VisiCalc (for "visible calculator") was the first spreadsheet computer program for personal computers, originally released for Apple II by VisiCorp in 1979. It is often considered the application that turned the microcomputer from a hobby for computer enthusiasts into a serious business tool, prompting IBM to introduce the IBM PC two years later. VisiCalc is considered to be Apple II's killer app. It sold over 700,000 copies in six years, and as many as 1 million copies over its history.
Initially developed for the Apple II computer using a 6502 assembler running on the Multics time sharing system, VisiCalc was ported to numerous platforms, both 8-bit and some of the early 16-bit systems. In order to do this, the company developed porting platforms that produced bug compatible versions. The company took the same approach when the IBM PC was launched, producing a product that was essentially identical to the original 8-bit Apple II version. Sales were initially brisk, with about 300,000 copies sold.
VisiCalc used the A1 notation in formulas.When Lotus 1-2-3 was launched in 1983, taking full advantage of the expanded memory and screen of the PC, VisiCalc sales ended almost overnight. Sales declined so rapidly, that the company was soon insolvent. Lotus Development purchased the company in 1985, and immediately ended sales of VisiCalc and the company's other products.
Hello, I need help deciding on whether to take ODE (MAP2302) and Calc III during the summer. Would it be wise to take ODE along with Calc III in the same semester? Some people have told me to take Calc III first because there are a few things in ODE that are taught in Calc III, but others have...
Hi PF! :')
Ultimately, I've taken zero AP classes in my entire time in high school and, at first, I didn't see this as a problem. But now there are a couple of people who've told me otherwise (in terms of getting into college for undergrad). SO, if I take calc III at my local community college...
Hi! So I just breezed through a summer Calc II course (took E&M and Modern Physics last semester) and will be approaching Solid State Physics and Calc III this coming semester together. I've taken my school's upper division Linear Algebra course and passed before last semester and continue to do...
Homework Statement
Find the volume of the given solid:
Under the surface z = xy and above the triangle with verticies (1,1), (4,1) and (1,.2)
Homework Equations
Double Integral
The Attempt at a Solution
I drew the triangle, and found the the equations of the lines to be:
x = 1;
y = 1;
y = -3x...
Hi,
I'm currently reading Calc III by Marsden & Weinstein. One of the examples shows a plane being drawn through three points. While I understand their solutiom, I'm very curious as to why my solutiom doesn't work.
1. Homework Statement
Write the equatiom for a plane through A = (1, 1, 1), B...
This is the problem I'm trying to solve. The directions require me to rewrite as a single integral and evaluate. But I'm having trouble setting the bounds for a complete compounded integral. The graph of the region would look something like this...
Where the shaded area is the region. I...
1. Problem: ellipse x^2/a^2 + y^2/b^2 = 1 encloses circle x^2 + y^2 = 2x. Find values of a and b that minimize the area of the ellipse.Homework Equations : [/B]A = pi*a*b for an ellipse.The Attempt at a Solution : [/B]I tried a bunch of crazy stuff... I know I need to find where the tangents...
Hi,
I am taking Calc III, but I am having a hard time understanding some of the concepts. Right now I am struggling with understanding the curvature of a line. What I have in my notes is this:
Curvature
second derivative (rate of change of tangent line)(rate of change w/ respect to arc length)...
Homework Statement
Find a vector in the direction opposite to <-4,1,2>, that has a magnitude of 3.
Homework Equations
I think that I did the first part of the problem correctly:
<-4,1,2>
magnitude= sqrt[ (-4)^2+1^2+2^2 ]
= sqrt(16+1+4)
= sqrt(21)...
SPOILER: This will be a somewhat depressing rant.
I like math (or, I THOUGHT I did), but have been feeling incredibly lazy and powerless recently. I'm currently a freshman undergrad, and I just failed Calc III. I've been barely scraping by recently, having gotten a 40 on the first midterm and a...
Homework Statement
Evaluate the limit
1 1 1
lim ∫ ∫ ... ∫ cos^2((pi/2n)(x1 + x2 +... xn))dx1 dx2 ... dxn
0 0 0
n→∞Homework Equations
Well, I know that we can change this using a double angle rule, so that the integrals become 1/2 + 1/2 cos (2*pi/2n)(x1 +...
Homework Statement
The range of a projectile fired (in a vacuum) with initial velocity V0 and inclination angle θ from the horizontal is R = (1/32) * (V0)2 * sin(2θ).
Use differentials to approximate the change in range if V0 is increased from 400 ft/s to 410 ft/s and θ is increased from...
Homework Statement
http://i.minus.com/jDtSwpCGlrMhP.jpg
Homework Equations
Solving for dx/dy (change in x with respect to y) I get a solution that isn't one of the answer choices.
The Attempt at a Solution
3y^2 = 8x' + x'/x
Coordinate:
x = 1 (given)
y = 2 (solved for in...
i asked this question before, but i didn't ask it quite right so i didn't get a satisfactory answer..
curvature is define as how quickly/ abruptly a curve changes with respect to its arc length.okay so the normal vecor (N = T ') is the change in the tangent vector of a curve with respect to...
Homework Statement
The problem is attached with my work so far.
Consider the vector Field F, where C is the perimeter of the circle of radius 3 centered at (2,5) Homework Equations
∫ Mdx+Ndy----->∫∫ (∂N/∂x)-(∂M/∂y) da
The Attempt at a Solution
Attached is my work thus far. I am having...
The problem is from the MIT Open CourseWare Calculus eBook by Strang. Chapter 12.2, #3:
A ball is thrown at 60 degrees with initial velocity of 20m/sec to clear a wall 2m high. How far away is the wall?
Finding flight time T, range R, and max height Y(max) is the easy part. How do I find...
Hey Everyone!
So basically my question is if it's possible to take calc III or Diffeq without having taken Calc II. I know a decent amount of Calc II but I'm not 100% sure of everything that it covers. If it would be possible, which class would be easier? I know that it definitely depends on...
Calculus III, find shortest distance, 3 dimension problem? check my answer please??
What is the shortest distance from the point P = (0, 1, 2) to the line given by l(t) = (1+t, 2-2t, 3+3t)?
use distance formula
d = sqrt ((x-0)^(2) + (y-1)^(2) + (z-2)^(2))
d^(2) = ((x)^(2) + (y-1)^(2) +...
Hi. I took Calc III and Linear alg over the summer. The course was 6 weeks and we did not cover everything in each chapter. From Calc III, we didn't cover things like curl, divergence, and Green's Theorem. In Linear Algebra, we didn't do orthogonal functions, diagonalization, Eigenvectors, or...
And not taking ODE's? Is this doable? I understand the basics of most concepts as I am currently self-learning from online resources and textbooks, but I decided not take the class during the summer as I'm already taking calc III. The problem is that when the year starts up again PDE's is taught...
I feel very comfortable doing this because I've taken numerical analysis and written a short term paper on numerical approximations for PDEs. I am very strong in linear algebra and have calc I/II.
The reason I ask for advice is because I have just graduated from undergrad with a degree in...
So, I technically got this problem correct (our professor gave us the answers but not the total solution). My question is more of a logic one- an answer that I'll need to apply this concept to problems on the exam. I included it at the bottom of the post, after I explained the problem
Find...
This summer I plan on taking calc II at my local community college, and next semester I will definitely be taking calc III, intro to computer science, and probably a science course (physics I or chemistry). This leaves a spot open for a math course (I am planning on majoring in math), which will...
Hello, this is my first post!
I am interested in studying PDEs (heat/wave equations, etc.). At my university, the only listed prereq. for PDEs is ODEs, which can be taken after Calc II. So, essentially, one could enroll in PDEs without taking Calc III, but I am not sure if that would be...
Homework Statement
Find the Frénet-frame of the streamline \textbf{r}(t) = \left(\frac{1}{2} \cosh t, e^t, \frac{1}{2} \cosh t\right) at the point (1,1,1)
Homework Equations
\textbf{T}(t) = \frac{\textbf{r}'(t)}{||\textbf{r}'||}
\textbf{B}(t) = \frac{\textbf{r}'(t) \times...
Homework Statement
z = cos(x^2 + 3y^2)
x = ucosv
y=usinv
find dz/dv
Homework Equations
The Attempt at a Solution
I think I can do these fairly well, but I'm a little unsure of the "protocol" for which variables to put back in. Sometimes (in this case) I can't really put...
Homework Statement
I really, really don't understand. My work shows one thing, and a simple look at the function shows another.
f(x,y) = .25x^2 + 5y^7 + 6y^2 - 3x
Find global max and min if they exist.
Homework Equations
The Attempt at a Solution
Took partial derivatives...
I come across questions where I have to match the equation with its contour map and graph.
Examples:
z = sin(xy)
z = sin(x-y)
Right now I'm using Wolfram Alpha for all of these, but supposing these appear on an exam... how do I graph it by hand? :confused: For example, for z =...
Homework Statement
attached.
Homework Equations
The Attempt at a Solution
I thought the problem was easy, but my answer is wrong (aparently; I still disagree.)
First I defined x = (y^3)(z^3) to be a surface of function F
So
F(x,y,z) = (y^3)(z^3) - x = 0
Then, the...
Homework Statement
Find the limit of f(x,y) = \frac{x^{2}-y^{2}}{\sqrt{x^{2}+y^{2}+81}-9}
as (x,y) \rightarrow (0,0)
The Attempt at a Solution
Ok, I looked at the examples in the book, and it seems pretty straight forward... I first look at f(x,0) to see what happens as we approach...
Homework Statement
Hey guys, I have two separate questions.
1.)
I am asked for a unit vector pointing from P = (1,2) to Q = (4,6)
In physics, every vector I've ever worked with started at the origin, so these feel weird.
I initially thought that it would simply be 3i + 4j, the...
Homework Statement
We define the function f: \mathbb{R}^2 \to \mathbb{R} as
\begin{equation}
f(x,y) = \frac{xy^2 ln(x^2 + y^2)}{x^2 + y^2}
\end{equation}
if (x,y) \neq (0,0). Also note that f(0,0) = 0.
Show that f is continuous at (0,0)
Homework Equations
The Attempt at a...
Homework Statement
The Position Function of a spaceship is
r(t) = (5t+9)i+(2t2-1)j+t2k
and the coordinates of a space station are P(54,89,45). The captain wants the spaceship to reach the space station in constant velocity. When should the engines be turned off?
Homework Equations
r'(t)...
Homework Statement
Find an equation for the plane containing the line in the xy-plane where y = 1, and the line in the xz-plane where z = 2
Homework Equations
Ax+By+C= f(x,y) or (z)
The Attempt at a Solution
Ok so i started off by graphing and i see when x and y are 0 z = 2 and...
Homework Statement
Use the Divergence Theorem to evaluate ∫∫S (8x + 10y + z2)dS where S is the sphere x2 + y2 + z2 = 1.
Homework Equations
∫∫S F dS = ∫∫∫B Div(F) dV
The Attempt at a Solution
I dunno, this isn't a vector field so I don't know how to take the divergence of it so...
Homework Statement
Let r = x i + y j + z k and R = |r|. Let F = r/R^p.
find div(F) in terms of r.. i can't figure out how to express it in therms of r
Homework Equations
div(F) = the gradient added together
I am currently enrolled in Calculus AB and am going to take the Calculus BC exam. I taught myself most topics in single variable calc over the summer so I am very confident that I can pass the BC exam.
Provided I do, I would have the opportunity the take Calc III (and possibly partial diff...
This current semester I was enrolled in O-chem and had to drop it because Calc II, baby-linear algebra, Physics I, and another light course took much more time than I had anticipated. I am told that Calc III and DEQ are both easier than Calc II. I don't want to sign up for O-chem and drop it a...
Alright so I register for calc III and took my first two lectures last week in it. I was doing very well in the class and even was told by my teacher I was doing a good job. However I got a email from the department saying I need Linear Algebra before taking calc III. First of all from my...
I have a couple of questions, but probably only need one worked out to figure out the rest.
1. Find a function f(x,y,z) whose level surface f=8 is the graph of the function 3x+4y
=> I know that a level surface for f(x,y,z) is the solution to f(x,y,z)=k. However, now I'm stuck. I know how...
Homework Statement
f(x,y)=xy-y^2 is bound by a rectangle with vertices at (2,-1), (2,2), (-1,2), and (-1,-1.)
Find all 2D, 1D, and 0D critical points.Homework Equations
The Attempt at a Solution
2D Points:
f(x,y)=xy-y^2
f_x=y=0 \Rightarrow y=0
f_y=x-2y=0 \rightarrow x-2(0)=0 \Rightarrow x=0...
Okay so registration is coming up and again its time for some tough decisions that will severely impact the upcoming months.
I am currently an EE student taking Calc 2 and Physics I. Next semester I was planning on doing Calc 3 and Physics 2 and in the summer taking ODE and Circuit analysis...
I'm starting to think about next semester's schedule, and it looks if I won't be able to take Physics II b/c I retook calc I (had AP credit but didn't use it). Calc II is a Pre-req for Physics II.
I really want to be a physics minor, or even double major. If I took Physics II over the...
Homework Statement
Hi there. I got next problem, and I must say if it is differentiable in all of its domain.
f(x,y)=\begin{Bmatrix} (x+y)^2\sin(\displaystyle\frac{\pi}{x+y}) & \mbox{ if }& y\neq{-x}\\0 & \mbox{if}& y=-x\end{matrix}
So, I thought trying with the partial derivatives...
Homework Statement
I must say if the function is continuous in the point (0,0). Which is \displaystyle\lim_{(x,y) \to{(0,0)}}{f(x,y)}=f(0,0)
The function:
f(x,y)=\begin{Bmatrix} (x+y)^2\sin(\displaystyle\frac{\pi}{x^2+y^2}) & \mbox{ if }& y\neq{-x}\\1 & \mbox{if}& y=-x\end{matrix}
I think...
Homework Statement
[PLAIN]http://img843.imageshack.us/img843/3995/calc3.jpg
The Attempt at a Solution
Im here asking for some help in direction on how to do these problems so that I can find the solution by myself... I would really really appreciate any help anyone could provide...
So my engineering program has me taking LA and Diff. Eq. in the same semester, after Calc II and before Calc III. I don't understand why that is...what would be the idea behind this?
Is it a good idea to take Calc III + Linear Algebra I + Discrete Mathematics all in the same semester? In terms of scheduling for the Fall 2010 semester, this type of courseload was the best way for me to setup my schedule...
I've done some self study for Calc III and Linear Algebra I so it's...