A BOOK OF PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS

By V. CAERO

CONTENTS CHAPTER 1 FIRST?ORDER DIFFERENTIAL EQUATIONS DEFINITION OF DIFFERENTIAL EQUATIONS SLOPE FIELDS AND SOLUTION CURVES SEPARATION OF VARIABLES FIRST?ORDER LINEAR DES THE SUBSTITUTION METHODS POLYNOMIAL SUBSTITUTION HOMOGENEOUS DES BERNOULLI DES RICCATI DES THE EXACT DES SUMMARY CHAPTER 2 MATHEMATICAL MODELS NEWTON’S LAW OF COOLING TORRICELLI’S LAW FOR DRAINING THE POPULATION MODEL INTRODUCTION GENERAL POPULATION EQUATION THE LOGISTIC EQUATION DOOMSDAY VS EXTINCTION ACCELERATION?VELOCITY MODEL NEWTON’S LAWS OF MOTION VELOCITY AND ACCELERATION MODELS AIR RESISTANCE MODEL GRAVITATIONAL ACCELERATION WINDY DAY PLANE LANDING A SWIMMER’S PROBLEM RIVER FERRYBOAT?DOCKING PROBLEM EQUATION FOR COMPOUND INTEREST CHAPTER 3 LINEAR DES OF HIGHER ORDER CLASSIFICATIONS OF LINEAR DES LINEAR INDEPENDENCE HOMOGENEOUS DES DES WITH CONSTANT COEFFICIENTS DES WITH VARIABLE COEFFICIENTS INHOMOGENEOUS LINEAR DES METHOD OF UNDETERMINED COEFFICIENTS VARIATION OF PARAMETERS CHAPTER 4 SYSTEMS OF LINEAR DES BASICS OF SYSTEM OF DES FIRST?ORDER SYSTEMS AND APPLICATIONS ONE BLOCK AND ONE SPRING TWO BLOCKS AND TWO SPRINGS KIRCHHOFF CIRCUIT LAWS THE SUBSTITUTION METHOD THE OPERATOR METHOD THE EIGEN?ANALYSIS METHOD EXAMPLES OF SYSTEMS OF DES PREDATOR?PREY DES CASCADE OF TANKS CHAPTER 5 LAPLACE TRANSFORMS LAPLACE TRANSFORMS PROPERTIES OF LAPLACE TRANSFORMS LAPLACE TRANSFORMS FOR POLYNOMIALS THE TRANSLATOR PROPERTY TRANSFORMS OF STEP AND DELTA FUNCTIONS THE T?MULTIPLICATION PROPERTY PERIODIC FUNCTIONS DIFFERENTIATION AND INTEGRATION PROPERTY INVERSE LAPLACE TRANSFORMS THE CONVOLUTION OF TWO FUNCTIONS APPLICATIONS