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https://github.com/feenix100/notebook_templates

Jupyter Notebook Templates for Math with LaTeX
https://github.com/feenix100/notebook_templates

jupyter-notebook latex math matplotlib

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Jupyter Notebook Templates for Math with LaTeX

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README 

        

# College Algebra Jupyter Notebook Templates



Welcome to the College Algebra Jupyter Notebook Templates! This repository provides a structured set of Jupyter notebook templates designed to help you learn and solve problems in college algebra. Each template includes sections with LaTeX examples for mathematical notation and practical problem-solving exercises.

I use VS Code to edit and view notebooks, however there are many options.



## Getting Started



To use these templates, follow the steps below:



### Setting Up a Virtual Environment



1. **Create a Virtual Environment:**

   ```sh

   python -m venv myenv

   ```



### Prerequisites



Ensure you have the following installed on your system:



- Python 3.6 or higher



2. **Activate the Virtual Environment:**

   - On Windows:

     ```sh

     myenv\Scripts\activate

     ```

   - On macOS and Linux:

     ```sh

     source myenv/bin/activate

     ```



3. **Install Jupyter and Matplotlib:**

   ```sh

   pip install jupyter matplotlib

   ```



4. **Clone the Repository:**

   ```sh

   git clone 

   cd 

   ```



5. **Start Jupyter Notebook:**

   ```sh

   jupyter notebook

   ```



6. **Or, use VS Code.**

   ```sh

   Install extensions for python and jupyter notebooks.

   ```

   



## Template Structure



Each template covers different topics in college algebra. Here is the structure and explanation of the sections included:



### 1. Basic Algebraic Operations



Perform basic algebraic operations such as addition, subtraction, multiplication, and division of algebraic expressions.



**LaTeX Examples:**

- Addition: $a + b$

- Subtraction: $a - b$

- Multiplication: $a \times b$ or $a \cdot b$

- Division: $\frac{a}{b}$

- Exponentiation: $a^b$

- Square Root: $\sqrt{a}$

- Fraction: $\frac{a}{b}$

- Parentheses: $(a + b)$



**Example: Simplify an Expression**

Simplify the following expression: $(2x + 3) - (x - 5)$



**Solution:**

To simplify, distribute the negative sign and combine like terms:

$$(2x + 3) - (x - 5) = 2x + 3 - x + 5 = x + 8$$



### 2. Solving Equations and Inequalities



Solve linear, quadratic, and higher-order equations, as well as inequalities.



**LaTeX Examples:**

- Linear Equation: $ax + b = c$

- Quadratic Equation: $ax^2 + bx + c = 0$

- Inequality: $x > 5$ or $x \leq 10$

- Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$



**Example: Solve a Quadratic Equation**

Solve the equation: $x^2 - 4x + 3 = 0$



**Solution:**

Factor the quadratic equation:

$$x^2 - 4x + 3 = (x - 1)(x - 3) = 0$$

Set each factor to zero:

$$x - 1 = 0 \quad \text{or} \quad x - 3 = 0$$

Thus, $x = 1$ or $x = 3$.



### 3. Functions and Their Properties



Explore functions, their domains, ranges, and key properties.



**LaTeX Examples:**

- Function Notation: $f(x) = x^2 + 3x + 2$

- Domain and Range: For $f(x) = \frac{1}{x}$, Domain: $x \neq 0$, Range: $y \neq 0$

- Function Properties: $f(0)$, $f'(x)$, $f''(x)$



**Example: Define a Function and Find Its Domain**

Define the function $f(x) = x^2 + 3x + 2$ and find its domain.



**Solution:**

The domain of a polynomial function is all real numbers: $\mathbb{R}$.



### 4. Polynomial and Rational Functions



Work with polynomial and rational functions, including their graphs and asymptotes.



**LaTeX Examples:**

- Polynomial Function: $p(x) = 3x^3 - 2x^2 + x - 1$

- Rational Function: $r(x) = \frac{x^2 - 1}{x + 1}$

- Asymptote: $y = \frac{1}{x}$ has a horizontal asymptote at $y = 0$



**Example: Find the Roots of a Polynomial**

Find the roots of the polynomial $x^3 - 6x^2 + 11x - 6$.



**Solution:**

Factor the polynomial:

$$x^3 - 6x^2 + 11x - 6 = (x - 1)(x - 2)(x - 3)$$

Set each factor to zero:

$$x - 1 = 0 \quad \text{or} \quad x - 2 = 0 \quad \text{or} \quad x - 3 = 0$$

Thus, the roots are $x = 1$, $x = 2$, and $x = 3$.



### 5. Exponential and Logarithmic Functions



Study exponential and logarithmic functions and their applications.



**LaTeX Examples:**

- Exponential Function: $f(x) = a \cdot b^x$

- Logarithmic Function: $f(x) = \log_b(x)$ or $f(x) = \ln(x)$

- Exponential Growth/Decay: $y = y_0 e^{kt}$



**Example: Solve an Exponential Equation**

Solve the equation $e^x = 5$.



**Solution:**

To solve for $x$, take the natural logarithm of both sides:

$$x = \ln(5)$$



### 6. Systems of Equations and Matrices



Solve systems of equations using matrix representation and row reduction.



**LaTeX Examples:**

- System of Equations: $\begin{cases} ax + by = c \\ dx + ey = f \end{cases}$

- Matrix Representation: $\mathbf{A} = \begin{pmatrix} a & b \\ d & e \end{pmatrix}$

- Row Reduction: $\mathbf{A} \rightarrow \mathbf{R}$



**Example: Solve a System of Equations**

Solve the system: $\begin{cases} 2x + 3y = 5 \\ x - y = 2 \end{cases}$



**Solution:**

Use matrix representation and row reduction to find the solution.



### 7. Sequences, Series, and Probability



Work with arithmetic and geometric sequences, series, and basic probability.



**LaTeX Examples:**

- Arithmetic Sequence: $a_n = a_1 + (n-1)d$

- Geometric Sequence: $a_n = a_1 \cdot r^{(n-1)}$

- Series: $S_n = \frac{n}{2} (a_1 + a_n)$

- Probability: $P(A) = \frac{|A|}{|S|}$



**Example: Find the Sum of an Arithmetic Series**

Find the sum of the first 10 terms of the arithmetic series where $a_1 = 2$ and $d = 3$.



**Solution:**

Use the formula for the sum of an arithmetic series:

$$S_{10} = \frac{10}{2} (2 + (2 + (10-1) \cdot 3)) = 5 \cdot (2 + 29) = 5 \cdot 31 = 155$$



### 8. Slope of a Line



Calculate the slope of a line using the slope formula.



**LaTeX Examples:**

- Slope Formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$



**Example: Calculate the Slope**

Calculate the slope of the line passing through the points (1, 2) and (3, 4).



**Solution:**

Using the slope formula:

$$m = \frac{4 - 2}{3 - 1} = \frac{2}{2} = 1$$



### 9. Graphing Algebraic Equations



Plot linear equations using Matplotlib.



**Example: Plot a Linear Equation**



```python

import matplotlib.pyplot as plt

import numpy as np



x = np.linspace(-10, 10, 400)

y = 2 * x + 3



plt.plot(x, y, label='y = 2x + 3')

plt.xlabel('x')

plt.ylabel('y')

plt.title('Graph of y = 2x + 3')

plt.legend()

plt.grid(True)

plt.show()

```



## License



This repository is licensed under the GNU License. See the [LICENSE](LICENSE) file for more information.



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Feel free to add more sections or modify the existing ones to suit your needs.