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tanszek:oktatas:techcomm:mathematical_expressions_in_tex_language

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tanszek:oktatas:techcomm:mathematical_expressions_in_tex_language [2024/09/02 14:52] – [4. Aligning Equations] kissatanszek:oktatas:techcomm:mathematical_expressions_in_tex_language [2024/09/10 08:55] (current) – [5. Exercise] kissa
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 ===== Introduction to LaTeX for Mathematical Expressions ===== ===== Introduction to LaTeX for Mathematical Expressions =====
  
-The goal of the lesson is to become familiar with the TeX language, specifically for the purpose of writing mathematical expressions.+The goal of the lesson is to become familiar with LaTeX, specifically for the purpose of writing mathematical expressions.
  
 ==== 1. Introduction to LaTeX ==== ==== 1. Introduction to LaTeX ====
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 **What is LaTeX?** **What is LaTeX?**
  
-  - LaTeX is a high-quality typesetting system, primarily used for technical and scientific documents. It is particularly powerful for formatting complex mathematical equations and formulas, making it a preferred choice in academia and research.+LaTeX is a high-quality typesetting system, primarily used for technical and scientific documents. It is particularly powerful for formatting complex mathematical equations and formulas, making it a preferred choice in academia and research.
  
 **What are the advantages of LaTeX?** **What are the advantages of LaTeX?**
  
-  - **Precision and Control**: LaTeX allows precise formatting of documents and mathematical expressions. +  * **Handling Complex Documents**: It is ideal for mathematical formulas, citations, and cross-referencing in technical writing. 
-  - **Consistency**: LaTeX automatically manages references, labels, and numbering, ensuring consistency throughout your document. +  * **Consistent Layout**: Automatically ensures a uniform, professional design by separating content from formatting. 
-  - **Professional Quality**: Documents created in LaTeX look professional and are publication-ready.+  * **Scalability**: Suitable for large projects, allowing version control and modular structure. 
 +  * **Longevity**: LaTeX's plain text format ensures long-term compatibility and durability. 
 +  * **Academic Preference**: Often required in academic and scientific publishing.
  
 **Getting Started:** **Getting Started:**
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 **Basic Document Structure:** **Basic Document Structure:**
  
-<code>+<code LaTeX>
 \documentclass{article}  % Specifies the document class (article, report, book, etc.) \documentclass{article}  % Specifies the document class (article, report, book, etc.)
 \begin{document}          % Begins the content of the document \begin{document}          % Begins the content of the document
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   - **\begin{document}** and **\end{document}**: Everything between these commands will be included in the output document.   - **\begin{document}** and **\end{document}**: Everything between these commands will be included in the output document.
  
----- 
 ==== 2. Writing Basic Mathematical Expressions ==== ==== 2. Writing Basic Mathematical Expressions ====
  
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 == Example == == Example ==
  
-<code>+<code LaTeX>
 \documentclass{article} \documentclass{article}
 \begin{document} \begin{document}
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 == Examples == == Examples ==
  
-<code>+<code LaTeX>
 \documentclass{article} \documentclass{article}
 \begin{document} \begin{document}
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   - Another common symbol is the **infinity symbol**, represented as ''\infty'', and it is displayed as $\infty$    - Another common symbol is the **infinity symbol**, represented as ''\infty'', and it is displayed as $\infty$ 
   - For **greater than or equal to** and **less than or equal to** symbols, use ''\geq'' and ''\leq'', which render as $\geq$ and $\leq$, respectively.   - For **greater than or equal to** and **less than or equal to** symbols, use ''\geq'' and ''\leq'', which render as $\geq$ and $\leq$, respectively.
 +
 +=== Summation ===
 +
 +The general form of summation in LaTeX is written using the ''\sum'' command. For example, the sum from $i=1$ to $n$ is given by:
 +
 +$$\sum_{i=1}^{n} i^2$$
 +
 +This expression sums the squares of integers from 1 to $n$.
 +
 +=== Derivative ===
 +
 +The derivative of a function $f(x)$ with respect to $x$ is represented in LaTeX using the ''\frac'' command for fractions. The notation for the derivative of $f(x)$ with respect to $x$ is:
 +
 +$$\frac{d}{dx} f(x)$$
 +
 +This gives the rate of change of $f(x)$ with respect to $x$.
 +
 +=== Partial Derivative ===
 +
 +For partial derivatives, the ''\partial'' command is used. The partial derivative of a function $f(x, y)$ with respect to $x$ is:
 +
 +$$\frac{\partial}{\partial x} f(x, y)$$
 +
 +This expression gives the partial derivative of $f$ with respect to $x$, holding other variables constant.
 +
 +=== Partial Integration ===
 +
 +Partial integration, also known as integration by parts, can be expressed in LaTeX. For the specific example of integrating $x \sin(x)$ from $a$ to $b$, the integral is written as:
 +
 +\[
 +\int_{a}^{b} x \sin(x) \, dx
 +\]
 +
 +This represents the definite integral of $x \sin(x)$ with respect to $x$ from $a$ to $b$.
 +
 ==== 4. Aligning Equations ==== ==== 4. Aligning Equations ====
  
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 == Example == == Example ==
  
-<code>+<code LaTeX>
 \documentclass{article} \documentclass{article}
 \usepackage{amsmath} \usepackage{amsmath}
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   - Example:   - Example:
  
-<code>+<code LaTeX>
 \begin{equation} \label{eq:quadratic} \begin{equation} \label{eq:quadratic}
 x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
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 ==== 5. Exercise ==== ==== 5. Exercise ====
  
-Reproduce the following mathematical proof in LaTeX. Use inline and display math, as well as special symbols! Save the result in PDF format!+Reproduce the following mathematical proof in LaTeX. Use inline and display math, as well as basic and special symbols! Save the result in PDF format!
  
 {{:tanszek:oktatas:techcomm:pasted:20240902-144955.png}} {{:tanszek:oktatas:techcomm:pasted:20240902-144955.png}}
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 <code> <code>
-Proof: √2 is Irrational}+Proof: √2 is Irrational
  
-Assume, for contradiction, that √2 is rational. Then it can be expressed as a fraction a/b, where a and b are coprime integers.+Assume, for contradiction, that 2 is rational. Then it can be expressed as a fraction a/b, where a and b are coprime integers.
  
 Then: Then:
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 This implies that b2 is even, so b must also be even. This implies that b2 is even, so b must also be even.
  
-But if both a and b are even, they are not coprime, which contradicts our original assumption. Therefore, √2 must be irrational.+But if both a and b are even, they are not coprime, which contradicts our original assumption. Therefore, 2 must be irrational.
 </code> </code>
  
tanszek/oktatas/techcomm/mathematical_expressions_in_tex_language.1725288721.txt.gz · Last modified: 2024/09/02 14:52 by kissa