Mathematical Methods in the Physical Sciences
Encyclopedia
Mathematical Methods in the Physical Sciences is a 1966 textbook by mathematician
Mary L. Boas
intended to develop skills in mathematical problem solving needed for junior to senior-graduate courses in engineering
, physics
, and chemistry
. The book provides a comprehensive survey of analytic techniques
and provides careful statements of important theorems while omitting most detailed proofs. Each section contains a large number of problems, with selected answers. Numerical computational approaches
using computers are outside the scope of the book.
The book, now in its third edition, is still widely used in university classrooms
and is frequently cited in other textbooks and scientific papers.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
Mary L. Boas
Mary L. Boas
Mary Layne Boas was an American mathematician and physics professor best known as the author of Mathematical Methods in the Physical Sciences , an undergraduate textbook that is still widely used in college classrooms in 2010...
intended to develop skills in mathematical problem solving needed for junior to senior-graduate courses in engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
, physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, and chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
. The book provides a comprehensive survey of analytic techniques
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
and provides careful statements of important theorems while omitting most detailed proofs. Each section contains a large number of problems, with selected answers. Numerical computational approaches
Computational physics
Computational physics is the study and implementation of numerical algorithms to solve problems in physics for which a quantitative theory already exists...
using computers are outside the scope of the book.
The book, now in its third edition, is still widely used in university classrooms
and is frequently cited in other textbooks and scientific papers.
Chapters
- Infinite series, power series
- Complex numberComplex numberA complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
s - Linear algebraLinear algebraLinear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...
- Partial differentiation
- Multiple integralMultiple integralThe multiple integral is a type of definite integral extended to functions of more than one real variable, for example, ƒ or ƒ...
s - Vector analysis
- Fourier seriesFourier seriesIn mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...
and transformsFourier transformIn mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions... - Ordinary differential equations
- Calculus of variationsCalculus of variationsCalculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
- Tensor analysis
- Special functionsSpecial functionsSpecial functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications....
- Series solution of differential equations; Legendre, Bessel, Hermite, and Laguerre functions
- Partial differential equations
- Functions of a complex variable
- Integral transforms
- ProbabilityProbabilityProbability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
and statisticsStatisticsStatistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....