TY  - BOOK
AU  - Boyce,William E.
AU  - DiPrima,Richard C.
TI  - Elementary differential equations and boundary value problems
SN  - 0471433381 (acidfree paper)
AV  - QA371 BOY 2004
U1  - 515/.35 22
PY  - 2004///
CY  - Hoboken, NJ
PB  - Wiley
KW  - Differential equations
KW  - Boundary value problems
N1  - Includes bibliographical references and index; Chapter 1; Introduction --; 1.1; Some Basic Mathematical Models; Direction Fields --; 1.2; Solutions of Some Differential Equations --; 1.3; Classification of Differential Equations --; 1.4; Historical Remarks --; Chapter 2; First Order Differential Equations --; 2.1; Linear Equations with Variable Coefficients --; 2.2; Separable Equations --; 2.3; Modeling with First Order Equations --; 2.4; Differences Between Linear and Nonlinear Equations --; 2.5; Autonomous Equations and Population Dynamics --; 2.6; Exact Equations and Integrating Factors --; 2.7; Numerical Approximations: Euler's Method --; 2.8; The Existence and Uniqueness Theorem --; 2.9; First Order Difference Equations --; Chapter 3; Second Order Linear Equations --; 3.1; Homogeneous Equations with Constant Coefficients --; 3.2; Fundamental Solutions of Linear Homogeneous Equations --; 3.3; Linear Independence and the Wronskian --; 3.4; Complex Roots of the Characteristic Equation --; 3.5; Repeated Roots; Reduction of Order --; 3.6; Nonhomogeneous Equations; Method of Undetermined Coefficients --; 3.7; Variation of Parameters --; 3.8; Mechanical and Electrical Vibrations --; 3.9; Forced Vibrations --; Chapter 4; Higher Order Linear Equations --; 4.1; General Theory of nth Order Linear Equations --; 4.2; Homogeneous Equations with Constant Coeffients --; 4.3; The Method of Undetermined Coefficients --; 4.4; The Method of Variation of Parameters --; Chapter 5; Series Solutions of Second Order Linear Equations --; 5.1; Review of Power Series --; 5.2; Series Solutions near an Ordinary Point, Part I --; 5.3; Series Solutions near an Ordinary Point, Part II --; 5.4; Regular Singular Points --; 5.5; Euler Equations --; 5.6; Series Solutions near a Regular Singular Point, Part I --; 5.7; Series Solutions near a Regular Singular Point, Part II --; 5.8; Bessel's Equation --; Chapter 6; The Laplace Transform --; 6.1; Definition of the Laplace Transform --; 6.2; Solution of Initial Value Problems --; 6.3; Step Functions --; 6.4; Differential Equations with Discontinuous Forcing Functions --; 6.5; Impulse Functions --; 6.6; The Convolution Integral --; Chapter 7; Systems of First Order Linear Equations --; 7.1; Introduction --; 7.2; Review of Matrices --; 7.3; Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors --; 7.4; Basic Theory of Systems of First Order Linear Equations --; 7.5; Homogeneous Linear Systems with Constant Coefficients --; 7.6; Complex Eigenvalues --; 7.7; Fundamental Matrices --; 7.8; Repeated Eigenvalues --; 7.9; Nonhomogeneous Linear Systems --; Chapter 8; Numerical Methods --; 8.1; The Euler or Tangent Line Method --; 8.2; Improvements on the Euler Method --; 8.3; The Runge-Kutta Method --; 8.4; Multistep Methods --; 8.5; More on Errors; Stability --; 8.6; Systems of First Order Equations --; Chapter 9; Nonlinear Differential Equations and Stability --; 9.1; The Phase Plane; Linear Systems --; 9.2; Autonomous Systems and Stability --; 9.3; Almost Linear Systems --; 9.4; Competing Species --; 9.5; Predator-Prey Equations --; 9.6; Liapunov's Second Method --; 9.7; Periodic Solutions and Limit Cycles --; 9.8; Chaos and Strange Attractors; the Lorenz Equations --; Chapter 10; Partial Differential Equations and Fourier Series --; 10.1; Two-Point Boundary Valve Problems --; 10.2; Fourier Series --; 10.3; The Fourier Convergence Theorem --; 10.4; Even and Odd Functions --; 10.5; Separation of Variables; Heat Conduction in a Rod --; 10.6; Other Heat Conduction Problems --; 10.7; The Wave Equation; Vibrations of an Elastic String --; 10.8; Laplace's Equation --; Appendix A; Derivation of the Heat Conduction Equation --; Appendix B; Derivation of the Wave Equation --; Chapter 11; Boundary Value Problems and Sturm-Liouville Theory --; 11.1; The Occurrence of Two Point Boundary Value Problems --; 11.2; Sturm-Liouville Boundary Value Problems --; 11.3; Nonhomogeneous Boundary Value Problems --; 11.4; Singular Sturm-Liouville Problems --; 11.5; Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion --; 11.6; Series of Orthogonal Functions: Mean Convergence
UR  - http://www.loc.gov/catdir/bios/wiley047/2003070545.html
UR  - http://www.loc.gov/catdir/description/wiley041/2003070545.html
UR  - http://www.loc.gov/catdir/toc/wiley041/2003070545.html
ER  -