Differential Equations and Linear Algebra (4th Edition) - 4th Edition - by Stephen W. Goode, Scott A. Annin - ISBN 9780321964670
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Differential Equations and Linear Algeb...
4th Edition
Stephen W. Goode, Scott A. Annin
Publisher: PEARSON
ISBN: 9780321964670

Solutions for Differential Equations and Linear Algebra (4th Edition)

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Chapter 1.11 - Some Higher-order Differential EquationsChapter 1.12 - Chapter ReviewChapter 2.1 - Matrices: Definitions And NotationChapter 2.2 - Matrix AlgebraChapter 2.3 - Terminology For Systems Of Linear EquationsChapter 2.4 - Row-echelon Matrices And Elementary Row OperationsChapter 2.5 - Gaussian EliminationChapter 2.6 - The Inverse Of A Square MatrixChapter 2.7 - Elementary Matrices And The Lu FactorizationChapter 2.8 - The Invertible Matrix Theorem IChapter 2.9 - Chapter ReviewChapter 3.1 - The Definition Of The DeterminantChapter 3.2 - Properties Of DeterminantsChapter 3.3 - Cofactor ExpansionsChapter 3.4 - Summary Of DeterminantsChapter 3.5 - Chapter ReviewChapter 4.1 - Vectors In R.nChapter 4.2 - Definition Of A Vector SpaceChapter 4.3 - SubspacesChapter 4.4 - Spanning SetsChapter 4.5 - Linear Dependence And Linear IndependenceChapter 4.6 - Bases And DimensionChapter 4.7 - Change Of BasisChapter 4.8 - Row Space And Column SpaceChapter 4.9 - The Rank-nullity TheoremChapter 4.11 - Chapter ReviewChapter 5.1 - Definition Of An Inner Product SpaceChapter 5.2 - Orthogonal Sets Of Vectors And Orthogonal ProjectionsChapter 5.3 - The Gram-schmidt ProcessChapter 5.4 - Least Squares ApproximationChapter 5.5 - Chapter ReviewChapter 6.1 - Definition Of A Linear TransformationChapter 6.2 - Transformations Of R.2Chapter 6.3 - The Kernel And Range Of A Linear TransformationChapter 6.4 - Additional Properties Of Linear TransformationsChapter 6.5 - The Matrix Of A Linear TransformationChapter 6.6 - Chapter ReviewChapter 7.1 - The Eigenvalue/eigenvector ProblemChapter 7.2 - General Results For Eigenvalues And EigenvectorsChapter 7.3 - DiagonalizationChapter 7.4 - An Introduction To The Matrix Exponential FunctionChapter 7.5 - Orthogonal Diagonalization And Quadratic FormsChapter 7.6 - Jordan Canonical FormsChapter 7.7 - Chapter ReviewChapter 8.1 - General Theory For Linear Differential EquationsChapter 8.2 - Constant Coefficient Homogeneous Linear Differential EquationsChapter 8.3 - The Method Of Undetermined Coefficients: AnnihilatorsChapter 8.5 - Oscillations Of A Mechanical SystemChapter 8.6 - Rlc CircuitsChapter 8.7 - The Variation Of Parameters MethodChapter 8.8 - A Differential Equation With Nonconstant CoefficientsChapter 8.9 - Reduction Of OrderChapter 8.10 - Chapter ReviewChapter 9.1 - First-order Linear SystemsChapter 9.2 - Vector FormulationChapter 9.3 - General Results For First-order Linear Differential SystemsChapter 9.4 - Vector Differential Equations: Nondefective Coefficient MatrixChapter 9.5 - Vector Differential Equations: Defective Coefficient MatrixChapter 9.6 - Variation-of-parameters For Linear SystemsChapter 9.7 - Some Applications Of Linear Systems Of Differential EquationsChapter 9.8 - Matrix Exponential Function And Systems Of Differential EquationsChapter 9.9 - The Phase Plane For Linear Autonomous SystemsChapter 9.10 - Nonlinear SystemsChapter 9.11 - Chapter ReviewChapter 10.1 - Definition Of The Laplace TransformChapter 10.2 - The Existence Of The Laplace Transform And The Inverse TransformChapter 10.3 - Periodic Functions And The Laplace TransformChapter 10.4 - The Transform Of Derivatives And Solution Of Initial-value ProblemsChapter 10.5 - The First Shifting TheoremChapter 10.6 - The Unit Step FunctionChapter 10.7 - The Second Shifting TheoremChapter 10.8 - Impulsive Driving Terms: The Dirac Delta FunctionChapter 10.9 - The Convolution IntegralChapter 10.10 - Chapter ReviewChapter 11.1 - A Review Of Power SeriesChapter 11.2 - Series Solutions About An Ordinary PointChapter 11.3 - The Legendre EquationChapter 11.4 - Series Solutions About A Regular Singular PointChapter 11.5 - Frobenius TheoryChapter 11.6 - Bessel's Equation Of Order PChapter 11.7 - Chapter ReviewChapter A - Review Of Complex NumbersChapter B - Review Of Partial FractionsChapter C - Review Of Integration Techniques

Book Details

Differential Equations and Linear Algebra is designed for use in combined differential equations and linear algebra courses. It is best suited for students who have successfully completed three semesters of calculus. Differential Equations and Linear Algebra presents a carefully balanced and sound integration of both differential equations and linear algebra. It promotes in-depth understanding rather than rote memorization, enabling readers to fully comprehend abstract concepts and leave the course with a solid foundation in key areas. Flexible in format, it explains concepts clearly and logically with an abundance of examples and illustrations, without sacrificing level or rigor. The Fourth Edition includes many updated problems to support the material, with varying difficulty levels from which students/instructors can choose.

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