\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}