Summary

Engineering Science II Laboratory #02

Vector and Vector Calculus Visualization in 3D

In this laboratory experience, you will explore vector calculus and its applications in EE science. The lab guides you through a set of concepts, such as vectors, dot product, cross product, gradient, divergence, and curl. You will calculate vectors and perform vector operations between the three major coordinate systems – Cartesian, cylindrical and spherical – after which you will calculate and plot results in a 3D space. There will be a summary on the use of MATLAB, as a software tool for carrying out the calculations learned during the lab experience.

During this lab, you will:

a) Understand the use of coordinate systems to represent 3D vector operations.

b) Study the three most fundamental coordinate system transformations (Cartesian, cylindrical, and spherical coordinate systems)

c) Develop basic skills in the use of MATLAB to manage vector operations (i.e. dot product, cross product, gradient, divergence, and curl)

d) Improve your understanding of vector calculus by plotting vectors in Cartesian, cylindrical and spherical coordinate systems.

e) Gain knowledge about vector fields and relevant applications in Electrical Engineering. By the end of this experience, you should be able to understand how to transform vectors and points between

coordinate systems. Also, you should comprehend the concept of vector fields in two-dimensional and three- dimensional spaces. Likewise, you will get a sense on the physical meaning of the Curl, Divergence and Gradient operators – more specifically, their importance when applied to engineering situations.

Laboratory Report (post lab) this what post lab should include (see last page in the exp) its more clear

see the template (post lab format)

1

A one paragraph summary of the laboratory assignment.

5 pt

2

What is the physical meaning of the gradient operator?

1 pt

3

How does the MATLAB command diff(T,x) help solve problems involving the gradient?

0.5 pt

4

Explain curl.

1 pt

5

Explain divergence.

1 pt

6

Fill in the blanks with the words scalar or vector:

The gradient operator is applied to a ____________ field and the answer is a _________ field.

The divergence operator is applied to a __________ field and the answer is a __________ field.

The curl operator is applied to a ___________ field and the answer is a ___________ field.

0.25pt for each blank

{Optional} – Suggestions to improve the laboratory experience.