Macsyma’s
General Simplifier: Philosophy and Operation by Richard Fateman,
first published in the Macsyma Users Conference, Washington
D.C. 1979, in: MUC-79, 563-582. Notes have been added to the
original paper by the author from today's perspective. A subsection
that was not written as of 1979 has also been added in 2017.
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.
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).
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.
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.
The
Maxima Book This is a very incomplete and in some places out
of date user oriented manual. It is a work in progress, but is
provided here in the hope it might be useful. Update: This new
version isn't all that different, but it has been updated a bit with
regards to plotting and a couple other minor changes. Emaxima and
install docs have not been updated yet. Mathematical content is
essentially unchanged. Pictures should be of slightly better
quality.
Computer
Based Tools for Engineers
by Javed Alam
The different sessions provide the necessary theory and the solution
using Maxima for problems encountered in Engineering computing.
Any questions about Maxima or this site can be sent to our
mailing list.