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Maxima – Documentation

Books and articles which mention Maxima or Macsyma.

• BibTeX format bibliography of papers on MACSYMA/VAXIMA before 1994.
• Classical Differential Geometry of Surfaces by Dr. Wolfgang Lindner.
  An introduction to the Elementary Differential Geometry of 2D surfaces using the CAS Maxima. Code for the calculation of the 1st and 2nd fundamental form, for the shape operator, the Gauss and mean curvature are presented in form of user-defined functions. The Christoffel symbols, the Riemann tensors, the Ricci tensor and the curvature scalar R are also discussed via the Maxima package ctensor. An implementation of the covariant differentiation of vector fields are also given.
• Classical Mechanics with Maxima by Todd Timberlake.
  The code lines of the book with understandable book-independent comments are here: AnnotatedCode (a zip archive containing the Maxima code files for the book, but with annotations and some additional material, including a notebook describing how to export graphics from Maxima). The code of Chapter 1 gives a compact introduction for the general use of Maxima.
• Computer-Supported Calculus by A. Ben-Israel, R. Gilbert, Springer, Wien (2002). ISBN 3-211-82924-5.
  This is a new type of calculus book: Students who master this text will be well versed in calculus and, in addition, possess a useful working knowledge of one of the most important mathematical software systems, namely, MACSYMA.
• Definite Integration using the Generalized Hypergeometric Functions (scanned PDF) by Ioannis Dimitrios Avgoustis, master's thesis (MIT), 1977.
  A design for the definite integration of approximately fifty Special Functions is described. The Generalized Hypergeometric Functions are utilized as a basis for the representation of the members of the above set of Special Functions. Only a relatively small number of formulas that generally involve Generalized Hypergeometric Functions are utilized for the integration stage. A last and crucial stage is required in the integration process: the reduction of the Generalized Hypergeometric Function to Elementary and/or Special Functions.
• Dynamical systems by J. E. Villate, Porto (2007).
  English translation of the first 3 chapters from the book Sistemas Dinâmicos.
  In this book we intend to explore some topics on dynamical systems, using an active teaching approach, supported by computing tools and trying to avoid too may abstract details.
• Dynamics and Dynamical systems by J. E. Villate, Porto (2019).
  This book aims at giving the reader some basic knowledge of mechanics and the computational techniques used to solve dynamical systems. The Computer Algebra System (CAS) Maxima is used to introduce those computational techniques. The main theme of the book is mechanics, including some contemporary subjects such as nonlinear systems and chaos.
• Finite Elements for Truss and Frame Structures. An Introduction Based on the Computer Algebra System Maxima. by Andreas Öchsner and Resam Makvandi. Springer-Verlag, Berlin (2019). DOI: 10.1007/978-3-319-94941-3
  This book is intended as a study aid for the finite element method. Based on the free computer algebra system Maxima, we offer routines to symbolically or numerically solve problems from the context of plane truss and frame structures.
• Introductory Differential Equations with Maxima by Dr. Wolfgang Lindner
  This booklet starts with analytical solution methods for ODEs, from direct solution techniques to exact ODE's. The numerical solution methods for IVP's range from Euler's to Runge--Kutta (RK3, RK4). All these methods are easily coded in MAXIMA using a special user function ITERATE: this little helper function allows to concentrate on the discussed methods in 1-5 liners and to provide a unified index free treatment. Systems of ODEs are numerically solved using RK variants, likewise ODEs of 2nd order. Boundary value problems (BVP) are solved with the shooting method and the Finite Difference Method (FDM).
• Macsyma: A Personal History by Joel Moses, invited presentation in Milestones in Computer Algebra, May 2008, Tobago.
• Mathematical Modeling and Simulation by Kai Velten, Wiley-VCH, 2009. http://books.google.com/books?id=Czp1N5UWpyEC
  A book on modeling and simulation exclusively based on open source software. It includes many examples from such diverse fields as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical, and process engineering. Requiring only little mathematical prerequisite in calculus and linear algebra, this lucidly written text is accessible to scientists, engineers, and students at the undergraduate level. The book addresses a broad range of models from elementary statistical models to ODE and PDE models. The reader is introduced into CAELinux, Calc, Code-Saturne, Maxima, R, and Salome-Meca.
• On Rationally Parametrized Modular Equations by Robert S. Maier, 2006.
  Many rationally parametrized elliptic modular equations are derived. Each comes from a family of elliptic curves attached to a genus-zero congruence subgroup Γ0(N), as an algebraic transformation of elliptic curve periods, parametrized by a Hauptmodul (function field generator). The periods satisfy a Picard-Fuchs equation, of hypergeometric, Heun, or more general type; so the new modular equations are algebraic transformations of special functions. When N=4,3,2 they are modular transformations of Ramanujan's elliptic integrals of signatures 2,3,4. This gives a modern interpretation to his theories of integrals to alternative bases: they are attached to certain families of elliptic curves. His anomalous theory of signature 6 turns out to fit into a general Gauss-Manin rather than a Picard-Fuchs framework.
• Proceedings of the 1977 MACSYMA Users' Conference (scanned PDF, 48 M)
• Proceedings of the 1984 MACSYMA Users' Conference (scanned PDF, 29 M)
• Scientific Programming; Numeric, Symbolic, and Graphical Computing with Maxima. by Jorge Alberto Calvo, 2018.
  This book offers an introduction to computer programming, numerical analysis, and other mathematical ideas that extend the basic topics learned in calculus. It illustrates how mathematicians and scientists write computer programs, covering the general building blocks of programming languages and a description of how these concepts fit together to allow computers to produce the results they do.
• The 192 Solutions of the Heun Equation, by Robert S. Maier, Mathematics of Computation, vol. 76 (2007), pp. 811-843.
  A machine-generated list of 192 local solutions of the Heun equation is given. They are analogous to Kummer's 24 solutions of the Gauss hypergeometric equation, since the two equations are canonical Fuchsian differential equations on the Riemann sphere with four and three singular points, respectively. Tabulation is facilitated by the identification of the automorphism group of the equation with n singular points as the Coxeter group D_n. Each of the 192 expressions is labeled by an element of D_4. Of the 192, 24 are equivalent expressions for the local Heun function Hl, and it is shown that the resulting order-24 group of transformations of Hl is isomorphic to the symmetric group S_4. The isomorphism encodes each transformation as a permutation of an abstract four-element set, not identical to the set of singular points.

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