The Net Advance of Physics:
DIFFERENTIAL EQUATIONS

DIFFERENTIAL EQUATIONS:

• General:
  • Introduction to Mathematical Physics. Calculus of Variations and Boundary-value Problems by V. M. Adamyan and M. Ya. Sushko [2013/05] 355 pp. textbook in Ukrainian.
  • Algebraic background for numerical methods, control theory and renormalization by Dominique Manchon [2015/01]
  • Differential Equations of Mathematical Physics by Max Lein [2015/08]
  • A Friendly Introduction to Differential Equations by Mohammed K. A. Kaabar [2018/07] 165 pp.
  • Introduction to Engineering Mathematics and Analysis: Modeling Physical Systems Using the Language of Mathematics by B. D. Wood [2023/05] Undergraduate textbook, 474 pp.

• Types: NON-LINEAR; PARTIAL; PSEUDODIFFERENTIAL;

• Type: HYPERGEOMETRIC:
  • A physicist's guide to the solution of Kummer's equation and confluent hypergeometric functions by W. N. Mathews Jr. et al. [2021/11]

• Type: INTEGRABLE SYSTEM:
  • Aspects of Integrability of Differential Systems and Fields by Costas J. Papachristou [2015/11]
  • Discrete integrable systems, Darboux transformations, and Yang-Baxter maps by Deniz Bilman and Sotiris Konstantinou-Rizos [2016/12]

• Type: MATHIEU'S:
  • Approximate solutions to Mathieu's equation by Samuel A. Wilkinson et al. [2017/10]

• Type: MATRIX-VALUED:
  • Infinitesimal symmetry transformations of matrix-valued differential equations by Costas J. Papachristou [2018/04]

• Type: ORDINARY:
  • Symmetries of Ordinary Differential Equations: A Short Introduction by Sebastian Walcher [2019/11]
  • An overview of numerical and analytical methods for solving ordinary differential equations by B. Denis [2020/12]
  • Introduction to Engineering Mathematics and Analysis: Modeling Physical Systems Using the Language of Mathematics by B. D. Wood [2023/05] Undergraduate textbook, 474 pp.

• Type: STOCHASTIC:
  • Path Integral Methods for Stochastic Differential Equations by Carson C. Chow and Michael A. Buice [2010/09]
  • Calculo Estocastico, EDEs y EDPs by Rafael Serrano [2015/04] In Spanish.
  • Introduction to Stochastic Differential Equations for Finance by Andrew Papanicolaou [2015/04]
  • A Hitch-hiker's Guide to Stochastic Differential Equations: Solution Methods for Energetic Particle Transport in Space Physics and Astrophysics by R. Du Toit Strauss and Frederic Effenberger [2017/03]

• Type: STOCHASTIC: Aspect: MOMENT EVOLUTION:
  • Moment Closure -- A Brief Review by Christian Kuehn [2015/05]

• Aspects: GREEN'S FUNCTIONS:
  • Green's functions in quantum-mechanics courses by W. J. Herrera et al. [2021/07]

• Aspects: INTEGRABILITY:
  • Aspects of Integrability of Differential Systems and Fields by Costas J. Papachristou [2015/11]

• Aspects: LAPLACE TRANSFORMS:
  • A Friendly Introduction to Differential Equations by Mohammed K. A. Kaabar [2018/07] 165 pp.

• Aspects: QUALITATIVE SOLUTIONS:
  • Qualitative analysis of differential equations by Alexander V. Panfilov [2018/03] 113 pp.

• Aspects: SYMMETRY:
  • Infinitesimal symmetry transformations of matrix-valued differential equations by Costas J. Papachristou [2018/04]
  • Symmetries of Ordinary Differential Equations: A Short Introduction by Sebastian Walcher [2019/11]

THE NET ADVANCE OF PHYSICS