Essentials of Calculus
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In our eReader you can find the full English version of the book. Read Essentials of Calculus Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Essentials of Calculus
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To quickly assess the difficulty of the text, read a short excerpt:
X 2 y>dx + bx*ydy. 4 . T dx + x log xdy 5. (x 2 — y) dx — x dy. X 6. O 2 - 2 xy — y) dx - (x 2 — 2 xy + x) dy.
7. (x 2 — axy + y 2 ) dx + (y 2 + xy — ax 2 ) dy.
8. (sin y — e x y) dx + (x cos y — e x ) dy.
9. Show a geometrical interpretation of the differential y dx — x dy, and from purely geometrical considerations show that the integral ( 2 ' 2 (ydx — xdy) must depend upon the path. ** Vl 10. For a gas that follows the law pv = BT, we have I = p, whence dQ = cdT + pdv. Show that while dQ is ...not an exact differential, — & is an exact differential.
/»2, 2 11. Find the value of the integral \ (ydx — x dy) for the following paths between (0, 0) and (2, 2) : (a) A path made up of the straight line joining (0, 0) to (2, 0) and the straight line joining (2, 0) to (2, 2). (&) A path made up of the F-axis from (0, 0) to (0, 2) and the line joining (0, 2) to (2, 2). (c) The curve y = x 3 - 3 x.
12. Find the value of the integral \ (2 xy dx+x 2 dy). Show by choos- «/o, o ing two or more paths that the integral is independent of the path.
What to read after Essentials of Calculus?
You can find similar books in the "Read Also" column, or choose other free books by Edgar Jerome Townsend to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
X 2 y>dx + bx*ydy. 4 . T dx + x log xdy 5. (x 2 — y) dx — x dy. X 6. O 2 - 2 xy — y) dx - (x 2 — 2 xy + x) dy.
7. (x 2 — axy + y 2 ) dx + (y 2 + xy — ax 2 ) dy.
8. (sin y — e x y) dx + (x cos y — e x ) dy.
9. Show a geometrical interpretation of the differential y dx — x dy, and from purely geometrical considerations show that the integral ( 2 ' 2 (ydx — xdy) must depend upon the path. ** Vl 10. For a gas that follows the law pv = BT, we have I = p, whence dQ = cdT + pdv. Show that while dQ is ...not an exact differential, — & is an exact differential.
/»2, 2 11. Find the value of the integral \ (ydx — x dy) for the following paths between (0, 0) and (2, 2) : (a) A path made up of the straight line joining (0, 0) to (2, 0) and the straight line joining (2, 0) to (2, 2). (&) A path made up of the F-axis from (0, 0) to (0, 2) and the line joining (0, 2) to (2, 2). (c) The curve y = x 3 - 3 x.
12. Find the value of the integral \ (2 xy dx+x 2 dy). Show by choos- «/o, o ing two or more paths that the integral is independent of the path.
What to read after Essentials of Calculus?
You can find similar books in the "Read Also" column, or choose other free books by Edgar Jerome Townsend to read onlineMoreLess
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