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+# 29) HW3 Solution
+
+In this assignment we covered some of the topics of the Fortran programming language seen in class, such as some basic I/O.
+
+We revisted an interpolation method seen in class, [Lagrange's interpolation method](https://sdsu-comp526.github.io/fall24/slides/module7-1_interpolation.html), and we learned how to _use_ Lagrange’s interpolating formula to approximate a function $f(x)$ over a domain $[a,b]$.
+
+Remeber: Interpolation $\neq$ Function Approximation.
+
+But we can _use interpolation_ to accurately _approximate_ continuous functions.
+
+
+```{literalinclude} ../fortran_programs/midterm/main_lagrange.f90
+:language: fortran
+:linenos: true
+```
+
+## Extra Credit Question in Julia
+
+The Fortran program above produced the appximating polynomial over a domain of 50 equally spaced points. Let's use Julia to read these values in, plot the original function $f(x)$, the approximating interpolating polynomial $p(x)$ and the discrete set of data points $(x_i,y_i)$.
+
+```julia
+using Plots
+using LaTeXStrings
+default(linewidth=4, legendfontsize=12)
+
+s = 50
+x_domain = LinRange(0,2,s)
+p = zeros(length(x_domain))
+
+f(x) = exp.(-3 .* x)
+
+x_data = LinRange(0,2,5)
+y_data = f.(x_data)
+
+# open output.txt data and store values in the array called p
+open("output.txt","r") do f
+    line = 1
+    while ! eof(f)
+        l = readline(f)
+        p[line] = parse.(Float64,l)
+        line += 1
+    end
+end
+
+# Plots
+scatter(x_data,y_data, markersize = 6, label = L"(x_i, y_i)")
+png(plot!(x_domain, [f.(x_domain) p ], linestyle = [:solid :dash], label = [" exp(-3x)" "p(x)"], title="Lagrange interpolation"), "lagrange_plot.png")
+```