Changed problem solving strategies tutorial to apply to computational methods. And added to TOC list in tutorials/readme.md

1 files changed, 11 insertions, 70 deletions

diff --git a/tutorials/module_2/2_problem_solving_strategies.md b/tutorials/module_2/2_problem_solving_strategies.md
index cfc9c19..1a50aec 100644
--- a/tutorials/module_2/2_problem_solving_strategies.md
+++ b/tutorials/module_2/2_problem_solving_strategies.md
@@ -1,6 +1,6 @@
 # Algorithmic thinking
 
-## ## Learning Objectives
+## Learning Objectives
 
 By the end of this lesson, students will be able to:
 
@@ -9,85 +9,50 @@ By the end of this lesson, students will be able to:
 - Use software tools to implement, test, and refine engineering solutions.
 
 ---
-
 ## 1. Define the Problem
 
-In many fields of engineering we must. Before writing code or building models, clearly define the engineering problem.
+Like many other classes we need to frame the problem before working it. So before jumping straight into coding or building models, clearly define the engineering problem.
 
 - **List knowns and unknowns.** What inputs are given? What outputs are required?
-    
 - **Establish system constraints and assumptions.** Identify physical laws, design requirements, and performance limits.
-    
 - **Clarify computational objectives.** What are you trying to calculate, simulate, or optimize?
-    
-
-**Example:** Given force and displacement data from a materials test, write a program to compute and plot stress-strain behavior.
 
 ---
+## 2. Think Algorithmically
 
-## 2. Develop a Strategy
-
-To think algorithmically, break the problem into logical steps that a computer can follow.
+Since we are going to use computers to calculate our solution we first need to break the problem into logical steps that a computer can follow.
 
 - **Define the inputs and outputs.** What variables will the program take in, and what results will it produce?
-- **Break the problem into sub-tasks.** Identify steps such as data input, processing, and visualization.
+- **Break the problem into sub-tasks.** Identify steps such as data input, logic processing and output.
 - **Outline the algorithm.** Write pseudocode or flowcharts that describe the computational steps.
 - **Identify patterns or formulas.** Can loops, conditionals, or equations be used to automate parts of the solution?
-    
 
 **Example:** For processing stress-strain data:
-
 1. Import data from a file.
 2. Convert force and displacement to stress and strain.
 3. Plot the stress-strain curve.
 4. Identify the yield point or modulus.
-    
 
 ---
+## 3. Write & Execute the Code
 
-## 3. Execute the Code
-
-- **Choose the right tools.** Use Python, MATLAB, or similar platforms.
+- **Choose the right tools.** Are there libraries I can use to get to my objective more effectively?
 - **Write modular code.** Use functions to separate different tasks (e.g., reading data, computing values, plotting).
 - **Check for syntax and logic errors.** Debug line-by-line using print statements or a debugger.
 
 **Example:** Write a Python script that uses NumPy and Matplotlib to load a CSV file, compute stress and strain, and generate plots.
 
 ---
-
 ## 4. Test and Validate
 
-- **Run test cases.** Use small inputs with known outputs to check correctness.
-- **Compare with theoretical or experimental results.** Does the output match expected behavior?
+- **Assess the feasibility of your results.** Do the values align with expected physical behavior?
+- **Compare against established benchmarks.** Validate solutions using experimental data, literature values, or known theoretical limits.
 - **Check units and scaling.** Ensure computations are consistent with physical meaning.
 
 **Example:** If your plot shows stress values in the thousands when you expect hundreds, check unit conversions in your formula.
 
 ---
-
-## 5. Refine and Optimize
-
-- **Improve readability and efficiency.** Refactor code to use vectorized operations or clearer variable names.
-- **Add flexibility.** Allow the user to change input files or parameters without modifying code.
-- **Document the process.** Include comments and a user guide.
-
-**Example:** Upgrade your script so that it can analyze any stress-strain dataset provided in a CSV file with minimal setup.
-
----
-
-## 6. Troubleshooting Strategies
-
-When your code doesn’t work as expected:
-
-- **Isolate the error.** Use print statements or breakpoints to trace the bug.
-- **Check assumptions.** Are inputs being read correctly? Are formulas implemented correctly?
-- **Consult documentation.** Use official libraries’ documentation or community resources like Stack Overflow.
-
-**Example:** If an array is returning NaN values, check whether division by zero is occurring or if missing data is in the input file.
-
----
-
-## 7. Case Study: Simulating a Spring-Mass System
+## Case Study: Simulating a Spring-Mass System
 
 **Scenario:** Model the motion of a mass-spring-damper system using a numerical solver.
 
@@ -96,28 +61,4 @@ When your code doesn’t work as expected:
 3. **Execute the Code:** Write a Python function that computes motion over time.
 4. **Test the Model:** Compare results with analytical solutions for undamped or lightly damped systems.
 5. **Refine the Model:** Add adjustable damping and stiffness parameters.
-6. **Troubleshoot Issues:** If the model becomes unstable, reduce the time step or use a more accurate integrator.
-
----
-## Summary
-
-To solve engineering problems with computers:
-
-1. **Define the problem and computational goals.**
-2. **Develop an algorithmic strategy.**
-3. **Implement the solution in code.**
-4. **Test and validate with known cases.**
-5. **Refine the code and enhance usability.**
-6. **Troubleshoot and learn from failures.**
-
-With algorithmic thinking and the right tools, engineers can automate analysis, simulate systems, and make data-driven decisions more efficiently.
-
----
-
-## 4. Verify and Interpret Results
-
-- **Assess the feasibility of your results.** Do the values align with expected physical behavior?
-- **Compare against established benchmarks.** Validate solutions using experimental data, literature values, or known theoretical limits.
-- **Conduct a sensitivity analysis.** Examine how slight variations in input parameters influence the outcome.
-
-**Example:** If a rocket nozzle expansion ratio results in an unrealistic exit velocity, revisit the assumptions regarding isentropic flow and compressibility effects.
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+6. **Troubleshoot Issues:** If the model becomes unstable, reduce the time step or use a more accurate integrator.
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