國立虎尾科技大學 |

Exercises and Problems in Mathematical Methods of Physics

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Exercises and Problems in Mathematical Methods of Physics/ by Giampaolo Cicogna.
作者:	Cicogna, Giampaolo.
面頁冊數:	X, 182 p. 8 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Physics. -
電子資源:	https://doi.org/10.1007/978-3-319-76165-7
ISBN:	9783319761657

Exercises and Problems in Mathematical Methods of Physics
Cicogna, Giampaolo.

Exercises and Problems in Mathematical Methods of Physics[electronic resource] /by Giampaolo Cicogna. - 1st ed. 2018. - X, 182 p. 8 illus.online resource. - Undergraduate Lecture Notes in Physics,2192-4791. - Undergraduate Lecture Notes in Physics,.

1 Hilbert spaces -- 1.1 Complete sets, Fourier expansions -- 1.1.1 Preliminary notions. Subspaces. Complete sets -- 1.1.2 Fourier expansions -- 1.1.3 Harmonic functions; Dirichlet and Neumann Problems -- 1.2 Linear operators -- 1.2.1 Linear operators defined giving T en = vn, and related Problems -- 1.2.2 Operators of the form T x = v(w;x) and T x = ån vn(wn;x) -- 1.2.3 Operators of the form T f (x) = j(x) f (x) -- 1.2.4 Problems involving differential operators -- 1.2.5 Functionals -- 1.2.6 Time evolution Problems. Heat equation -- 1.2.7 Miscellaneous Problems -- 2 Functions of a complex variable -- 2.1 Basic properties of analytic functions -- 2.2 Evaluation of integrals by complex variable methods -- 2.3 Harmonic functions and conformal mappings -- 3 Fourier and Laplace transforms. Distributions -- 3.1 Fourier transform in L1(R) and L2(R) -- 3.1.1 Basic properties and applications -- 3.1.2 Fourier transform and linear operators in L2(R) -- 3.2 Tempered distributions and Fourier transforms -- 3.2.1 General properties -- 3.2.2 Fourier transform, distributions and linear operators -- 3.2.3 Applications to ODE’s and related Green functions -- 3.2.4 Applications to general linear systems and Green functions -- 3.2.5 Applications to PDE’s -- 3.3 Laplace transforms -- vvi Contents -- Groups, Lie algebras, symmetries in physics -- 4.1 Basic properties of groups and representations -- 4.2 Lie groups and algebras -- 4.3 The groups SO3; SU2; SU3 -- 4.4 Other direct applications of symmetries to physics -- Answers and Solutions. .

This book presents exercises and problems in the mathematical methods of physics with the aim of offering undergraduate students an alternative way to explore and fully understand the mathematical notions on which modern physics is based. The exercises and problems are proposed not in a random order but rather in a sequence that maximizes their educational value. Each section and subsection starts with exercises based on first definitions, followed by groups of problems devoted to intermediate and, subsequently, more elaborate situations. Some of the problems are unavoidably "routine", but others bring to the forenontrivial properties that are often omitted or barely mentioned in textbooks. There are also problems where the reader is guided to obtain important results that are usually stated in textbooks without complete proofs. In all, some 350 solved problems covering all mathematical notions useful to physics are included. While the book is intended primarily for undergraduate students of physics, students of mathematics, chemistry, and engineering, as well as their teachers, will also find it of value. .

ISBN: 9783319761657

Standard No.: 10.1007/978-3-319-76165-7doiSubjects--Topical Terms:

564049
Physics.

LC Class. No.: QC5.53

Dewey Class. No.: 530.15

Exercises and Problems in Mathematical Methods of Physics
LDR:04027nam a22003975i 4500 001 995223
003 DE-He213
005 20200702033530.0
007 cr nn 008mamaa
008 201225s2018 gw | s |||| 0|eng d
020 $a 9783319761657 $9 978-3-319-76165-7
024 7 $a 10.1007/978-3-319-76165-7 $2 doi
035 $a 978-3-319-76165-7
050 4 $a QC5.53
072 7 $a PHU $2 bicssc
072 7 $a SCI040000 $2 bisacsh
072 7 $a PHU $2 thema
082 0 4 $a 530.15 $2 23
100 1 $a Cicogna, Giampaolo. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1202963
245 1 0 $a Exercises and Problems in Mathematical Methods of Physics $h [electronic resource] / $c by Giampaolo Cicogna.
250 $a 1st ed. 2018.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a X, 182 p. 8 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Undergraduate Lecture Notes in Physics, $x 2192-4791
505 0 $a 1 Hilbert spaces -- 1.1 Complete sets, Fourier expansions -- 1.1.1 Preliminary notions. Subspaces. Complete sets -- 1.1.2 Fourier expansions -- 1.1.3 Harmonic functions; Dirichlet and Neumann Problems -- 1.2 Linear operators -- 1.2.1 Linear operators defined giving T en = vn, and related Problems -- 1.2.2 Operators of the form T x = v(w;x) and T x = ån vn(wn;x) -- 1.2.3 Operators of the form T f (x) = j(x) f (x) -- 1.2.4 Problems involving differential operators -- 1.2.5 Functionals -- 1.2.6 Time evolution Problems. Heat equation -- 1.2.7 Miscellaneous Problems -- 2 Functions of a complex variable -- 2.1 Basic properties of analytic functions -- 2.2 Evaluation of integrals by complex variable methods -- 2.3 Harmonic functions and conformal mappings -- 3 Fourier and Laplace transforms. Distributions -- 3.1 Fourier transform in L1(R) and L2(R) -- 3.1.1 Basic properties and applications -- 3.1.2 Fourier transform and linear operators in L2(R) -- 3.2 Tempered distributions and Fourier transforms -- 3.2.1 General properties -- 3.2.2 Fourier transform, distributions and linear operators -- 3.2.3 Applications to ODE’s and related Green functions -- 3.2.4 Applications to general linear systems and Green functions -- 3.2.5 Applications to PDE’s -- 3.3 Laplace transforms -- vvi Contents -- Groups, Lie algebras, symmetries in physics -- 4.1 Basic properties of groups and representations -- 4.2 Lie groups and algebras -- 4.3 The groups SO3; SU2; SU3 -- 4.4 Other direct applications of symmetries to physics -- Answers and Solutions. .
520 $a This book presents exercises and problems in the mathematical methods of physics with the aim of offering undergraduate students an alternative way to explore and fully understand the mathematical notions on which modern physics is based. The exercises and problems are proposed not in a random order but rather in a sequence that maximizes their educational value. Each section and subsection starts with exercises based on first definitions, followed by groups of problems devoted to intermediate and, subsequently, more elaborate situations. Some of the problems are unavoidably "routine", but others bring to the forenontrivial properties that are often omitted or barely mentioned in textbooks. There are also problems where the reader is guided to obtain important results that are usually stated in textbooks without complete proofs. In all, some 350 solved problems covering all mathematical notions useful to physics are included. While the book is intended primarily for undergraduate students of physics, students of mathematics, chemistry, and engineering, as well as their teachers, will also find it of value. .
650 0 $a Physics. $3 564049
650 0 $a Fourier analysis. $3 639284
650 0 $a Operator theory. $3 527910
650 0 $a Functions of complex variables. $3 528649
650 0 $a Integral transforms. $3 678414
650 0 $a Operational calculus. $3 1253881
650 0 $a Group theory. $3 527791
650 1 4 $a Mathematical Methods in Physics. $3 670749
650 2 4 $a Fourier Analysis. $3 672627
650 2 4 $a Operator Theory. $3 672127
650 2 4 $a Functions of a Complex Variable. $3 672126
650 2 4 $a Integral Transforms, Operational Calculus. $3 672154
650 2 4 $a Group Theory and Generalizations. $3 672112
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319761640
776 0 8 $i Printed edition: $z 9783319761664
830 0 $a Undergraduate Lecture Notes in Physics, $x 2192-4791 $3 1253454
856 4 0 $u https://doi.org/10.1007/978-3-319-76165-7
912 $a ZDB-2-PHA
912 $a ZDB-2-SXP
950 $a Physics and Astronomy (SpringerNature-11651)
950 $a Physics and Astronomy (R0) (SpringerNature-43715)