Simulate and illustrate a waterfall plot and an x-t diagram for Burgers equation, evolution in time using the following data: Diffusion constant                        =  0.003Length of domain                          = 40  Number of discretization points  = 2000   **Please upload all the generated images in one file.

Fourier transform is fundamental in computational mathematics, enabling real-time image and audio compression, global communication networks, modern devices and hardware, numerical physics, engineering at scale, and advanced data analysis.

Match different type of Fourier method:

The Singular Value Decomposition (SVD) is not numerically stable for providing a hierarchical representation of the data based on a new coordinate system defined by dominant correlations within the data.

Which of the following is a true statement about the talocrural joint in comparison to the hip joint?

A soccer player was in a game and had an impact from behind to his/her standing leg sending his/her knee into a valgus moment. What would this mechanism of injury MOST LIKELY result in?

You want to facilitate knee extension and want to mobilize the patellofemoral joint to facilitate the patella’s normal gliding from flexion to extension. In which direction would you mobilize the patella to facilitate its normal gliding?

An individual with genu valgus -“knocked knees”- could very likely exhibit an associated hip and foot deformity. What do you expect at the hip level and the foot level?

________________________________________ is defined as an increase of the angle of inclination of the femoral neck-head on the femoral shaft that is greater than 150 degrees.

A patient with neck pain brings you a picture of his workstation. You observe that the patient sits with a forward head position to maintain his eyes in line with the computer screen. What changes in the spine curvature do you observe?