Chapter1 BASIC CONCEPTS 1
Chapter2 CLASSIFICATIONS OF FIRST-ORDER DIFFERENTIAL EQUATIONS 8
Chapter3 SEPARABLE FIRST-ORDER DIFFERENTIAL EQUATIONS 14
Chapter4 EXACT FIRST-ORDER DIFFERENTIAL EQUATIONS 24
Chapter5 LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS 35
Chapter6 APPLICATIONS OF FIRST-ORDER DIFFERENTIAL EQUATIONS 43
Chapter7 LINEAR DIFFERENTIAL EQUATIONS:THEORY OF SOLUTIONS 67
Chapter8 SECOND-ORDER LINEAR HOMOGENEOUS DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS 77
Chapter9 nTH-ORDER LINEAR HOMOGENEOUS DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS 83
Chapter10 THE METHOD OF UNDETERMINED COEFFICIENTS 88
Chapter11 VARIATION OF PARAMETERS 97
Chapter12 INITIAL-VALUE PROBLEMS 104
Chapter13 APPLICATIONS OF SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS 108
Chapter14 THE LAPLACE TRANSFORM 125
Chapter15 INVERSE LAPLACE TRANSFORMS 138
Chapter16 CONVOLUTIONS AND THE UNIT STEP FUNCTION 146
Chapter17 SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS BY LAPLACE TRANSFORMS 154
Chapter18 SOLUTIONS OF LINEAR SYSTEMS BY LAPLACE TRANSFORMS 161
Chapter19 MATRICES 166
Chapter20 eA? 175
Chapter21 REDUCTION OF LINEAR DIFFERENTIAL EQUATIONS TO A FIRST-ORDER SYSTEM 183
Chapter22 SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS BY MATRIX METHODS 191
Chapter23 LINEAR DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS 199
Chapter24 REGULAR SINGULAR POINTS AND THE METHOD OF FRONBNIUS 213
Chapter25 GAMMA AND BESSEL FUNCTIONS 228
Chapter26 GRAPHICAL METHODS FOR SOLVING FIRST-ORDER DIFFERENTIAL EQUATIONS 236
Chapter27 NUMERICAL METHODS FOR SOLVING FIRST-ORDER DIFFERENTIAL EQUATLONS DIFFERENTIAL EQUATIONS 254
Chapter28 NUMERICAL METHODS FOR SYSTEMS 272
Chapter29 SECOND-ORDER BOUNDARY-VALUE PROBLEME 288
Chapter30 EIGENFUNCTION EXPANSIONS 298
Appendix A LAPLACE TRANSFORMS 305
ANSWERS TO SUPPLEMENTARY PROBLEMS 311
INDEX 355