** These projects are under M408D-->kawasaki-408d.bk **

Selected Topics in Differential and Integral Calculus (M408D):

• Polar Coordinates
• Sequences
• Infinite Series
• Taylor & Maclaurin Series
• Graphs
• Quadric Surfaces

Polar Coordinates

What is the best way to learn Polar Coordinates besides plotting? Plot_polar allows you to choose R and theta, and the point will be displayed when you hit plot. You may plot as many points you want and erase them when desired.

Each application will present instructions and a series of exercises for a better comprehension of the subject.

Graphing in Polar Coordinates

Graphing in polar coordinates is a hard task. With Polar you may watch a curve being graphed. You can either choose a curve from the menu, or you can enter an equation "r(t) = .. " in the entry widget. To watch the plot of the curve slide the value of variable "t".

<- four-leaved-rose  <- spirals

<- conics          <- conchleoids

<- cissoid of Diocles  <- nephroid

It is possible to write equations with two or three parameters (A, B, and I for integer values), to change their values and to re-plot the curves. To facilitate comparisons between curves, several curves can be displayed at the same time.

[Polar Coordinates] [Sequences] [Infinite Series] [Taylor & Maclaurin Series] [Graphs] [Quadric Surfaces]

Sequences & Series

Enter a sequence:

PlotSequences plots the first 100 elements of a sequence, giving a lower bound and a maximum value. Notice that this will not tell you if a sequence converges or diverges, but it will give you a pretty good idea of how the sequence behaves.

[Polar Coordinates] [Sequences] [Infinite Series] [Taylor & Maclaurin Series] [Graphs] [Quadric Surfaces]

Infinite Series

This is the page #1 of a little Demo.

This figure is used to motivate the concept of a convergent infinite series. A square of side 1 is displayed. This unit square is divided into two halves, then one of the halves is cut into two quarters and then one of the quarters into two eights and so on. The process shows that the sum of the areas of such rectangles fill the square.

This is the page #2 of the same Demo

Now we have a rectangle of sides "A" and 1. The height is divided into two segments of length "R" and "1-R". At the point of division, a horizontal line partition the rectangle into two rectangles of areas "AR" and "A(1-R)". The rectangle of area "AR" is partitioned by vertical lines into rectangles of lengths: "A(1-R)", "A(1-R)R", "A(1-R)(R)R",.... And hence the sum of the areas of all the rectangles should equal the "A".

[Polar Coordinates] [Sequences] [Infinite Series] [Taylor & Maclaurin Series] [Graphs] [Quadric Surfaces]

Graphs

Enter a function:

In PlotSurface just enter a two variable function ("f(x,y)") and hit plot. The surface will be displayed, and you can rotate the image by pressing "up", "down", "right", "left","k" and "l" keys.

[Polar Coordinates] [Sequences] [Infinite Series] [Taylor & Maclaurin Series] [Graphs] [Quadric Surfaces]

Quadric Surfaces

This is an animation. Reload in case "gif" is not moving.

hiperboloid (one sheet)

Quadrics plots the equation you choose from the menu. The equation is given with parameters A, B, and C. The graph is re-ploted each time you change the value of a parameter. Also, you can rotate the image by pressing "up", "down", "right", and "left" keys.

cone                            ellipsoid                                    hiperboloid (two sheets)    

[Home page] [Emacs Book Mode Projects]

I use a cool C-Library for most of my projects: the EZ-Widgets and Graphics Library written by Dr. Maorong Zou (Departmant of Mathematics, University of Texas at Austin).