gibson:teaching:spring-2018:math445:lab1

Most of these problems are taken from Attaway chapter 1, both 2nd and 3rd editions. Remember, Matlab's *help* function is your friend.

**Problem 1:** Evaluate these Matlab expressions in your head and write down the answer.
Then type them into Matlab and see how Matlab evaluates them. If you made a mistake, figure out what it was.

2/3

25/4*4

3+4^2

4\12 + 4

3^2

(5-2)*3

4*3^2-7

1.7 - 1.4 - 0.3

**Problem 2:** Translate these mathematical expressions into Matlab expressions, and then evaluate them.

cube root of 19

3 to the 1.2

tangent of

**Problem 3:** Are any of your answers for problems 1 and 2 surprising? Which, and why?

**Problem 4:** Wind chill factor: The WCF supposedly conveys how cold it feels with a given air
temperature T (degrees Farenheit) and wind speed V (miles per hour). A formula
for WCF is

Create variables for temperature T and wind speed V and then using this formula, calculate the WCF for

**(a)** T = 20 F and V = 0 mph

**(b)** T = 20 F and V = 10 mph

**(c)** T = 20 F and V = 20 mph

**Problem 5:** The geometric mean g of n numbers is given by

This is useful, for example, in finding the average rate of return on an investment with varying yearly return.

**(a)** If an investment returns 15% its first year, 5% its second, and 10% its third, the average rate of return is

Compute the average rate of return, expressed as a percent.

**(b)** Which is better for the investor, a steady 5% per year return on investment, or alternating between 0% and 10% year by year?

**Problem 6:** The astoundingly brilliant but short-lived mathematician Srinivasa Ramanujan devised the following very powerful formula for for

You can get an approximation of using only arithmetic operations by evaluating and summing a finite number of terms of this series. What is the numerical approximation of using just the first term ()? Using the first and second ( and )? How many digits of accuracy does each of these approximation have? Be sure to use `format long`

.

(adapted from a problem in *Introduction to Matlab Programming* by Siauw and Bayen)

gibson/teaching/spring-2018/math445/lab1.txt · Last modified: 2018/01/22 20:13 by gibson