1

ChE-121

ASSIGNMENT No. 1

First Due (Marked 100% basis): Jan 20th, 2016, 9:00pm

Second and final due (Marked 70% basis): Jan 21st, 2016, 9:00pm

Instructions: Solve the problems by hand, scan your work and submit a pdf

document to the corresponding drop box on the course website. DO NOT

use any of the MATLAB built-in functions to write the algorithms.

1. Follow-up exercise: Draw a flowchart the returns the factorial of a number N.

Your flowchart must return an error if the user enter an invalid N, e.g. a negative

or real number N, and should also consider the case of N=0.

2. In mathematics, functions can often be represented by infinite series. For

example, the exponential function can be computed using:

!...

!3!21)exp(

32

n

xxxxx

n

where n represents the number of terms that are included in the infinite series

function to compute exp(x). The error in the computation of exp(x) using the

infinite series can be evaluated from as follows:

%100*true

approxtrueerror

where true represents the true value, obtained from the direct evaluation of exp(x),

whereas approx represents the value computed from the infinite series.

Design a flowchart that computes the exponential function using the infinite series

approximation. The flowchart will ask the user for the value in x that will be

evaluated and the number of terms n to be considered in the series. The flowchart

must print the value obtained from the series and the error associated with that

calculation. Assume that the symbol ! can be used in the flowchart to denote the

computation of a factorial number.

3. Draw a flowchart and write a Pseudocode that displays the roots of any second

order algebraic equation, e.g. ax2+bx+c=0.

4. A Fibonacci sequence is a sequence of numbers f0, f1, f2, f3, …, in which the

first two values (f0 and f1) are equal to 1, and each succeeding number is the sum

of the previous two numbers. Thus, the first few values of the Fibonacci sequence

are:

1 1 2 3 5 8 13 21 34 …

A function that computes the Fibonacci sequence is as follows:

2

1)2()1(

1,0 1)(

nnfnf

nnnf

Design a flowchart that returns the sum of all the elements included in a Fibonacci

sequence of n elements. The only input to the flowchart will be the integer

number n, which determines the number of elements in the Fibonacci sequence.

Assume that the user enters an integer number.

5. Draw a flowchart and write a Pseudocode that displays the number of positive,

negative and zero elements are in a vector of length N.