Mathematica

Hi there 

 

Who have an experince of using Mathematica program ??

  

Pease read the attached file.

 

Thx

Introduction to Modeling in the Sciences,

HW1

Assigned 27 June; Due 03 July (via Blackboard)

This is the first “homework” assignment. It is meant to give you more practice with the Mathematica methods and routines that you’ve learned. The entire assignment is worth 100 points. Create a new Mathematica Notebook file, and include at the top your name and date. Upload your notebook to Blackboard when done.

Plotting (20 points)

Using Mathematica, plot the following functions. You can use either Plot or Plot3D:

· sine(x), when x ranges from -10 to 10

· tangent(x), when x ranges from -5 Pi to 5 Pi

· x2 – y3, when x ranges from -5 to 5, and y ranges from 0.5 to 12.3

Truncation Errors (40 points)

Calculus shows that cos(x) equals the following infinite series:

Use Mathematica to:

· Calculate the “true” value of cos(2), to 10 decimal places

· Calculate the approximation for cos(2), using the first 5 terms of the above series

· Calculate absolute error between the “true” and “approximate” values of cos(2)

· Calculate relative error between the “true” and “approximate” values of cos(2)

Plotting and Manipulate (40 points)

You’ve been told that the behavior of a certain item on the stock market (whether it is “up” or “down”) is based purely on the temperature, in Celsius, according to the following equation:

4 y f(x,y) = Sin(x ) – Cos(12x ) + 0.7x

where x is the temperature. Your goal is to investigate the behavior of the function, with the aid of Mathematica. To do this:

· Define the function f(x,y)

· Plot the function f(x,4), when x ranges from -10 to 10

· Create a Manipulate, that plots f(x,y), where x ranges from -10 to 10, and contains a slider for the value of y, which ranges from -10 to 10, in integer increments.

Then, answer the following question:

Is there a value of y in the range {-10, 10} so that the value of f(x,y) is positive, even when x is negative?

CS298 Summer 2013, CWU, HW 1, Dr. Filip Jagodzinski page 1 of 1