Matlab exercise 1-4 | Mathematics homework help

Exercise 1

1. Arithmetic operations:

a) 3^6/(3^6 − 1) compare with (1 − 1/3^6 )^−1

b) 2 √7 − 2 (√7 + 2)2 − 1

c) Area = πr2 with radius r = π^1/3 − 1

2. Exponential and logarithms:

a) e^3 , ln e^3 , log10 e^3 , log10(10^5)

b) e^π√163

c) solve 3^x = 17 for x and check the result (soluton x = ln 17 / ln 3 , check by substitution)

3. Trigonometry:

a) sin π/6 , cos π , tan π/2

b) sin^2 π/6 + cos^2 π/6

c) y = cosh^2 x − sinh^2 x for x = 32π

4. Complex numbers:

a) (3 + 2i)/( 3 − 2i) , check the result by hand calculation

b) e^i/π5 , check the Euler-formula eix = cos x + isin x by computing both sides of the equation

c) execute the commands exp(pi/2*i) and exp(pi/2i) explain the difference

Exercise 2

1. Equation of straight line:

Compute the y-coordinate of the straight line

y = mx + c

with slope m = 0.5 and the intercept c = −2 at the following x-coordinates

x = 0, 1.5, 3, 4, 5, 7

2. Multiply, divide, and exponentiate vectors:

Create a vector t with 10 elemts: 1, 2, 3, . . . , 10 and compute the following

quantities:

x = tsin(t), y = (t − 1)/( t + 4) , z = sin(t^2)/t^2

3. Points on a circle:

All points with coordinates:

x = r cos θ , y = r sin θ , r = const

lie on a circle with radius r, i.e., they satisfy the

equation

x^2 + y^2 = r^2

a) Create a column vector for θ with the elements

0, π/4, π/2, 3π/4, π, 5π/4

b) Take r = 2 and compute the column vectors x and y.

c) Check that x and y satisfy the equation of circle, by computing the radius

r = (x^2 + y^2)^1/2

4. Matrices and vectors::

a) Create a vector and a matrix with the following commands:

v=0:0.2:12;

M=[sin(v); cos(v)];

b) Find the size of v and M.

c) Extract the first 10 elenents of each row of the matrix, and display them

as column vectors.

Exercise 3.

1. On-line help:

Type help function to get on-line help on function. Read through the help file.

2. Convert temperature:

Write a function that outputs a conversion-table for Celsius and Fahrenheit temperatures. The input of the function should be two numbers: Ti and Tf, specifying the lower and upper range of the table in Celsius. The output should be a two column matrix: the first column showing the temperature in Celsius from Ti to Tf in the increments of 1oC and the second column showing the corresponding temperatures in Fahrenheit.

a) create a column vector C from Ti to Tf

b) calculate the corresponding numbers in Fahrenheit: F= 9/5C + 32

c) make a final matrix temp=[C F]

3. Calculate factorials:

Write a function factorial to compute the factorial n! for an y integer n.The input should be the number n and the output n!. You might have to use a for loop or a while loop to do the calculation. (You can use the built-in function prod to calculate factorials. For example n!=prod(1:n). In this exercise use this function only for control.)

4. Compute the cross product:

Write a function file crossprod to compute the cross product of two vectors u, and v, given u = [u1, u2, u3], v = [v1, v2, v3], and u × v = [u2v3−u3v2, u3v1−u1v3, u1v2 −u2v1]. Check your function by taking cross products of pairs of unit vectors: (i,j), (i, k), etc. i = [1, 0, 0], j = [0, 1, 0], k = [0, 0, 1]. (Do not use the built-in function cross here.)

5. Sum

a geometric series: Write a function to compute the sum of the geometric series

1 + r + r2 + r3 + . . . + rn

for a given r and n. Thus the input to the function must be r and n and the output must be the sum of the series.

Exercise 4.

1. A simple sine plot: 

Plot y = sin x, 0 ≤ x ≤ 2π, taking 100 linearly spaced points in the given intervall. Label the axis and put “Plot created by yourname“ in the title. 

2. Line-styles:

Make the same plot as before, but rather than displaying the graph as a curve, show the unconnected data points. Display the data points by small circles. Now combine the two plots in one command, to show the line through the data points as well as the distinct data points.

3. An exponentially decaying sine plot:

Plot y= e−0.4x sinx, 0 ≤x≤ 4π, taking 10, 50, and 100 points in the interval.

4. Space curves:

Use the command plot3(x,y,z) to plot the circular helix 

x(t) = sin t,

y(t) = cost, z(t) = t, 0 ≤ x ≤ 20.

5. On-line-help:

Type help plot on the Matlab promt and hit return. If too much text flashes by the screen, type more on, hit return, and then type help plot again. This should give you paged output. Read through the on-line help. To move the next page of the screen output, simply press the space bar.

6. Log scale plots:

Create a vector x = 0 : 10 : 1000. 

Plot x vs.x3 using the three log scale plot commands. Hint: First, compute y = x3 and then, use semilogx(x,y) etc.

7. Overlay plots:

Plot y = cos x and z = 1 − 1/2x^2 + 1/24x^4 for 0 ≤x≤π on the same plot.

Hint: You can use i) plot(x,y,x,z,’:’), ii) hold on command after the first plot command . . . , iii) line(x,y,’…’) after the first plot command . . . 

Try the command legend(’cos(x)’,’z’).

Essay Help
Calculate your paper price
Pages (550 words)
Approximate price: -

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

Professional and Experienced Academic Writers

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

24/7 Customer Support

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

Calculate the price of your order

Total price:
$0.00

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

Essays

Essay Writing Service

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.

Admissions

Admission Essays & Business Writing Help

An admission essay is an essay or other written statement by a candidate, often a potential student enrolling in a college, university, or graduate school. You can be rest assurred that through our service we will write the best admission essay for you.

Reviews

Editing Support

Our academic writers and editors make the necessary changes to your paper so that it is polished. We also format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.

Reviews

Revision Support

If you think your paper could be improved, you can request a review. In this case, your paper will be checked by the writer or assigned to an editor. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied with the service offered.