Multivariable Calculus

I will be  on vacation for a couple of days so thought of refeshing myself with problems on Multivariable Calculus .As I am  working full time on other projects this break will help me dustoff my rusted brain.

Thanks to open source,math proffs and MIT open courseware giving access to textbooks,problems and Lectures.Here is the list for  people who are interested

1)Geoge Cain and James Herod, Multivariable Caclulus

2)Gilbert Strang, Calculus (especially chapters 11-15)

3)Michael Corral, Vector Calculus

4)Jeff Knisley, Multivariable Calculus Online (weird formatting)

5)James Byrnie Shaw, Vector Calculus with Applications to Physics (from 1922)

6)Stephen Cowley, Vector Calculus

7)Oliver Knill, Multivariable Calculus

8)Carlos Rodriguez, Multivariable Calculus

9)Kenneth Kuttler, Many Variable Advanced Calculus and Math 214

10)Dan Sloughter, The Calculus of Functions of Several Variables (pdf)

MIT OPEN COURSEWARE (18.02)

Spring 2006 (Mattuck and Jerison): Assignments | Exams

Spring 2007 (Auroux): Lecture Notes | Assignments | Exams

MORE PROBLEM SETS / EXAMS / COURSE SITES

Phillips Exeter Academy puts their MV problem sets online here. (Problem Sets)

An honors multivariable calculus class from Swarthmore (Problem Sets)

Problem sets for Tessler’s Math 10C course (Problem Sets on course webpage)
Exams for Tessler’s Math 10C course (Midterm 1, Midterm 2) [from course webpage]

Davis Arnold’s multivariable calculus page [here]: uses MATLAB to explore multivariable calculus — with great tutorials and problems for each topic.

cstitz42’s VIDEOS FOR MULTIVARIABLE CALC [here]

donnylee’s VIDEOS on MULTIPLE INTEGRALS [here]

The Mathematician in Love

The Mathematician in Love
William John Macquorn Rankine

I.

A mathematician fell madly in love
With a lady, young, handsome, and charming:
By angles and ratios harmonic he strove
Her curves and proportions all faultless to prove.
As he scrawled hieroglyphics alarming.

II.

He measured with care, from the ends of a base,
The arcs which her features subtended:
Then he framed transcendental equations, to trace
The flowing outlines of her figure and face,
And thought the result very splendid.

III.

He studied (since music has charms for the fair)
The theory of fiddles and whistles, –
Then composed, by acoustic equations, an air,
Which, when ’twas performed, made the lady’s long hair
Stand on end, like a porcupine’s bristles.

IV.

The lady loved dancing: — he therefore applied,
To the polka and waltz, an equation;
But when to rotate on his axis he tried,
His centre of gravity swayed to one side,
And he fell, by the earth’s gravitation.

V.

No doubts of the fate of his suit made him pause,
For he proved, to his own satisfaction,
That the fair one returned his affection; — “because,
“As everyone knows, by mechanical laws,
“Re-action is equal to action.”

VI.

“Let x denote beauty, — y, manners well-bred, –
“z, Fortune, — (this last is essential), –
“Let L stand for love” — our philosopher said, –
“Then L is a function of x, y, and z,
“Of the kind which is known as potential.”

VII.

“Now integrate L with respect to d t,
“(t Standing for time and persuasion);
“Then, between proper limits, ’tis easy to see,
“The definite integral Marriage must be: –
“(A very concise demonstration).”

VIII.

Said he — “If the wandering course of the moon
“By Algebra can be predicted,
“The female affections must yield to it soon” –
– But the lady ran off with a dashing dragoon,
And left him amazed and afflicted.