000			04796nam a22003017a 4500
999			_c95387 _d95387
005			20260421102601.0
008			260421s2024 maua 000 0 eng
020			_a9798214031958
041			_aeng
050	0	0	_aQA371 _b.Z55 2024
082	0	0	_a515.35 _223
100	1		_aZill, Dennis G., _d1940- _eauthor.
245	1	0	_aDifferential equations with boundary-value problems / _cDennis G. Zill, Loyola Marymount University.
250			_aTenth edition.
250			_aMetric version / _bprepared by Aly El-Iraki
264		1	_aBoston, MA : _bCengage Learning, _c[2024]
264		4	_c©2024.
300			_ax, 583, 77. pages : _billustrations (some color) ; _c29 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
500			_aIncludes index.
505	0		_81. INTRODUCTION TO DIFFERENTIAL EQUATIONS. Definitions and Terminology. Initial-Value Problems. Differential Equations as Mathematical Models. Chapter 1 in Review. 2. FIRST-ORDER DIFFERENTIAL EQUATIONS. Solution Curves Without a Solution. Separable Equations. Linear Equations. Exact Equations. Solutions by Substitutions. A Numerical Method. Chapter 2 in Review. 3. MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS. Linear Models. Nonlinear Models. Modeling with Systems of First-Order DEs. Chapter 3 in Review. 4. HIGHER-ORDER DIFFERENTIAL EQUATIONS. Theory of Linear Equations. Reduction of Order. Homogeneous Linear Equations with Constant Coefficients. Undetermined Coefficients-Superposition Approach. Undetermined Coefficients-Annihilator Approach. Variation of Parameters. Cauchy-Euler Equation. Green's Functions. Solving Systems of Linear DEs by Elimination. Nonlinear Differential Equations. Chapter 4 in Review. 5. MODELING WITH HIGHER-ORDER DIFFERENTIAL EQUATIONS. Linear Models: Initial-Value Problems. Linear Models: Boundary-Value Problems. Nonlinear Models. Chapter 5 in Review. 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Review of Power Series. Solutions About Ordinary Points. Solutions About Singular Points. Special Functions. Chapter 6 in Review. 7. THE LAPLACE TRANSFORM. Definition of the Laplace Transform. Inverse Transform and Transforms of Derivatives. Operational Properties I. Operational Properties II. Dirac Delta Function. Systems of Linear Differential Equations. Chapter 7 in Review. 8. SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS. Theory of Linear Systems. Homogeneous Linear Systems. Nonhomogeneous Linear Systems. Matrix Exponential. Chapter 8 in Review. 9. NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS. Euler Methods and Error Analysis. Runge-Kutta Methods. Multistep Methods. Higher-Order Equations and Systems. Second-Order Boundary-Value Problems. Chapter 9 in Review. 10. SYSTEMS OF NONLINEAR DIFFERENTIAL EQUATIONS. Autonomous Systems. Stability of Linear Systems. Linearization and Local Stability. Autonomous Systems as Mathematical Models. Chapter 10 in Review. 11. FOURIER SERIES. Orthogonal Functions. Fourier Series. Fourier Cosine and Sine Series. Sturm-Liouville Problem. Bessel and Legendre Series. Chapter 11 in Review. 12. BOUNDARY-VALUE PROBLEMS IN RECTANGULAR COORDINATES. Separable Partial Differential Equations. Classical PDEs and Boundary-Value Problems. Heat Equation. Wave Equation. Laplace's Equation. Nonhomogeneous Boundary-Value Problems. Orthogonal Series Expansions. Higher-Dimensional Problems. Chapter 12 in Review. 13. BOUNDARY-VALUE PROBLEMS IN OTHER COORDINATE SYSTEMS. Polar Coordinates. Polar and Cylindrical Coordinates. Spherical Coordinates. Chapter 13 in Review. 14. INTEGRAL TRANSFORM METHOD. Error Function. Laplace Transform. Fourier Integral. Fourier Transforms. Finite Fourier Transforms. Chapter 14 in Review. 15. NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS. Laplace's Equation. Heat Equation. Wave Equation. Chapter 15 in Review. Appendix A: Integral-Defined Functions. Appendix B: Matrices. Appendix C: Table of Laplace Transforms. Answers to Selected Odd-Numbered Problems. Index.
545	0		_aDennis G. Zill Dennis Zill received a PhD in Applied Mathematics from Iowa State University, and is a former professor of Mathematics at Loyola Marymount University in Los Angeles, Loras College in Iowa, and California Polytechnic State University. He is also the former chair of the Mathematics department at Loyola Marymount University, where he currently holds a rank as Professor Emeritus of Mathematics. Zill holds interests in astronomy, modern literature, music, golf, and good wine, while his research interests include Special Functions, Differential Equations, Integral Transformations, and Complex Analysis.
650		0	_aDifferential equations _vTextbooks.
650		0	_aBoundary value problems _vTextbooks.
942			_2ddc _cBK