By Wilfred Kaplan
The 5th version of this best textual content deals large education in vectors and matrices, vector research, and partial differential equations. Vectors are brought on the outset and serve at many issues to point geometrical and actual value of mathematical relatives. Numerical tools are touched upon at numerous issues, as a result of their useful worth and the insights they offer approximately theory.
Vectors and Matrices; Differential Calculus of services of numerous Variables; Vector Differential Calculus; quintessential Calculus of capabilities of numerous Variables; Vector crucial Calculus; Two-Dimensional idea; 3-dimensional idea and purposes; countless sequence; Fourier sequence and Orthogonal features; capabilities of a posh Variable; usual Differential Equations; Partial Differential Equations
For all readers attracted to complicated calculus.
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Extra resources for Advanced Calculus (5th Edition)
All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. October 14, 2010 14:9 THM/NEIL Page-25 27410_01_ch01_p01-42 CHAPTER 1 First-Order Differential Equations 26 (d) Show that δ(x, y) = x y −3 is also an integrating factor on any rectangle where x = 0 and y = 0.
2) = −k A 2gh(t). dt To illustrate these ideas, consider the problem of draining a hemispherical tank of radius 18 feet that is full of water and has a circular drain hole of radius 3 inches at the bottom. How long will it take for the tank to empty? 2) contains two unknown functions, so we must eliminate one. To do this, let r (t) be the radius of the surface of the fluid at time t, and consider an interval of time from t0 to t0 + t. The volume V of water draining from the tank in this time equals the volume of a disk of thickness h (the change in depth) and radius r (t ∗ ) for some t ∗ between t0 and t0 + t.
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 4 Homogeneous, Bernoulli, and Riccati Equations 29 This is linear when P(x) is identically zero.
Advanced Calculus (5th Edition) by Wilfred Kaplan