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Ball State >> MATHS >> 374 (Spring, 2008)
374 5.1 Note: When m1, m2, m3, and m4 are distinct real numbers, m1 x , m2 x , m3 x , m4 x is linearly independent. In[1]:= Out[1]= In[2]:= In[3]:= F m1 x m1 x , , m2 x , , m3 x , m4 x , m2 x m3 x m4 x Wronskian F : Table D F, x, i 1 ...
Ball State >> MATHS >> 374 (Spring, 2008)
Modeling Heat Flow in a Thermos Michael A. Karls James E. Schershel Ball State University April 17, 2003 The Coffee Cup Problem Freshly poured coffee has a temperature of 80 oC. Assume that the room temperature is a constant 20 o C, and that af...
Ball State >> MATHS >> 374 (Spring, 2008)
159 Lecture 6 Recurrence Relations in Excel Recurrence Relations Recall the idea of recurrence relation, which we saw briefly in Lecture 1. In Example 4, we found 1+2+n in Excel by letting x(0) = 1 and defining x(n) := x(n-1) + n for n 2. A rec...
Ball State >> MATHS >> 374 (Spring, 2008)
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Ball State >> MATHS >> 374 (Spring, 2008)
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Ball State >> MATHS >> 374 (Spring, 2008)
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Ball State >> MATHS >> 374 (Spring, 2008)
MATHS 390: An Example of Hill\'s System Encrypting a Message In[1]:= Out[1]= In[2]:= Out[2]= In[3]:= Out[3]= In[4]:= Out[4]= PlainText \"meetmeattheusualplaceattenratherthaneightoclock \" meetmeattheusualplaceattenratherthaneightoclock Length Charact...
Ball State >> MATHS >> 374 (Spring, 2008)
159 Lecture 20 Introduction to MATLAB What is MATLAB? MATLAB, which stands for MATrix LABoratory is a highperformance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment where ...
Ball State >> MATHS >> 374 (Spring, 2008)
159 Lecture 10: Entering Text and Formatting; Using the Help Browser Note: To type a command in a Mathematica notebook, use the mouse to move the cursor until it is horizontal, click the left mouse button, and type the command. To enter a command, us...
Ball State >> MATHS >> 374 (Spring, 2008)
159 Lecture 13: Parameterized Curves and Surfaces; Animation Note: To type a command in a Mathematica notebook, use the mouse to move the cursor until it is horizontal, click the left mouse button, and type the command. To enter a command, use the mo...
Ball State >> MATHS >> 374 (Spring, 2008)
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Ball State >> MATHS >> 374 (Spring, 2008)
374 Note for Chapter 4: How to find a Wronskian of {f1, f2, . , fn}, using Mathematica Define the functions: In[1]:= f1 x f2 x f3 x : E^x : Sin x : Cos x Make an n x n matrix of functions whose ith row contains the (i-1)st derivatives of {f1, f2, ...
Ball State >> MATHS >> 374 (Spring, 2008)
Fenced Area Problem x A(x) = 2400x-2x^2 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 Initial Guess 500 Changing Cell Area Enclosed Target Cell x 1939 1944 1949 1954 1959 1964 1969 1974 Best-Fit Line y Y = a*x+b 32800 55800 73600 138000 2020...
Ball State >> MATHS >> 374 (Spring, 2008)
299X-159 Lecture 8 Optimization with the Excel Solver Optimization Problems Many problems involve optimization of a function by making an appropriate choice of inputs to get the best possible output. Examples include: Maximizing an area enclosed ...
Ball State >> MATHS >> 374 (Spring, 2008)
159 Lecture 3 Fall 2008 Finance Applications with Excel Annuities an Amortization Example 1 Suppose we invest $500 at the end of each year for 5 years, at an interest rate of 4%, compounded annually. How much money will we have at the end of year...
Ball State >> MATHS >> 374 (Spring, 2008)
159 Lecture 1 Fall 2008 Introduction to Excel Excel 2003 Definitions and Terminology Title Bar Name Box Pulldown Menus Cell D15 Column D Sheet Tab 2 Standard Toolbar Formula Bar Row 15 Excel 2003 Definitions and Terminology Label (text) Consta...
Ball State >> MATHS >> 374 (Spring, 2008)
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Ball State >> MATHS >> 374 (Spring, 2008)
374: How to Factor Polynomials with Mathematica Here is how to factor a polynomial such as D3 In[1]:= Out[1]= 3 D2 4: Factor D ^ 3 2 D 2 3 D^2 D 4 1 Here is how to find roots of a polynomial equation such as D3 In[2]:= Out[2]= 3 D2 4 0. So...
Ball State >> MATHS >> 374 (Spring, 2008)
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Ball State >> MATHS >> 374 (Spring, 2008)
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Ball State >> MATHS >> 374 (Spring, 2008)
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Ball State >> MATHS >> 374 (Spring, 2008)
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Ball State >> MATHS >> 374 (Spring, 2008)
CHANGE THE NUMBERS IN THE BLUE BOXES AND WATCH THE FUNCTION CHANGE. FOR A NEW FUNCTION, CHANGE THE FUNCTION DEFINITION IN THE GREEN BOXES. (USE THE FILL COMMAND!) f(x)=cos(x) 0 <=x<= 9.42 step size= 0.94 FUNCTION AND TANGENT LINE VALUES x f(x) L(x) h...
Ball State >> MATHS >> 374 (Spring, 2008)
159 Lecture 2 Fall 2008 Finance Applications with Excel Simple and Compound Interest Finance Applications Excel is a useful tool for working with financial applications that arise in areas such as business, economics, or actuarial science, includi...
Ball State >> MATHS >> 390 (Spring, 2008)
Technology Training Support Services Microsoft Office 2007: Using the Ribbon Linda Putman lputman@bsu.edu 285-1321 University Libraries essential resources for research, learning, and friends Copyright 2007, Technology Training Support Services &...
Ball State >> MATHS >> 390 (Spring, 2008)
159 Lecture 4 Logical Functions and Conditional Formatting in Excel Logical Functions Excels built-in logical functions are useful for introducing conditional statements, i.e. decision making functions into a spreadsheet! The functions are: TRUE ...
Ball State >> MATHS >> 390 (Spring, 2008)
Creating Macros with Excel 2003 Macros are recorded keystrokes to automate tasks you perform regularly using Excel. To create a macro, you simply start recording (Tools>Macro>Record New Macro), give your macro a new name and assign a key stroke that...
Ball State >> MATHS >> 390 (Spring, 2008)
159 Lecture 14: Importing and Exporting Data Note: To type a command in a Mathematica notebook, use the mouse to move the cursor until it is horizontal, click the left mouse button, and type the command. To enter a command, use the mouse to move the ...
Ball State >> MATHS >> 390 (Spring, 2008)
159 Lecture 19 Elementary Matrix Theory Matrix Definition A matrix is a rectangular array of elements (usually numbers) written in rows and columns. Example 1: Some matrices: 2 Matrix Definition Example 1 (cont.): Matrix A is a 3 x ...
Ball State >> MATHS >> 390 (Spring, 2008)
159 Lecture 7 Population Models in Excel Toads Again! Lets look at the toad data again, but this time let n be the number of years after 1939 and x(n) be the area covered by toads at year n. Using Excel, we find that the best-fit exponential functi...
Ball State >> MATHS >> 390 (Spring, 2008)
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Ball State >> MATHS >> 390 (Spring, 2008)
159 Lecture 17: Simple Programming In[1]:= In[2]:= Off General:spell Off General:spell1 Note: To type a command in a Mathematica notebook, use the mouse to move the cursor until it is horizontal, click the left mouse button, and type the command. T...
Ball State >> MATHS >> 390 (Spring, 2008)
159 Lecture 5 Mathematical Functions in Excel Mathematical Functions Excel has many built-in mathematical functions! The complete list can be found online here: http:/office.microsoft.com/en-us/excel/C Here are some familiar mathematical functio...
Ball State >> MATHS >> 390 (Spring, 2008)
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Ball State >> MATHS >> 390 (Spring, 2008)
How to Make a Histogram Using Excel 2007 By Emily W. Clark, Ph.C., Department of Psychology, University of Washington Data Analysis ToolPak Microsoft Excel provides a set of data analysis tools called the Analysis ToolPak that you can use to save s...
Ball State >> MATHS >> 390 (Spring, 2008)
159 Lecture 9 - Basic Syntax and Basic Commands Note: To type a command in a Mathematica notebook, use the mouse to move the cursor until it is horizontal, click the left mouse button, and type the command. To enter a command, use the mouse to move t...
Ball State >> MATHS >> 390 (Spring, 2008)
159 Lecture 18 Solving Systems of Equations A System of Equations Consider the system of two equations in two unknowns: x + 2y = 1 (1) 3x + 4y = -1 (2) Recall from algebra class that two ways to solve a problem like this are substitution and e...
Ball State >> MATHS >> 390 (Spring, 2008)
374: Using Mathematica to Create Implicit Plots Here is how to plot a function defined implicitly by an equation such as x2 In[1]:= 6 xy y2 Cfor C 10. True ContourPlot x2 10 6xy y2 10, x, 10, 10 , y, 10, 10 , Axes True, Frame 5 Out[1]= ...
Ball State >> MATHS >> 390 (Spring, 2008)
a 1 3 c x 0 b 2 4 d y 0 ax+by = = cx+dy e 1 -1 f ...
Ball State >> MATHS >> 390 (Spring, 2008)
! \" # $ & % $ ...
Ball State >> MATHS >> 390 (Spring, 2008)
159 Lecture 12: Calculus Commands Note: To type a command in a Mathematica notebook, use the mouse to move the cursor until it is horizontal, click the left mouse button, and type the command. To enter a command, use the mouse to move the cursor unti...
Ball State >> MATHS >> 390 (Spring, 2008)
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Ball State >> MATHS >> 390 (Spring, 2008)
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Ball State >> MATHS >> 390 (Spring, 2008)
Mathematics in Art A self-directed tour for the Ball State University Museum of Art Mathematics and art both help us to better understand our civilization. The study of patterns, symmetry, and balance has mathematical, cultural, and artistic applic...
Ball State >> MATHS >> 390 (Spring, 2008)
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Ball State >> MATHS >> 390 (Spring, 2008)
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Ball State >> MATHS >> 390 (Spring, 2008)
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Ball State >> MATHS >> 390 (Spring, 2008)
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Ball State >> MATHS >> 390 (Spring, 2008)
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Ball State >> MATHS >> 390 (Spring, 2008)
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Ball State >> MATHS >> 390 (Spring, 2008)
374 Section 1.5: Direction Fields Via Mathematica Here is a way to get Mathematica to plot a direction field for the differential equation In[1]:= In[2]:= In[3]:= dy dx f x, y y2 x2 . VectorFieldPlots`; f x ,y : y^2 x^2 VectorFieldPlot 1, f x, ...
Ball State >> MATHS >> 390 (Spring, 2008)
159 Lecture 16: Numerical Computation Note: To type a command in a Mathematica notebook, use the mouse to move the cursor until it is horizontal, click the left mouse button, and type the command. To enter a command, use the mouse to move the cursor ...
Ball State >> MATHS >> 390 (Spring, 2008)
159 Lecture 15: Optimization Note: To type a command in a Mathematica notebook, use the mouse to move the cursor until it is horizontal, click the left mouse button, and type the command. To enter a command, use the mouse to move the cursor until it ...
Ball State >> MATHS >> 390 (Spring, 2008)
...
Ball State >> MATHS >> 390 (Spring, 2008)
Does the Wave Equation Really Work? Michael A. Karls Ball State University November 5, 2005 Modeling a Vibrating String Donald C. Armstead Michael A. Karls The Harmonic Oscillator Problem A 20 g mass is attached to the bottom of a vertical spr...
Ball State >> MATHS >> 390 (Spring, 2008)
...
Ball State >> MATHS >> 390 (Spring, 2008)
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Ball State >> MATHS >> 390 (Spring, 2008)
A @ 75 B$ 1) 986 4 \" \" 20 31) \'(% #! $ @F) 986 75 4 \" ...
Ball State >> MATHS >> 390 (Spring, 2008)
159 Lecture 11: Working with Tables Note: To type a command in a Mathematica notebook, use the mouse to move the cursor until it is horizontal, click the left mouse button, and type the command. To enter a command, use the mouse to move the cursor un...
Ball State >> MATHS >> 390 (Spring, 2008)
...
Ball State >> MATHS >> 390 (Spring, 2008)
374 5.1 Note: When m1, m2, m3, and m4 are distinct real numbers, m1 x , m2 x , m3 x , m4 x is linearly independent. In[1]:= Out[1]= In[2]:= In[3]:= F m1 x m1 x , , m2 x , , m3 x , m4 x , m2 x m3 x m4 x Wronskian F : Table D F, x, i 1 ...
Ball State >> MATHS >> 390 (Spring, 2008)
Modeling Heat Flow in a Thermos Michael A. Karls James E. Schershel Ball State University April 17, 2003 The Coffee Cup Problem Freshly poured coffee has a temperature of 80 oC. Assume that the room temperature is a constant 20 o C, and that af...
Ball State >> MATHS >> 390 (Spring, 2008)
159 Lecture 6 Recurrence Relations in Excel Recurrence Relations Recall the idea of recurrence relation, which we saw briefly in Lecture 1. In Example 4, we found 1+2+n in Excel by letting x(0) = 1 and defining x(n) := x(n-1) + n for n 2. A rec...
Ball State >> MATHS >> 390 (Spring, 2008)
...
Ball State >> MATHS >> 390 (Spring, 2008)
...
Ball State >> MATHS >> 390 (Spring, 2008)
...
Ball State >> MATHS >> 390 (Spring, 2008)
MATHS 390: An Example of Hill\'s System Encrypting a Message In[1]:= Out[1]= In[2]:= Out[2]= In[3]:= Out[3]= In[4]:= Out[4]= PlainText \"meetmeattheusualplaceattenratherthaneightoclock \" meetmeattheusualplaceattenratherthaneightoclock Length Charact...
Ball State >> MATHS >> 390 (Spring, 2008)
159 Lecture 20 Introduction to MATLAB What is MATLAB? MATLAB, which stands for MATrix LABoratory is a highperformance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment where ...
Ball State >> MATHS >> 390 (Spring, 2008)
159 Lecture 10: Entering Text and Formatting; Using the Help Browser Note: To type a command in a Mathematica notebook, use the mouse to move the cursor until it is horizontal, click the left mouse button, and type the command. To enter a command, us...
Ball State >> MATHS >> 390 (Spring, 2008)
159 Lecture 13: Parameterized Curves and Surfaces; Animation Note: To type a command in a Mathematica notebook, use the mouse to move the cursor until it is horizontal, click the left mouse button, and type the command. To enter a command, use the mo...
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