The initial heat over a steel plate is given by the function:
Plot the surface over the grid defined by: −2.1 < x < 2.1, −6 < y < 6, where the grid width is 0.15 in both directions.
x = -2.1:0.15:2.1;
y = -6:0.15:6;
for i = 1:numel(x)
for k = 1:numel(y)
U(i,k) = 80*(y(k). ∧ 2).*(exp(-x(i). ∧ 2-0.3*y(k). ∧ 2));
Draw a graph of the population of the USA from 1790 to 2000, using the following model:
Where t is the date in years.
Actual data (in 1000s) for every decade from 1790 to 1950 are as follows:
3929, 5308, 7240, 9638, 12866, 17069, 23192, 31443, 38558, 50156, 62948, 75995, 91972, 105711, 122775, 131669, 150697. Superimpose this data on the graph P(t) (plot this data in circles and red, and do not join them with lines).
t = 1790:10:2000;
for i = 1:numel(t)
P(i) = 197273000/(1+exp(-0.03134*(t(i)-1913.25)));
The spiral of Archimedes may be represented in polar coordinates by the equation:
Where a is some constant, write some command-line statements to draw the spiral for some value of r.
a = 2;
q = 1.25;
th = 0:pi/40:5*pi;
plot(a*th.*cos(th), a*th.*sin(th)), ...
title('(a) Archimedes') % or use polar
plot(a/2*q. ∧ th.*cos(th), a/2*q. ∧ th.*sin(th)), ...
title('(b) Logarithmic') % or use polar
A rather beautiful fractal picture can be drawn by plotting the points (xk, yk) generated by the following difference equations:
Starting with x0=y0=0. Write a program to draw the picture (plot individual points; do not join them).
x(1) = 0;
y(1) = 0;
for i = 2:1000
x(i) = y(i-1)*(1+sin(0.7*x(i-1))) - 1.2*sqrt(abs(x(i-1)));
y(i) = 0.21 - x(i-1);
*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.
Graphics, Part 3
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
Educator.com recommends MATLAB and Simulink to use with our MATLAB course. MATLAB - Solve numerical problems quickly, so you can focus on coursework and projects rather than programming. Simulink - Model, simulate, and analyze dynamic systems. Target hardware support - Run Simulink models on Arduino, LEGO MINDSTORMS NXT, Raspberry Pi, and other hardware. 10 add-on products for math, statistics, and optimization; controls; signal and image processing; and test and measurement. The package includes a software activation key with instructions to download and install Student Version from www.mathworks.com