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diff --git a/book/module2/problem_solving_strategies.tex b/book/module2/problem_solving_strategies.tex new file mode 100644 index 0000000..4b908f8 --- /dev/null +++ b/book/module2/problem_solving_strategies.tex @@ -0,0 +1,127 @@ +\section{Algorithmic thinking}\label{algorithmic-thinking} + +\subsection{Learning Objectives}\label{learning-objectives} + +By the end of this lesson, students will be able to: + +\begin{itemize} +\tightlist +\item + Apply algorithmic thinking to solve engineering problems using + computational tools. +\item + Translate engineering problems into structured programming logic. +\item + Use software tools to implement, test, and refine engineering + solutions. +\end{itemize} + +\subsection{Define the Problem}\label{define-the-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. + +\begin{itemize} +\tightlist +\item + \textbf{List knowns and unknowns.} What inputs are given? What outputs + are required? +\item + \textbf{Establish system constraints and assumptions.} Identify + physical laws, design requirements, and performance limits. +\item + \textbf{Clarify computational objectives.} What are you trying to + calculate, simulate, or optimize? +\end{itemize} + +\subsection{Think Algorithmically}\label{think-algorithmically} + +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. + +\begin{itemize} +\tightlist +\item + \textbf{Define the inputs and outputs.} What variables will the + program take in, and what results will it produce? +\item + \textbf{Break the problem into sub-tasks.} Identify steps such as data + input, logic processing and output. +\item + \textbf{Outline the algorithm.} Write pseudocode or flowcharts that + describe the computational steps. +\item + \textbf{Identify patterns or formulas.} Can loops, conditionals, or + equations be used to automate parts of the solution? +\end{itemize} + +\textbf{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. + +\subsection{Write \& Execute the Code}\label{write-execute-the-code} + +\begin{itemize} +\tightlist +\item + \textbf{Choose the right tools.} Are there libraries I can use to get + to my objective more effectively? +\item + \textbf{Write modular code.} Use functions to separate different tasks + (e.g., reading data, computing values, plotting). +\item + \textbf{Check for syntax and logic errors.} Debug line-by-line using + print statements or a debugger. +\end{itemize} + +\textbf{Example:} Write a Python script that uses NumPy and Matplotlib +to load a CSV file, compute stress and strain, and generate plots. + +\subsection{Test and Validate}\label{test-and-validate} + +\begin{itemize} +\tightlist +\item + \textbf{Assess the feasibility of your results.} Do the values align + with expected physical behavior? +\item + \textbf{Compare against established benchmarks.} Validate solutions + using experimental data, literature values, or known theoretical + limits. +\item + \textbf{Check units and scaling.} Ensure computations are consistent + with physical meaning. +\end{itemize} + +\textbf{Example:} If your plot shows stress values in the thousands when +you expect hundreds, check unit conversions in your formula. + +\subsection{Case Study: Simulating a Spring-Mass +System}\label{case-study-simulating-a-spring-mass-system} + +\textbf{Scenario:} Model the motion of a mass-spring-damper system using +a numerical solver. + +\begin{enumerate} +\def\labelenumi{\arabic{enumi}.} +\tightlist +\item + \textbf{Define the Problem:} Set up the differential equation from + Newton's Second Law. +\item + \textbf{Develop a Strategy:} Discretize time, apply numerical + integration (e.g., Euler or Runge-Kutta). +\item + \textbf{Execute the Code:} Write a Python function that computes + motion over time. +\item + \textbf{Test the Model:} Compare results with analytical solutions for + undamped or lightly damped systems. +\item + \textbf{Refine the Model:} Add adjustable damping and stiffness + parameters. +\item + \textbf{Troubleshoot Issues:} If the model becomes unstable, reduce + the time step or use a more accurate integrator. +\end{enumerate} |