000 07675cam a22006018i 4500
001 9781351014953
003 FlBoTFG
005 20220711212225.0
006 m o d
007 cr |||||||||||
008 210607s2021 flu ob 001 0 eng
040 _aOCoLC-P
_beng
_erda
_cOCoLC-P
020 _a9781351014953
_q(ebook)
020 _a1351014951
020 _a9781351014939
_q(electronic bk. : EPUB)
020 _a1351014935
_q(electronic bk. : EPUB)
020 _a9781351014946
_q(electronic bk. : PDF)
020 _a1351014943
_q(electronic bk. : PDF)
020 _a9781351014922
_q(electronic bk. : Mobipocket)
020 _a1351014927
_q(electronic bk. : Mobipocket)
020 _z9780815361466
_q(hardback)
020 _z9781032067988
_q(paperback)
024 7 _a10.1201/9781351014953
_2doi
035 _a(OCoLC)1257316015
035 _a(OCoLC-P)1257316015
050 0 0 _aQA184.2
072 7 _aMAT
_x000000
_2bisacsh
072 7 _aMAT
_x002000
_2bisacsh
072 7 _aMAT
_x003000
_2bisacsh
072 7 _aPBT
_2bicssc
082 0 0 _a512/.5
_223
100 1 _aVasundhara Devi, J.,
_eauthor.
_914479
245 1 0 _aLinear algebra to differential equations /
_cJ. Vasundhara Devi, Sadashiv G. Deo, Ramakrishna Khandeparkar.
250 _aFirst edition.
264 1 _aBoca Raton, FL :
_bChapman & Hall, CRC Press,
_c2021.
300 _a1 online resource
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
520 _a"Linear Algebra to Differential Equations concentrates on the essential topics necessary for all engineering students in general and computer science branch students, in particular. Specifically, the topics dealt will help the reader in applying linear algebra as a tool. The advent of high-speed computers has paved the way for studying large systems of linear equations as well as large systems of linear differential equations. Along with the standard numerical methods, methods that curb the progress of error are given for solving linear systems of equations. The topics of linear algebra and differential equations are linked by Kronecker products and calculus of matrices. These topics are useful in dealing with linear systems of differential equations and matrix differential equations. Differential equations are treated in terms of vector and matrix differential systems, as they naturally arise while formulating practical problems. The essential concepts dealing with the solutions and their stability are briefly presented to motivate the reader towards further investigation. This book caters to the needs of Engineering students in general and in particular, to students of Computer Science & Engineering, Artificial Intelligence, Machine Learning and Robotics. Further, the book provides a quick and complete overview of linear algebra and introduces linear differential systems, serving the basic requirements of scientists and researchers in applied fields. Features Provides complete basic knowledge of the subject Exposes the necessary topics lucidly Introduces the abstraction and at the same time is down to earth Highlights numerical methods and approaches that are more useful Essential techniques like SVD and PCA are given Applications (both classical and novel) bring out similarities in various disciplines: Illustrative examples for every concept: A brief overview of techniques that hopefully serves the present and future needs of students and scientists"--
_cProvided by publisher.
505 0 _a<P><STRONG>1. Vectors and Matrices.</STRONG> 1.1. Introduction. 1.2. Scalars and Vectors. 1.3. Introduction to Matrices. 1.4. Types of Matrices. 1.5. Elementary Operations and Elementary Matrices. 1.6. Determinants. 1.7. Inverse of a Matrix. 1.8. Partitioning of Matrices. 1.9. Advanced Topics: Pseudo Inverse and Congruent Inverse. 1.10. Conclusion. <STRONG>2. Linear System of Equations.</STRONG> 2.1. Introduction. 2.2. Linear System of Equations. 2.3. Rank of a Matrix. 2.4. Echelon Form and Normal Form. 2.4. Echelon Form and Normal Form. 2.5. Solutions of a Linear System of Equations. 2.6. Cayley Hamilton Theorem. 2.7. Eigen Values and Eigen Vectors. 2.8. Singular Values and Singular Vectors. 2.9. Quadratic Forms. 2.10. Conclusion. <STRONG>3. Vector Spaces.</STRONG> 3.1. Introduction. 3.2. Vector Space and a Subspace. 3.3. Linear Independence, Basis and Dimension. 3.4. Change of Basis -- Matrix. 3.5. Linear Transformations. 3.6. Matrices of Linear Transformations. 3.7. Inner Product Space. 3.8. Gram-Schmidt Orthogonalization. 3.9. Linking Linear Algebra to Differential Equations. 3.10. Conclusion. <STRONG>4. Numerical Methods in Linear Algebra.</STRONG> 4.1. Introduction. 4.2. Elements of Computation and Errors. 4.3. Direct Methods for Solving a Linear System of Equations. 4.4. Iterative Methods. 4.5. Householder Transformation. 4.6. Tridiagonalization of a Symmetric Matrix by Plane Rotation. 4.7. QR Decomposition. 4.8. Eigen Values: Bounds and Power Method. 4.9. Krylov Subspace Methods. 4.10. Conclusion.<STRONG> 5. Applications.</STRONG> 5.1. Introduction. 5.2. Finding Curves through Given Points. 5.3. Markov Chains. 5.4. Leontief's Models. 5.5. Cryptology. 5.6. Application to Computer Graphics. 5.7. Application to Computer Graphics. 5.8. Bioinformatics. 5.9. Principal Component Analysis (PCA). 5.10. Big Data. 5.11. Conclusion. <STRONG>6. Kronecker Product.</STRONG> 6.1. Introduction. 6.2. Primary Matrices. 6.3. Kronecker Products. 6.4. Further Properties of Kronecker products. 6.5. Kronecker product of two linear transformations. 6.6. Kronecker Product and Vector Operators. 6.7. Permutation Matrices and Kronecker Products. 6.8. Analytical functions and Kronecker Product. 6.9. Kronecker Sum. 6.10. Lyapunov Function. 6.11. Conclusion. <STRONG>7. Calculus of Matrices. </STRONG>7.1. Introduction. 7.2. Derivative of a Matrix Valued Function with respect to a Scalar. 7.3. Derivative of a Vector Valued Function w.r.t. a Vector. 7.4. Derivative of a Scalar Valued Function w.r.t. a Matrix. 7.5. Derivative of a Matrix Valued Function w.r.t. its Entries and Vice versa. 7.6. The Matrix Differential. 7.7. Derivative of a Matrix w.r.t. a Matrix. 7.8. Derivative Formula using Kronecker Products. 7.9. Another Definition for Derivative of a Matrix w.r.t. a Matrix. 7.10. Conclusion. <STRONG>8. Linear Systems of Differential Equations.</STRONG> 8.1. Introduction. 8.2. Linear Systems. 8.3. Fundamental Matrix. 8.4. Method of Successive Approximations. 8.5. Nonhomogeneous Systems. 8.6. Linear Systems with Constant Coefficients. 8.7. Stability Analysis of a System. 8.8. Election Mathematics. 8.9. Conclusion. <STRONG>9. Linear Matrix Differential Equations.</STRONG> 9.1. Introduction. 9.2. Initial Value Problem (IVP). 9.3. LMDE X' = A(t)X. 9.4. The LMDE X' = AXB. 9.5. More General LMDE. 9.6. A Class of LMDE of Higher Order. 9.7. Boundary Value Problem of LMDE. 9.8. Trigonometric and Hyperbolic Matrix Functions. 9.9. Conclusion. </P>
588 _aOCLC-licensed vendor bibliographic record.
650 0 _aAlgebras, Linear.
_94004
650 0 _aDifferential equations.
_914480
650 7 _aMATHEMATICS / General
_2bisacsh
_914481
650 7 _aMATHEMATICS / Algebra / General
_2bisacsh
_913209
650 7 _aMATHEMATICS / Applied
_2bisacsh
_96859
700 1 _aDeo, Sadashiv G.,
_d1933-
_eauthor.
_914482
700 1 _aKhandeparkar, Ramakrishna,
_eauthor.
_914483
856 4 0 _3Taylor & Francis
_uhttps://www.taylorfrancis.com/books/9781351014953
856 4 2 _3OCLC metadata license agreement
_uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
942 _cEBK
999 _c70718
_d70718