Class Notes (810,860)
United States (314,398)
ENG 6 (40)
Lecture 10

# ENG 06: Engineering Problem Solving with MATLAB – Lecture 10 notes

3 Pages
63 Views

School
University of California - Davis
Department
Engineering
Course
ENG 6
Professor
Professor Rajeevan Amirtharajah
Semester
Spring

Description
ENG 06 – Lecture 10; 2/7/2013 Interpolation and Curve Fitting  Least squares regression: minimizes area between data and line you predict  polyfit: fits line to data  polyval: takes coefficients of polynomial (for example, from polyfit) and a vector of x points to evaluate at that polynomial  Regression example: linear fit o Torque needed to turn torsion spring of mousetrap through an angle is given in data points o Find constants for model given by T = k1 + k2x  >> xp=[0.698132, 0.959931, 1.134464, 1.570796, 1.919862];  >> yp=[0.188224, 0.209138, 0.230052, 0.250965, 0.313707];  >> coeffs = polyfit(xp,yp,1);   >> xfit=[0.6:0.01:2];yfit = polyval(coeffs,xfit);  >> plot(xp,yp,'O'); hold on; plot(xfit,yfit); hold off;  >> coeffs  coeffs = 0.0961 0.1177  Interpolation or Regression? o For acceleration/velocity/distance problems, need to differentiate and integrate o Best to fit a known function that can be “easily differentiated or integrated o Use a spline fit  physics of gravity tells us that it should follow a smooth curve  Gives us just one function to work with  Fitting to More complicated functions o Linearizing: making a few substitutions for variables which result in an equation for a line  Linear vs. Nonlinear fitting o Linear in terms of fitting constants:  Y = a + bt  Y = a + bt + ct^2  y = asin(t) + bcos(t)  y = asin(3t)  y = ae^-t o Not linear in terms of all the fitting constants  y = asin(bt) + ccos(dt)  y = asing(bt)  y = ae^-bt  Linearizing Commonly Found Nonlinear functions o Log functions:  y = Klog(x) + c  Looks like a straight line when you plot y values vs. log of x values  plot(log(x),y)  also semilogx(x,y)  creates a logarithmic x axis o Exponential functions: y = Ce^Kx  Plot log of y values vs. x values to make it look like a straight line  plot(x,log(y))  can also use semilogy(x,y)  creates an exponential y axis
More Less

Related notes for ENG 6

Log In

OR

Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.

Request Course
Submit