Clarify that implementation is needed in the .m files

1) eulerMethod.m is not implemented and simply returns the initial
values
2) gauss2pt.m is not implemented and simply returns the average value
3) simpsonsRule.m is not implemented and simply returns 0
4) eulerMethodDE.m is not implemented and simply returns the initial
values
5) rk4.m is not implemented and returns nothing

If you are a faculty member who would like solution implementations for
reference, please contact [email protected]

Author: eszmw

NumericalIntegration/eulerMethod.m

@@ -1,19 +1,20 @@
-function [xApprox,yApprox]=eulerMethod(f,init,n,h)
-% The eulerMethod function takes four arguments
-% f is a function handle
-% init = x0 is the initial value
-% h is the step size and 
-% n is the number of steps to estimate
-% 
-% The function returns an (n+1)x2 matrix of 
-% estimated (xi,yi) values
-
-% Initialize the output with the initial value
-% Initialize the output with the initial value
-xApprox = nan(n+1,1);
-yApprox = nan(n+1,1);
-xApprox(1) = init;
-yApprox(1) = f(init);
-
-
+function [xApprox,yApprox]=eulerMethod(f,init,n,h)
+% The eulerMethod function takes four arguments
+% f is a function handle
+% init = x0 is the initial value
+% h is the step size and 
+% n is the number of steps to estimate
+% 
+% The function returns an (n+1)x2 matrix of 
+% estimated (xi,yi) values
+
+% Initialize the output with the initial value
+% Initialize the output with the initial value
+xApprox = nan(n+1,1);
+yApprox = nan(n+1,1);
+xApprox(1) = init;
+yApprox(1) = f(init);
+
+% Fill in the details of the implementation here
+
 end

NumericalIntegration/gauss2pt.m

@@ -1,11 +1,12 @@
-function Fapprox = gauss2pt(f,a,b)
-% gauss2pt takes three arguments
-% f is a function handle
-% a and b are the bounds of a definite integral
-%
-% Fapprox returns the Gaussian 2 point approximation of the 
-% integral from a to b of f(x) dx
-
-
-Fapprox = f((b+a)/2);
+function Fapprox = gauss2pt(f,a,b)
+% gauss2pt takes three arguments
+% f is a function handle
+% a and b are the bounds of a definite integral
+%
+% Fapprox returns the Gaussian 2 point approximation of the 
+% integral from a to b of f(x) dx
+
+% Fill in the details of the implementation here so your 
+% code will return a correct approximation of the area
+Fapprox = f((b+a)/2);
 end

NumericalIntegration/simpsonsRule.m

@@ -1,12 +1,14 @@
-function area = simpsonsRule(f,a,b,n)
-% simpsonsRule takes four arguments
-% f is a function handle
-% a and b are the endpoints of the integral
-% n is the number of intervals to use for the approximation
-%
-% area is the value computed by using a three-point Simpson's rule
-% approximation on each subinterval
-
-area = 0;
-
+function area = simpsonsRule(f,a,b,n)
+% simpsonsRule takes four arguments
+% f is a function handle
+% a and b are the endpoints of the integral
+% n is the number of intervals to use for the approximation
+%
+% area is the value computed by using a three-point Simpson's rule
+% approximation on each subinterval
+
+% Fill in the details of the implementation here so your 
+% code will return a correct approximation of the area
+area = 0;
+
 end

NumericalODEs/eulerMethodDE.m

@@ -1,19 +1,21 @@
-function [xApprox,yApprox]=eulerMethod(f,init,n,h)
-% The eulerMethod function takes four arguments
-% f is a function handle
-% init = [x0 f(x0)] is the initial condition
-% h is the step size and 
-% n is the number of steps to estimate
-% 
-% The function returns an (n+1)x2 matrix of 
-% estimated (xi,yi) values
-
-% Initialize the output with the initial value
-% Initialize the output with the initial value
-xApprox = nan(n+1,1);
-yApprox = nan(n+1,1);
-xApprox(1) = init(1);
-yApprox(1) = init(2);
-
-
+function [xApprox,yApprox]=eulerMethodDE(f,init,n,h)
+% The eulerMethodDE function takes four arguments
+% f is a function handle
+% init = [x0 f(x0)] is the initial condition
+% h is the step size and 
+% n is the number of steps to estimate
+% 
+% The function returns an (n+1)x2 matrix of 
+% estimated (xi,yi) values
+
+% Initialize the output with the initial value
+% Initialize the output with the initial value
+xApprox = nan(n+1,1);
+yApprox = nan(n+1,1);
+xApprox(1) = init(1);
+yApprox(1) = init(2);
+
+% Fill in the details of the implementation here
+
+
 end

NumericalODEs/rk4.m

@@ -1,9 +1,10 @@
-function [t,y] = rk4(f,tspan,y0,n)
-% rk4 implements a four-step Runge-Kutta method on function f
-%    over t = tspan(1) to t = tspan(2) where y(tspan(1))=y0 
-%    using n intervals
-%
-% t is a vector of t values and y is a vector of estimated y(t) values
-
-
+function [t,y] = rk4(f,tspan,y0,n)
+% rk4 implements a four-step Runge-Kutta method on function f
+%    over t = tspan(1) to t = tspan(2) where y(tspan(1))=y0 
+%    using n intervals
+%
+% t is a vector of t values and y is a vector of estimated y(t) values
+
+% Fill in the details of the implementation here
+
 end