Updated tutorials

12 files changed, 35 insertions, 8 deletions

diff --git a/tutorials/module_1/functions.md b/tutorials/module_1/functions.md
index 54c956d..a3d291d 100644
--- a/tutorials/module_1/functions.md
+++ b/tutorials/module_1/functions.md
@@ -5,6 +5,7 @@ Like a traditional mathematical functions, python functions can take an input, p
 Functions are defined by using the <code> def </code> keyword. Reminder: it is important to keep track of indentations as it signifies the end of the function when the indentation returns back to the same level.
 
 ## Defining Functions
+
 ### Simple function
 A simple function with no input variable can be useful if you need to re-use code multiple times without having to re-write it.
 
@@ -22,6 +23,7 @@ We can pass variables through to the function to be processed as follows:
 ```
 
 Note input variables can be of any data type (integer, float, string, etc.).
+
 ### Returning values from a function
 If we want to calculate a value and pass it back to the script for further use, we can use the `return` keyword. Let's define a linear function that takes two inputs, `x` and `b`, computes the corresponding `y` value, and returns it so it can be used elsewhere in the code.
 
@@ -32,6 +34,7 @@ If we want to calculate a value and pass it back to the script for further use,
 ```
 
 For multiple output variables we can add 
+
 ## Calling functions
 Now that we've covered defining functions we want to call the function in order to execute the block inside the function. To do this, we simply re-call the function name as follows.
 
diff --git a/tutorials/module_1/installing_anaconda.md b/tutorials/module_1/installing_anaconda.md
index c6a434d..62d8f56 100644
--- a/tutorials/module_1/installing_anaconda.md
+++ b/tutorials/module_1/installing_anaconda.md
@@ -1,11 +1,13 @@
 # Installing Anaconda
 
+^57b499
+
 This tutorial will cover the steps on how to install Anaconda. 
 
 *Note for Advanced users: For those who wish to have a lightweight installation, can install miniconda or miniForge, however for this course we will show you how to use Anaconda Navigator. If you've never used the programs before then using Anaconda is recommended.*
 
 ### What is Anaconda?
-Anaconda Distribution is a popular open-source Python distribution specifically designed for scientific computing, data science, machine learning, and artificial intelligence applications. It simplifies the set up and use of Python for data science, machine learning, and scientific computing. It comes with all the important tools you need, like NumPy, Pandas, and JupyterLab, so you don’t have to install everything separately. The Conda package manager helps you install and update software without worrying about breaking other programs. It also lets you create separate environments, so different projects don’t interfere with each other. Additionally, Anaconda includes programs like JupyterLab for interactive coding, and Spyer a MATLAB-like IDE.
+Anaconda Distribution is a popular open-source Python distribution specifically designed for scientific computing, data science, machine learning, and artificial intelligence applications. It simplifies the set up and use of Python for data science, machine learning, and scientific computing. It comes with all the important tools you need, like NumPy, Pandas, and JupyterLab, so you don’t have to install everything separately. The Conda package manager helps you install and update software without worrying about breaking other programs. It also lets you create separate environments, so different projects don’t interfere with each other. Additionally, Anaconda includes programs like JupyterLab for interactive coding, and Spyder a MATLAB-like IDE.
 
 
 ## Instructions
diff --git a/tutorials/module_1/intro_to_anaconda.md b/tutorials/module_1/intro_to_anaconda.md
index 05fe686..f123836 100644
--- a/tutorials/module_1/intro_to_anaconda.md
+++ b/tutorials/module_1/intro_to_anaconda.md
@@ -1,5 +1,7 @@
 # Introduction to Anaconda Navigator
 
+^ebc35b
+
 Anaconda Navigator is a program that we will be using in this course to manage Python environments, libraries and launch programs to help us write our python code.
 
 The Anaconda website nicely describes *Navigator* as:
diff --git a/tutorials/module_1/intro_to_programming.md b/tutorials/module_1/intro_to_programming.md
index 2f12a3a..d3e1845 100644
--- a/tutorials/module_1/intro_to_programming.md
+++ b/tutorials/module_1/intro_to_programming.md
@@ -1,4 +1,7 @@
 # Introduction to Programming
+
+^675b86
+
 ## The Importance of Programming in Engineering
 
 Engineering is all about solving problems, designing innovative solutions, and making systems work efficiently. Whether you’re designing cars, airplanes, rockets, or even everyday machines, programming plays a critical role in modern engineering.
diff --git a/tutorials/module_1/notebook_1/control_structures.ipynb b/tutorials/module_1/notebook_1/control_structures.ipynb
index dc40faa..4b0f049 100644
--- a/tutorials/module_1/notebook_1/control_structures.ipynb
+++ b/tutorials/module_1/notebook_1/control_structures.ipynb
@@ -369,7 +369,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.9"
+   "version": "3.13.2"
   }
  },
  "nbformat": 4,
diff --git a/tutorials/module_1/spyder_getting_started.md b/tutorials/module_1/spyder_getting_started.md
index faa5db5..b6a40ee 100644
--- a/tutorials/module_1/spyder_getting_started.md
+++ b/tutorials/module_1/spyder_getting_started.md
@@ -1,5 +1,7 @@
 # Getting started with Spyder
 
+^92e0ab
+
 In this tutorial we will cover the basics of using the Spyder IDE (Interactive Development Environment). If you've ever worked with MATLAB before, then this will feel familiar. Spyder is a program that allows you to write, run and de-bug code.
 
 ## Launching Spyder
diff --git a/tutorials/module_2/ai_assisted_programming.md b/tutorials/module_2/ai_assisted_programming.md
index 63479cc..4db6d9d 100644
--- a/tutorials/module_2/ai_assisted_programming.md
+++ b/tutorials/module_2/ai_assisted_programming.md
@@ -8,7 +8,7 @@ Don't try to get AI to do work *for you* but *with you*. You need to understand
 
 AI is a great learning tool, research as show that students can benefit from using AI as personal tutor [more](https://hbsp.harvard.edu/inspiring-minds/ai-as-personal-tutor).
 
-# Language based vs 
+## Language based vs Machine Learning
 ## Available tools
 Below is a comprehensive list of tools that are available at not cost to you.
 
diff --git a/tutorials/module_2/num_methods_1.md b/tutorials/module_2/num_methods_1.md
index 6d1ded3..1ab4fa8 100644
--- a/tutorials/module_2/num_methods_1.md
+++ b/tutorials/module_2/num_methods_1.md
@@ -1,5 +1,7 @@
 # Solving non-linear equations
 
+^ca27a3
+
 ## Introduction
 
 
diff --git a/tutorials/module_2/problem_solving_strategies.md b/tutorials/module_2/problem_solving_strategies.md
index c7f8dfd..0767c73 100644
--- a/tutorials/module_2/problem_solving_strategies.md
+++ b/tutorials/module_2/problem_solving_strategies.md
@@ -41,6 +41,7 @@ When writing code it is crucial to test and confirm your code. It is therefore i
 ## Exercise: Rubrics Cube problem
 
 
+
 ## Exercise: Design a derivative finding algorithm
 Set up the problem and write pseudo-code to calculate the gradient of an unknown function.
 
diff --git a/tutorials/module_3/numerical_methods.md b/tutorials/module_3/numerical_methods.md
index 4b3f39a..449ece0 100644
--- a/tutorials/module_3/numerical_methods.md
+++ b/tutorials/module_3/numerical_methods.md
@@ -8,7 +8,7 @@ Numerical methods are techniques that transform mathematical problems into forms
 ## Numerical Differentiation
 Forwards difference
 Backwards difference
-
+Central Difference method
 [Read More](https://pythonnumericalmethods.studentorg.berkeley.edu/notebooks/chapter20.00-Numerical-Differentiation.html)
 
 ## Roots and Optimization
@@ -17,11 +17,16 @@ Bisection
 Modified Secant
 Newton-Raphson
 
+## System of Equations
+Guassian Method
+LU Decomposition
 
 ## Numerical Integration
 
+Midpoint
 Trapezoidal
-
+Romberg
+Gaussian
 Simpson's Rule
 
 [Read More](https://pythonnumericalmethods.studentorg.berkeley.edu/notebooks/chapter21.00-Numerical-Integration.html)
diff --git a/tutorials/module_3/supersonic.md b/tutorials/module_3/supersonic.md
deleted file mode 100644
index 92b3545..0000000
--- a/tutorials/module_3/supersonic.md
+++ /dev/null
@@ -1,2 +0,0 @@
-# Supersonic
-
diff --git a/tutorials/module_3/system_of_equations.md b/tutorials/module_3/system_of_equations.md
index e3ae314..9830060 100644
--- a/tutorials/module_3/system_of_equations.md
+++ b/tutorials/module_3/system_of_equations.md
@@ -1,2 +1,11 @@
-# System of Equations
+# Systems of Equations
+
+
+## Naive Gauss Elimination
+
+## Forward Elimination
+
+## Back Substitution
+
+## LU Decomposition