# Maths

### Mathematical history

Write a reflection paper of at least 1 page addressing the following topics and questions. In your paper, include your name, the course name and section, and the date in the header. Use Times New Roman, size 12 font and double space.

· Your mathematical history: In high school i have taken algebra I and II, Geometry.

o What math classes have you taken in the past?algebra I and II, geometry

o Share a memory that stands out from your previous math courses, either good or bad.I remember in the 10th grade I was taking geometry and the teacher called on me to do a problem and I could not get the correct answer and he screamed at me with a high pitch voice. I was terrified being in his class.

o Share an example of how you have had to use math outside of the classroom. As an certified medical assistant, I use math daily especially drawing up botox.

· Your feelings about math Basic math do not bother me because I am very good with that but algebra I am not so good.

· Your future as related to math. I think as long as I can do basic math I am okay in society.

o Are there math courses required for your degree? If so, what are they? What will you be taking next? Yes math is required with my degree as business administration. I do not know the next math I will be taking.

o Do you see this course as useful for you in your career or personal life? No I do not see this course useful in my career. As long as a person know basic math I think he or she will be okay.

### Arclength and Reparametrization

(1) Write a short essay on this topic, using examples: Why is it that we need to consider reparametrizations of a curve? Why have we chosen arclength as the “correct” parametrization? What is arclength, and how do we go about using it? How practical is reparametrization by arclength?

(2) Reparametrize the curve below by arclength: α(t) = (e ^t cos(t), e^t sin(t), e^t )

### Regular parametrized curves.

(1) There are several geometric reasons why we choose to work with only regular parametrized curves. Write a short essay to describe a few of those reasons, using examples to illustrate your points.

(2) Show that the curve β(t) = (sin(3t) cos(t),sin(3t) sin(t), 0) is a regular curve. Then find the equation of its tangent line at the time t = π/3.

### Frenet-Serret

Write a short essay that describes two different interpretations of the curvature κ of a space curve. Be sure to include as one of your descriptions a discussion of what κ means in terms of the motion of the Frenet-Serret framing of the curve.

### Integration method

Using differential equation find the solution

+ cosx tany dy/ dx

solve it using integration method

### Equation

Find the general solution of the equation

dy/dx-x=xy^2 . Also find the perpendicular

solution if y =1 when x = 0.

### Matrix

Julie and Steve are playing the games at the arcade, the first table shows the number of each type of ticket they won. find the total number of points the each won.

tickets won

player red yellow blue

julie 15 6 2

steve 17 3 4

a. write a matrix that represents the data in each table.

b. find the product matrix.

c. how many points did each player win?