Differential Equations : : A First Course on ODE and a Brief Introduction to PDE / / Shair Ahmad, Antonio Ambrosetti.
The first part of this book is mainly intended as a textbook for students at the Sophomore-Junior level, majoring in mathematics, engineering, or the sciences in general. The book includes the basic topics in Ordinary Differential Equations, normally taught at the undergraduate level, such as linear...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2023] 2024 |
Year of Publication: | 2023 |
Language: | English |
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Ambrosetti, Antonio, author. aut http://id.loc.gov/vocabulary/relators/aut Differential Equations : A First Course on ODE and a Brief Introduction to PDE / Shair Ahmad, Antonio Ambrosetti. Berlin ; Boston : De Gruyter, [2023] 2024 1 online resource (XVI, 362 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Textbook Frontmatter -- Memorial Dedicated to Professor Antonio Ambrosetti -- Preface -- Contents -- 1 A brief survey of some topics in calculus -- 2 First order linear differential equations -- 3 Analytical study of first order differential equations -- 4 Solving and analyzing some nonlinear first order equations -- 5 Exact differential equations -- 6 Second order linear differential equations -- 7 Higher order linear equations -- 8 Systems of first order equations -- 9 Phase plane analysis -- 10 Introduction to stability -- 11 Series solutions for linear differential equations -- 12 Laplace transform -- 13 A primer on equations of Sturm-Liouville type -- 14 A primer on linear PDE in 2D. I: first order equations -- 15 A primer on linear PDE in 2D. II: second order equations -- 16 The Euler-Lagrange equations in the Calculus of Variations: an introduction -- Solutions -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star The first part of this book is mainly intended as a textbook for students at the Sophomore-Junior level, majoring in mathematics, engineering, or the sciences in general. The book includes the basic topics in Ordinary Differential Equations, normally taught at the undergraduate level, such as linear and nonlinear equations and systems, Bessel functions, Laplace transform, stability, etc. It is written with ample flexibility to make it appropriate either as a course stressing application, or a course stressing rigor and analytical thinking. It also offers sufficient material for a one-semester graduate course, covering topics such as phase plane analysis, oscillation, Sturm-Liouville equations, Euler-Lagrange equations in Calculus of Variations, first and second order linear PDE in 2D. There are substantial lists of exercises at the ends of the chapters. In this edition complete solutions to all even number problems are given in the back of the book.The 2nd edition also includes some new problems and examples. An effort has been made to make the material more suitable and self-contained for undergraduate students with minimal knowledge of Calculus. For example, a detailed review of matrices and determinants has been added to the chapter on systems of equations. The second edition also contains corrections of some misprints and errors in the first edition. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 09. Dez 2023) Differentialgleichung. Laplace-Transformation. Ljapunov-Stabilitätstheorie. Qualitative Theorie. Sturm-Liouville-Problem. MATHEMATICS / Differential Equations / General. bisacsh Differential equations, Laplace Transforms., Lyapunov stability theory, qualitative theory, Sturm-Liouville problem. Ahmad, Shair, author. aut http://id.loc.gov/vocabulary/relators/aut EPUB 9783111185781 print 9783111185248 https://doi.org/10.1515/9783111185675 https://www.degruyter.com/isbn/9783111185675 Cover https://www.degruyter.com/document/cover/isbn/9783111185675/original |
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English |
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Ambrosetti, Antonio, Ambrosetti, Antonio, Ahmad, Shair, |
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Ambrosetti, Antonio, Ambrosetti, Antonio, Ahmad, Shair, Differential Equations : A First Course on ODE and a Brief Introduction to PDE / De Gruyter Textbook Frontmatter -- Memorial Dedicated to Professor Antonio Ambrosetti -- Preface -- Contents -- 1 A brief survey of some topics in calculus -- 2 First order linear differential equations -- 3 Analytical study of first order differential equations -- 4 Solving and analyzing some nonlinear first order equations -- 5 Exact differential equations -- 6 Second order linear differential equations -- 7 Higher order linear equations -- 8 Systems of first order equations -- 9 Phase plane analysis -- 10 Introduction to stability -- 11 Series solutions for linear differential equations -- 12 Laplace transform -- 13 A primer on equations of Sturm-Liouville type -- 14 A primer on linear PDE in 2D. I: first order equations -- 15 A primer on linear PDE in 2D. II: second order equations -- 16 The Euler-Lagrange equations in the Calculus of Variations: an introduction -- Solutions -- Bibliography -- Index |
author_facet |
Ambrosetti, Antonio, Ambrosetti, Antonio, Ahmad, Shair, Ahmad, Shair, Ahmad, Shair, |
author_variant |
a a aa a a aa s a sa |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Ahmad, Shair, Ahmad, Shair, |
author2_variant |
s a sa |
author2_role |
VerfasserIn VerfasserIn |
author_sort |
Ambrosetti, Antonio, |
title |
Differential Equations : A First Course on ODE and a Brief Introduction to PDE / |
title_sub |
A First Course on ODE and a Brief Introduction to PDE / |
title_full |
Differential Equations : A First Course on ODE and a Brief Introduction to PDE / Shair Ahmad, Antonio Ambrosetti. |
title_fullStr |
Differential Equations : A First Course on ODE and a Brief Introduction to PDE / Shair Ahmad, Antonio Ambrosetti. |
title_full_unstemmed |
Differential Equations : A First Course on ODE and a Brief Introduction to PDE / Shair Ahmad, Antonio Ambrosetti. |
title_auth |
Differential Equations : A First Course on ODE and a Brief Introduction to PDE / |
title_alt |
Frontmatter -- Memorial Dedicated to Professor Antonio Ambrosetti -- Preface -- Contents -- 1 A brief survey of some topics in calculus -- 2 First order linear differential equations -- 3 Analytical study of first order differential equations -- 4 Solving and analyzing some nonlinear first order equations -- 5 Exact differential equations -- 6 Second order linear differential equations -- 7 Higher order linear equations -- 8 Systems of first order equations -- 9 Phase plane analysis -- 10 Introduction to stability -- 11 Series solutions for linear differential equations -- 12 Laplace transform -- 13 A primer on equations of Sturm-Liouville type -- 14 A primer on linear PDE in 2D. I: first order equations -- 15 A primer on linear PDE in 2D. II: second order equations -- 16 The Euler-Lagrange equations in the Calculus of Variations: an introduction -- Solutions -- Bibliography -- Index |
title_new |
Differential Equations : |
title_sort |
differential equations : a first course on ode and a brief introduction to pde / |
series |
De Gruyter Textbook |
series2 |
De Gruyter Textbook |
publisher |
De Gruyter, |
publishDate |
2023 |
physical |
1 online resource (XVI, 362 p.) Issued also in print. |
contents |
Frontmatter -- Memorial Dedicated to Professor Antonio Ambrosetti -- Preface -- Contents -- 1 A brief survey of some topics in calculus -- 2 First order linear differential equations -- 3 Analytical study of first order differential equations -- 4 Solving and analyzing some nonlinear first order equations -- 5 Exact differential equations -- 6 Second order linear differential equations -- 7 Higher order linear equations -- 8 Systems of first order equations -- 9 Phase plane analysis -- 10 Introduction to stability -- 11 Series solutions for linear differential equations -- 12 Laplace transform -- 13 A primer on equations of Sturm-Liouville type -- 14 A primer on linear PDE in 2D. I: first order equations -- 15 A primer on linear PDE in 2D. II: second order equations -- 16 The Euler-Lagrange equations in the Calculus of Variations: an introduction -- Solutions -- Bibliography -- Index |
isbn |
9783111185675 9783111185781 9783111185248 |
url |
https://doi.org/10.1515/9783111185675 https://www.degruyter.com/isbn/9783111185675 https://www.degruyter.com/document/cover/isbn/9783111185675/original |
illustrated |
Not Illustrated |
doi_str_mv |
10.1515/9783111185675 |
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Differential Equations : A First Course on ODE and a Brief Introduction to PDE / |
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