Differential Equation over Banach Algebra

Preprint English OPEN
Kleyn, Aleks;
(2018)
  • Subject: Mathematics - General Mathematics | 34A05, 35F10, 35F40

In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. I considered examples of differential equations in quaternion al... View more
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    17 references, page 1 of 2

    Appendix A. Summary of Statements . . . . . . . . . . . . . . . . . . . . . 45 A.1. Table of Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 A.2. Table of Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Let B1, ..., Bm

    = x1dx1 + dx1x1 + dx2x3 + x2dx3 Теорема 3.5.5. Пусть B - свободная конечно мерная ассоциативная D-

    ную функцию 4.3 u(x, y) = C, которая удовлетворяет равенствам (4.2.1), (4.2.2).

    Согласно теоремам [10]-8.3.1, A.2.1, равенство Z

    (4.2.11) u(x, y) = M (x, y) ◦ dx + C1(y)

    Теорема A.1.1. Для любого b ∈ A ddxb = 0 ⊗ 0

    Доказательство. Теорема является следствием теоремы [10]-B.1.1.

    Теорема A.1.5. Для любых b, c ∈ A  ddbxxc = b ⊗ c

    [2] James Stewart, Calculus, Cengage Learning, 2012, ISBN: 978-0-538-49781-7

    [3] William E. Boyce, Richard C. DiPrima, Elementary Differential Equations and Boundary Value Problems, John Wiley & Sons, Inc., 2009, ISBN 978-0-470-38334-6

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