College of Engineering and Computing

Department of Civil and Environmental Engineering

CGN 2420 – Computer Tools for Engineers

HOMEWORK 7:

Recommended Practice:

Chapter 4: 4.2, 4.3, 4.6, 4.9, 4.10, 4.12.

Chapter 5: 5.1, 5.6, 5.7, 5.9, 5.11, 5.16, 5.18, 5.19, 5.20.

Mandatory Problems:

1.- Given the following matrices and vectors:

? =

4 6 −1 3

? =

2 1 2 6 5 9 4 −4

? = 1 3 2 5 2 10 2 −6

? =

2 3 7 11 1 4 3 9 0 6 5 1 1 8 4 2

Define the matrices in Mathcad and solve for the following operations: a) BT transpose of matrix B.

b) B . V multiply matrix B by vector V.

c) |C| determinant of matrix C.

d) C-1 inverse of matrix C

e) AT+ B add matrix A transposed to matrix B.

f) AT . V multiply matrix A transposed by vector V.

g) [C] . x = V, solve for x using Cramer’s rule.

h) [C] . x = V, solve for x using function lsolve, then check solution as x = C-1 . V

2.- Let us suppose you got a job with Calculus City, and your tremendous mathematical skills made your boss give you the following assignment:

Determine the area of a park under development, so that the correct amount of some very expensive grass can be purchased for it. In the city records you find the following data that correspond to the streets bounding the park, dimensions are in kilometers.

1.- Coral Av. can be represented by the equation y(x) = x – 1 2.- Flagler St. is perfectly horizontal. 3.- Coordinates for Avila St. are as follows

x y 0 0

0.1 0.3 0.2 0.4 0.3 0.5 0.5 0.65

0.75 0.87 1 1.00

1.4 1.18 1.8 1.34 2.2 1.48 2.6 1.61 3 1.66

Upload Mathcad file and corresponding PDF file in Canvas.

Flagler St.

Calculus City Records

Use Mathcad to perform the area calculation. a) Use linfit to find a second order polynomial to fit the data given for Avila St. b) Find the point of intersection between Avila St. and Coral Av. c) Use the calculus tool bar to properly determine the area of the park. Check section 8.2 of your Mathcad textbook if you want to learn more about integration in Mathcad.