A Word from the Publisher 

ix  
Preface to the Fifth Edition 

xi  

Introduction to Differential Equations 


1  (27) 

Basic Definitions and Terminology 


2  (9) 


11  (17) 


25  (1) 


26  (2) 

FirstOrder Differential Equations 


28  (47) 


29  (4) 


33  (7) 


40  (6) 


46  (8) 


54  (8) 

Equations of Bernoulli, Ricatti, and Clairaut 


62  (5) 


67  (3) 


70  (5) 


72  (1) 


73  (2) 

Applications of FirstOrder Differential Equations 


75  (36) 


76  (5) 

Applications of Linear Equations 


81  (12) 

Applications of Nonlinear Equations 


93  (18) 


103  (1) 


104  (2) 

Essay: Population Dynamics 


106  (5) 





Linear Differential Equations of HigherOrder 


111  (72) 


112  (21) 

InitialValue and BoundaryValue Problems 


112  (3) 

Linear Dependence and Linear Independence 


115  (5) 

Solutions of Linear Equations 


120  (13) 

Constructing a Second Solution from a Known Solution 


133  (5) 

Homogeneous Linear Equations with Constant Coefficients 


138  (8) 

Undetermined CoefficientsSuperposition Approach 


146  (11) 


157  (5) 

Undetermined CoefficientAnnihilator Approach 


162  (7) 


169  (14) 


175  (2) 


177  (2) 


179  (4) 





Applications of SecondOrder Differential Equations: Vibrational Models 


183  (38) 


184  (8) 


192  (8) 


200  (9) 

Electric Circuits and Other Analogous Systems 


209  (12) 


214  (1) 


215  (3) 

Essay: Tacoma Narrows Suspension Bridge Collapse 


218  (3) 





Differential Equations with Variable Coefficients 


221  (59) 


222  (8) 

Review of Power Series; Power Series Solutions 


230  (9) 

Solutions About Ordinary Points 


239  (9) 

Solutions About Singular Points 


248  (17) 

Regular Singular Points; Method of FrobeniusCase I 


248  (9) 

Method of FrobeniusCases II and III 


257  (8) 


265  (15) 

Solution of Bessel's Equation 


266  (5) 

Solution of Legendre's Equation 


271  (6) 


277  (1) 


278  (2) 


280  (55) 


281  (9) 


290  (6) 

Translation Theorems and Derivatives of a Transform 


296  (11) 

Transforms of Derivatives, Integrals, and Periodic Functions 


307  (7) 


314  (14) 


328  (7) 


332  (1) 


332  (3) 

Systems of Linear Differential Equations 


335  (86) 


336  (7) 


343  (7) 

Systems of Linear FirstOrder Equations 


350  (5) 


355  (20) 

Basic Definitions and Theory 


355  (9) 

Gaussian and GaussJordan Elimination Methods 


364  (4) 


368  (7) 

Matrices and Systems of Linear FirstOrder Equations 


375  (16) 


375  (9) 


384  (7) 

Homogeneous Linear Systems 


391  (14) 

Distinct Real Eigenvalues 


391  (3) 


394  (4) 


398  (7) 

Undetermined Coefficients 


405  (4) 


409  (4) 


413  (8) 


416  (2) 


418  (3) 

Numerical Methods for Ordinary Differential Equations 


421  (1) 


422  (4) 


426  (6) 

The ThreeTerm Taylor Method 


432  (3) 


435  (4) 


439  (3) 


442  (6) 

HigherOrder Equations and Systems 


448  (4) 

SecondOrder BoundaryValue Problems 


452  (4) 


456  (1) 


457  (2) 

Essay: Nerve Impulse Models 


459  




APPENDIXES 



1  (3) 


4  (3) 

III Review of Determinants 


7  (4) 


11  
Answers to OddNumbered Problems 

1  (1) 
Index 

1  