Differential equations and linear algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Wellesley, MA
Wellesley - Cambridge Press
[2014]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 502 Seiten Diagramme |
| ISBN: | 9780980232790 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Table of Contents^
Preface v
1 First Order Equations 1
1.1 Four Examples : Linear versus Nonlinear ........................ 1
1.2 The Calculus You NeeçL........................................... 4
L3 The Exponentials e* and eat........................................ 9
1.4 Four Particular Solutions......................................... 17
1.5 Real and Complex Sinusoids........................................ 30
1.6 Models of Growth and Decay........................................ 40
1.7 The Logistic Equation............................................. 53
1.8 Separable Equations and Exact Equations........................... 65
2 Second Order Equations 73
2.1 Second Derivatives in Science and Engineering..................... 73
2.2 Key Facts About Complex Numbers................................... 82
2.3 Constant Coefficients A 9 B, C.................................... 90
2.4 Forced Oscillations and Exponential Response..................... 103
2.5 Electrical Networks and Mechanical Systems....................... 118
2.6 Solutions to Second Order Equations.............................. 130
2.7 Laplace Transforms Y(s) and F(s)................................. 139
3 Graphical and Numerical Methods 153
3.1 Nonlinear Equations yf — f(t9y).................................. 154
3.2 Sources, Sinks, Saddles, and Spirals............................ 161
3.3 Linearization and Stability in 2D and 3D......................... 170
3.4 The Basic Euler Methods.......................................... 184
3.5 Higher Accuracy with Runge-Kutta................................. 191
4 Linear Equations and Inverse Matrices 197
4.1 Two Pictures of Linear Equations................................. 197
4.2 Solving Linear Equations by Elimination.......................... 210
4.3 Matrix Multiplication............................................ 219
4.4 Inverse Matrices................................................. 228
4.5 Symmetric Matrices and Orthogonal Matrices....................... 238
iii
IV Table of Contents
5 Vector Spaces and Subspaces 251
5.1 The Column Space of a Matrix..................................... 251
5.2 The Nullspace of A : Solving Av = 0.............................. 261
5.3 The Complete Solution to Av = b.................................. 273
5.4 Independence, Basis and Dimension................................ 285
5.5 The Four Fundamental Subspaces................................... 300
5.6 Graphs and Networks.............................................. 313
6 Eigenvalues and Eigenvectors 325
6.1 Introduction to Eigenvalues...................................... 325
6.2 Diagonalizing a Matrix........................................... 337
6.3 Linear Systems y = Ay........................................... 349
6.4 The Exponential of a Matrix...................................... 362
6.5 Second Order Systems and Symmetric Matrices...................... 372
7 Applied Mathematics and A1 A 385
7.1 Least Squares and Projections.................................... 386
7.2 Positive Definite Matrices and the SVD........................... 396
7.3 Boundary Conditions Replace Initial Conditions................... 406
7.4 Laplace’s Equation and AT A...................................... 416
7.5 Networks and the Graph Laplacian................................. 423
8 Fourier and Laplace Transforms 432
8.1 Fourier Series................................................... 434
8.2 The Fast Fourier Transform....................................... 446
8.3 The Heat Equation................................................ 455
8.4 The Wave Equation................................................ 463
8.5 The Laplace Transform............................................ 470
8.6 Convolution (Fourier and Laplace)................................ 479
Matrix Factorizations 490
Properties of Determinants 492
Index 493
Linear Algebra in a Nutshell 502
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| id | DE-604.BV042382825 |
| illustrated | Not Illustrated |
| indexdate | 2025-05-07T04:00:37Z |
| institution | BVB |
| isbn | 9780980232790 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027818873 |
| oclc_num | 904785258 |
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| physical | x, 502 Seiten Diagramme |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Wellesley - Cambridge Press |
| record_format | marc |
| spellingShingle | Strang, Gilbert 1934- Differential equations and linear algebra Differentialgleichung (DE-588)4012249-9 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4035811-2 |
| title | Differential equations and linear algebra |
| title_auth | Differential equations and linear algebra |
| title_exact_search | Differential equations and linear algebra |
| title_full | Differential equations and linear algebra Gilbert Strang, Department of Mathematics, Massachusetts Institute of Technology |
| title_fullStr | Differential equations and linear algebra Gilbert Strang, Department of Mathematics, Massachusetts Institute of Technology |
| title_full_unstemmed | Differential equations and linear algebra Gilbert Strang, Department of Mathematics, Massachusetts Institute of Technology |
| title_short | Differential equations and linear algebra |
| title_sort | differential equations and linear algebra |
| topic | Differentialgleichung (DE-588)4012249-9 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Differentialgleichung Lineare Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027818873&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT stranggilbert differentialequationsandlinearalgebra |
Indexes
THWS Schweinfurt Zentralbibliothek Lesesaal
| Call Number: |
2000 SK 520 S897 |
|---|---|
| Copy 1 | ausleihbar Checked out – Due: 02.06.2026 Recall This |