARE_START;
  hadc.Init.ExternalTrigConvEdge = ADC_EXTERNALTRIGCONVEDGE_NONE;
  hadc.Init.DMAContinuousRequests = DISABLE;
  hadc.Init.Overrun = ADC_OVR_DATA_OVERWRITTEN;
  if (HAL_ADC_Init(&hadc) != HAL_OK)
  {
    Error_Handler();
  }

  /* Configure ADC channel */
  sConfig.Channel = ADC_CHANNEL_0; // PA0
  sConfig.Rank = 1;
  sConfig.SamplingTime = ADC_SAMPLETIME_13CYCLES_5;
  sConfig.SingleDiff = ADC_SINGLE_ENDED;
  sConfig.OffsetNumber = ADC_OFFSET_NONE;
  sConfig.Offset = 0;
  if (HAL_ADC_ConfigChannel(&hadc, &sConfig) != HAL_OK)
  {
    Error_Handler();
  }

  sConfig.Channel = ADC_CHANNEL_3; // PA3

  sConfig.Rank = 2;
  if (HAL_ADC_ConfigChannel(&hadc, &sConfig) != HAL_OK)
  {
    Error_Handler();
  }
}

int main(void)
{
  /* MCU Configuration */
  HAL_Init();
  SystemClock_Config();

  /* Initialize GPIOs and ADC */
  MX_GPIO_Init();
  MX_ADC_Init();

  /* Infinite loop */
  while (1)
  {
    /* Start ADC conversion */
    if (HAL_ADC_Start(&hadc) != HAL_OK)
    {
      Error_Handler();
    }

    /* Wait for conversion to complete */
    if (HAL_ADC_PollForConversion(&hadc, HAL_MAX_DELAY) != HAL_OK)
    {
      Error_Handler();
    }

    /* Read the converted value */
    uint32_t adcValue = HAL_ADC_GetValue(&hadc);

    /* Do something with the ADC value */
    // ...

    /* Stop ADC conversion */
    if (HAL_ADC_Stop(&hadc) != HAL_OK)
    {
      Error_Handler();
    }
  }
}

Make sure to handle any errors appropriately in the Error_Handler() function.

1. Build and flash your project to the STM32G030 microcontroller.

This code initializes the ADC peripheral and sets up PA0 and PA3 as analog inputs. Inside the infinite loop, it starts an ADC conversion, waits for it to complete, retrieves the converted value, and then stops the ADC conversion. You can perform any necessary processing or actions with the ADC value as required.

Remember to refer to the STM32G0 HAL reference manual and the STM32CubeG0 firmware package documentation for more details on the ADC and GPIO APIs and configurations specific to your needs.

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Styrofoam cutter DIY [ make it by yourself - 2 steps only ]

In this video you can see haw you can make Styrofoam cutter by yourself. 

 It is easy and cheep, but very useful tool.

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Amazing Home automation system with STM32F103 microcontroller Part 1

Amazing Home automation system with STM32F103 microcontroller

Visit my Youtube channnels :  Electro_Magic ; Practical Tips  ; Delphi practical school             

This is ongoing project of building Home automation system ( smart home system ), which will for the start have measurement of temperature and humidity.

It will consist of number of parts ( number of blog posts ).

It is planed to work with micro controller STM32F103C8T6

 and 3.5" TFT LCD.

Next step will be to control relays for ceiling fan, etc.

Next will be to add ESP8266 to have connection to the internet, so the system can be controlled remotely.

Till now I have managed to make a printed circuit board.

Home automation board bottom

Home automation board top

Not really nice to look at, but it is working, and working from the first attempt :-)

The PCB is designed in EasyEDA, and made with toner transfer method 

Except headers for STM32 and TFT LCD, I have also added 3.3V and 5.0V linear regulators.

Beside this, there is also part with MC34063 as a buck converter, which is in front of small linear regulators.

This part is made with intention to connect this device to external power source of 12V.

Of course, everything is programmed using Arduino IDE and STM32duino board.

For measuring temperature and humidity we use DHT11 sensor, which measures temperature and also humidity and uses just three wires, plus, ground and signal.

 

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DIY method of making PCB using toner transfer method

 

This is a DIY method of making PCB using toner transfer method. 

Visit my Youtube channnels :  Electro_Magic ; Practical Tips  ; Delphi practical school             

       

The most important thing is to have good print , done with good quality toner. 
Here we use some dangerous chemicals so be very careful if you going to do this at home.
Please check following video for details, and I will show you also few steps in following points.

As a first step we use sandpaper to remove any oxidation from copper plate, than clean it with paper tissue.

Than we use contact cleaner or acetone to clean any grease.

Then we secure the paper with printed circuit with adhesive tape.

Then  we use nail polish remover ( or acetone - nail polish remover is actually acetone ), take small amount and spread it evenly on the surface of the copper plate.

Ten minutes after we can start to remove paper very slowly.

After we removed first layer of paper we put board into the water, and slowly rubbing we remove the rest of the paper.

This rubbing should be done VERY carefully, so we do not damage toner traces.

And in the end , the result is very satisfactory.

Next step will be to do the etching, which could be done with HCL and hydrogen peroxide.

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Etching PCB with HCL and hydrogen peroxide

This is a DIY method of making PCB using HCL  and hydrogen peroxide .

Visit my Youtube channnels :  Electro_Magic ; Practical Tips  ; Delphi practical school             

The most important thing is to have good print , done with good quality toner. 
 Here we use some dangerous chemicals so be very careful if you going to do this at home.
Please check following video for details, and I will show you also few steps in following points.

First you must have good print, done with good quality toner.

      Then we put prepared PCB in plastic box.

For etching we use HCL and Hydrogen peroxide.We pour in HCL just enough to cover PCB, then we add a little of peroxide.

We immediately see how reactions with copper occur.

Here we see bubbles in the reaction of acid with copper.

After few minutes we can see full reaction .

After etching is done, we rinse pcb with water.

Use a steel sponge to remove any toner residue.

The PCB looks almost perfect.

It is very important to have a well-done print at the very beginning, with quality toner.

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Compress files and folders to zip file with Delphi (Tip for 10 )

Visit my Youtube channnels :  Electro_Magic ; Practical Tips  ; Delphi practical school             

This is an example of zipping ( compressing ) files and folders with Delphi using "FWZip" component which can be downloaded from following link :

https://github.com/AlexanderBagel/FWZip

In this video you can see full procedure of this example :

And following is full source of this example :

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Export Image To PDF with Delphi (Tip for 10 )

Visit my Youtube channnels :  Electro_Magic ; Practical Tips  ; Delphi practical school

This is example how one can export image from Delphi application to PDF file, using open source library SynPDF.

In the following video full procedure is described

Library can be downloaded from :
https://github.com/synopse/SynPDF

Following is full source code :
Edited 10.01.2018 : added code for the Form after main code.

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Draw shapes with Delphi (Tip for 10 )

In this tutorial you can learn how to draw shapes with Delphi.

This is actually example of how you can create your own Paint application.

In the video below you can see complete procedure of this tutorial.

Also, following is full source code :

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LAB power supply with current control (Tip for 10 )

LAB power supply with current control from 0 to 1.5 Ampere (Tip for 10 )

This is simpler version of variable power supply shown in this post.

Voltage is variable from 0 to 30 Volts and current from 0 to 1.5 Ampere.

LM317T is mostly in standard setup.

Potentiometer for voltage control is connected to ADJ pin of LM317T and negative voltage via trim pot, with which you can adjust minimum voltage.

Current control is done using  LM393 comparator and shunt resistror.

Output of LM393 is connected to ADJ pin of LM317T and regulates amperage, sensed over shunt resistor.

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Get Base File Info (Tip for 10 )

Here you can see example of getting basic file information.

Complete procedure of making this example program can be seen in the following video.

And following is full source code that you can use to test this example by yourself.

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LM317 Variable power supply with current control (Tip for 10 )

In this post I will show you easy to construct variable power supply using LM317 with some other components.

Final result is usable variable lab power supply with current control.

Current control is done using  LM393 comparator and shunt resistror.

Since I used one panel meter for voltage and current reading , I added LM358 OP amp to read current used by attached loads.

LM358 amplifies voltage detected on shunt resistor and amplify it to appropriate value which is set by variable trim pot.

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Get Computer Drives - Delphi Tutorial (Tip for 10 )

In this example you can see how we can get list of Computer Drives with icons and labels.

 First, check this video with details for this example .

 And of course following is the source code of this example :

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