Difference equations: theory, applications and advanced topics

THE DIFFERENCE CALCULUS GENESIS OF DIFFERENCE EQUATIONS DEFINITIONS DERIVATION OF DIFFERENCE EQUATIONS EXISTENCE AND UNIQUENESS THEOREM OPERATORS ∆ AND E ELEMENTARY DIFFERENCE OPERATORS FACTORIAL POLYNOMIALS OPERATOR ∆−1 AND THE SUM CALCULUS FIRST-ORDER DIFFERENCE EQUATIONS INTRODUCTION GENERAL LINEAR EQUATION CONTINUED FRACTIONS A GENERAL FIRST-ORDER EQUATION: GEOMETRICAL METHODS A GENERAL FIRST-ORDER EQUATION: EXPANSION TECHNIQUES LINEAR DIFFERENCE EQUATIONSINTRODUCTION LINEARLY INDEPENDENT FUNCTIONS FUNDAMENTAL THEOREMS FOR HOMOGENEOUS EQUATIONSINHOMOGENEOUS EQUATIONS SECOND-ORDER EQUATIONS STURM-LIOUVILLE DIFFERENCE EQUATIONS LINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS CONSTRUCTION OF A DIFFERENCE EQUATION HAVING SPECIFIED SOLUTIONS RELATIONSHIP BETWEEN LINEAR DIFFERENCE AND DIFFERENTIAL EQUATIONS INHOMOGENEOUS EQUATIONS: METHOD OF UNDETERMINED COEFFICIENTS INHOMOGENEOUS EQUATIONS: OPERATOR METHODS z-TRANSFORM METHOD SYSTEMS OF DIFFERENCE EQUATIONS LINEAR PARTIAL DIFFERENCE EQUATIONS INTRODUCTION SYMBOLIC METHODS LAGRANGE'S AND SEPARATION-OF-VARIABLES METHODS LAPLACE'S METHOD PARTICULAR SOLUTIONS SIMULTANEOUS EQUATIONS WITH CONSTANT COEFFICIENTS NONLINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS RICCATI EQUATIONS CLAIRAUT'S EQUATION NONLINEAR TRANSFORMATIONS, MISCELLANEOUS FORMS PARTIAL DIFFERENCE EQUATIONS APPLICATIONS INTRODUCTION MATHEMATICS PERTURBATION TECHNIQUES STABILITY OF FIXED POINTS THE LOGISTIC EQUATION NUMERICAL INTEGRATION OF DIFFERENTIAL EQUATIONS PHYSICAL SYSTEMS ECONOMICS WARFAREBIOLOGICAL SCIENCES SOCIAL SCIENCES MISCELLANEOUS APPLICATIONS ADVANCED TOPICSINTRODUCTION GENERALIZED METHOD OF SEPARATION OF VARIABLESCAUCHY-EULER EQUATION GAMMA AND BETA FUNCTIONS LAMBERT-W FUNCTION THE SYMBOLIC CALCULUS MIXED DIFFERENTIAL AND DIFFERENCE EQUATIONSEULER POLYNOMIALS FUNCTIONAL EQUATIONSFUNCTIONAL EQUATION f(x)2 + g(x)2 = 1 EXACT DISCRETIZATIONS OF DIFFERENTIAL EQUATIONSADVANCED APPLICATIONS FINITE DIFFERENCE SCHEME FOR THE RELUGA x - y - z MODEL DISCRETE-TIME FRACTIONAL POWER DAMPED OSCILLATOREXACT FINITE DIFFERENCE REPRESENTATION OF THE MICHAELIS-MENTON EQUATION DISCRETE DUFFING EQUATION DISCRETE HAMILTONIAN SYSTEMS ASYMPTOTICS OF SCHRODINGER-TYPE DIFFERENCE EQUATIONS BLACK-SCHOLES EQUATIONS Appendix: Useful Mathematical Relations Bibliography Index