gibson:teaching:spring-2016:math445:exam1sample

The exam will have around ten questions, some easy, some not so easy. For most questions, you will be asked to answer with Matlab code in correct syntax. E.g.

**Problem 1:** (totally straightforward) Given a matrix , write one line of Matlab code that would assign the 3rd row of into the variable .

**Problem 2:** (slightly tricky) Given a matrix , write one line of Matlab code that convert the th column of into a row vector and assign it to the variable .

**Problem 3:** (pretty straightforward) Given a vector , write one or two lines of Matlab code that would return all the odd-numbered elements of . (By “odd-numbered elements”, I mean the elements with odd indices, e.g. .)

**Problem 4:** (moderate) Write Matlab code that defines a function named `mysin`

that computes using the truncated power series

**Note: an earlier version of this problem had an error in the Taylor series of** .

**Problem 5:** (straightforward) Write Matlab code that would solve the system of equations.

**Problem 6:** (straightforward) Write a Matlab function that computes the mean (i.e. average) of
the components of a vector according to the formula

where is the length of the vector. Your function should evaluate this
sum directly using a **for** loop, not by calling Matlab's **sum** or
**mean** function. You did this for lab, now see if you can do it without looking at notes.

**Problem 7:** (straightforward) Write a few lines of Matlab code that would plot versus on the interval using a red dashed line. Label the axes.

**Problem 8:** (a little harder than 7) Write a few lines of Matlab code that would plot on the interval , using the plotting function that would best highlight the functional relation between and . Label the axes.

**Problem 9:** Deduce the functional relationship from this graph.

gibson/teaching/spring-2016/math445/exam1sample.txt · Last modified: 2016/03/02 12:38 by gibson