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Dottorato di Ricerca in Ingegneria dell'Innovazione Tecnologica (Academic Year 2022/2023) - Digital Technologies for Industry 4.0

Equazioni differenziali ordinarie



Slides

Lesson n. 1: The Heun Equations
   General overwiev
   The five Heun equations 		Go to this slide Artur Ishkhanyan
Lesson n. 2: Derivative Heun Equations
   Derivative of the general Heun function
   Expansions using dHEs 		Go to this slide Artur Ishkhanyan
Lesson n. 3: Transformation Of Variables
   Linearity preserving transformations
   Second indipendent solution 		Go to this slide Artur Ishkhanyan
Lesson n. 4: General Heun Equation
   Introduction
   Independent variable transformation
   Independent variable transformation 		Go to this slide Artur Ishkhanyan
Lesson n. 5: Ordinary Hypergeometric Expansions Of The Solutions Of The General Heun Equation part 1 Go to this slide Artur Ishkhanyan
Lesson n. 6: Ordinary Hypergeometric Expansions Of The Solutions Of The General Heun Equation part 2
   Finite-sum solutions
   The case ε ≤ - 2 		Go to this slide Artur Ishkhanyan
Lesson n. 7: Confluent Hypergeometric Expansions Of The Solutions Of the Confluent Heun Equation part 1
   Introduction
   Expansion 1 		Go to this slide Artur Ishkhanyan
Lesson n. 8: Confluent Hypergeometric Expansions Of The Solutions Of the Confluent Heun Equation part 2
   Expansion 2
   Expansion 3
   Physical example: quantum two-state problem 		Go to this slide Artur Ishkhanyan
Lesson n. 9: Hermite Function Expansions Of The Solutions Of BHE part 1
   Introduction
   Expansion 		Go to this slide Artur Ishkhanyan
Lesson n. 10: Hermite Function Expansions Of The Solutions Of BHE part 2
   Finite-sum solutions
   Biconfluent Heun potentials for the Schrodinger equation 		Go to this slide Artur Ishkhanyan
Lesson n. 11: Generalized Hypergeometric Solutions Of The General Heun Equation part 1
   Introduction
   Solution examples 		Go to this slide Artur Ishkhanyan
Lesson n. 12: Generalized Hypergeometric Solutions Of The General Heun Equation part 2
   Derivations
   A physical example:the third exactly solvable hypergeometric potential for the Schrodinger equation 		Go to this slide Artur Ishkhanyan
Lesson n. 13: Generalized Confluent Hypergeometric Solutions Of The Confluent Heun Equation part 1 Go to this slide Artur Ishkhanyan
Lesson n. 14: Generalized Confluent Hypergeometric Solutions Of The Confluent Heun Equation part 2
   Derivations for non-zero ε
   A physical example 		Go to this slide Artur Ishkhanyan
Lesson n. 15: Heun Function Solutions Of The Schrödinger Equation part 1
   Introduction
   Classical hypergeometric potentials 		Go to this slide Artur Ishkhanyan
Lesson n. 16: Heun Function Solutions Of The Schrödinger Equation part 2
   Discretization of Natanzon potentials
   Heun potentials for the Schrodinger equation 		Go to this slide Artur Ishkhanyan
Lesson n. 17: Quantum Two-State Problem: Solutions In Terms Of The Heun Functions
   Class property of solvable two-state models
   Heun function solutions of the two-state problem 		Go to this slide Artur Ishkhanyan
Lesson n. 18: Series Solutions Of Confluent Heun Equations In Terms Of Gamma Functions
   Introduction: the approach
   Extra singularity
   Heuristic observations 		Go to this slide Artur Ishkhanyan
Lesson n. 19: Solving Differential Equations With Mathematica Dsolve
   DSolve function
   Examples 		Go to this slide Artur Ishkhanyan
Lesson n. 20: Heun Functions in Wolfram Language
   Introduction
   Heun functions in Mathematica 		Go to this slide Artur Ishkhanyan