Next, the book explores linear systems of equations and matrices, applications of linear systems and matrices, determinants, inverses, and Cramer's rule.
Author: Kenneth M. Shiskowski
An accessible introduction to the theoretical and computational aspects of linear algebra using MapleTM Many topics in linear algebra can be computationally intensive, and software programs often serve as important tools for understanding challenging concepts and visualizing the geometric aspects of the subject. Principles of Linear Algebra with Maple uniquely addresses the quickly growing intersection between subject theory and numerical computation, providing all of the commands required to solve complex and computationally challenging linear algebra problems using Maple. The authors supply an informal, accessible, and easy-to-follow treatment of key topics often found in a first course in linear algebra. Requiring no prior knowledge of the software, the book begins with an introduction to the commands and programming guidelines for working with Maple. Next, the book explores linear systems of equations and matrices, applications of linear systems and matrices, determinants, inverses, and Cramer's rule. Basic linear algebra topics such as vectors, dot product, cross product, and vector projection are explained, as well as the more advanced topics of rotations in space, rolling a circle along a curve, and the TNB Frame. Subsequent chapters feature coverage of linear transformations from Rn to Rm, the geometry of linear and affine transformations, least squares fits and pseudoinverses, and eigenvalues and eigenvectors. The authors explore several topics that are not often found in introductory linear algebra books, including sensitivity to error and the effects of linear and affine maps on the geometry of objects. The Maple software highlights the topic's visual nature, as the book is complete with numerous graphics in two and three dimensions, animations, symbolic manipulations, numerical computations, and programming. In addition, a related Web site features supplemental material, including Maple code for each chapter's problems, solutions, and color versions of the book's figures. Extensively class-tested to ensure an accessible presentation, Principles of Linear Algebra with Maple is an excellent book for courses on linear algebra at the undergraduate level. It is also an ideal reference for students and professionals who would like to gain a further understanding of the use of Maple to solve linear algebra problems.
The book is also an ideal reference for students and professionals who would like to gain a further understanding of the use of Mathematica to solve linear algebra problems.
Author: Kenneth M. Shiskowski
Publisher: John Wiley & Sons
A hands-on introduction to the theoretical and computationalaspects of linear algebra using Mathematica® Many topics in linear algebra are simple, yet computationallyintensive, and computer algebra systems such as Mathematica®are essential not only for learning to apply the concepts tocomputationally challenging problems, but also for visualizing manyof the geometric aspects within this field of study. Principles ofLinear Algebra with Mathematica uniquely bridges the gap betweenbeginning linear algebra and computational linear algebra that isoften encountered in applied settings, and the commands required tosolve complex and computationally challenging problems usingMathematica are provided. The book begins with an introduction to the commands andprogramming guidelines for working with Mathematica. Next, theauthors explore linear systems of equations and matrices,applications of linear systems and matrices, determinants,inverses, and Cramer's rule. Basic linear algebra topics, such asvectors, dot product, cross product, and vector projection areexplored, as well as a unique variety of more advanced topicsincluding rotations in space, 'rolling' a circle along a curve, andthe TNB Frame. Subsequent chapters feature coverage of lineartransformations from Rn to Rm, the geometry of linear and affinetransformations, with an exploration of their effect on arclength,area, and volume, least squares fits, and pseudoinverses. Mathematica is used to enhance concepts and is seamlesslyintegrated throughout the book through symbolic manipulations,numerical computations, graphics in two and three dimensions,animations, and programming. Each section concludes with standardproblems in addition to problems that were specifically designed tobe solved with Mathematica, allowing readers to test theircomprehension of the presented material. All related Mathematicacode is available on a corresponding website, along with solutionsto problems and additional topical resources. Extensively class-tested to ensure an accessible presentation,Principles of Linear Algebra with Mathematica is an excellent bookfor courses on linear algebra at the undergraduate level. The bookis also an ideal reference for students and professionals who wouldlike to gain a further understanding of the use of Mathematica tosolve linear algebra problems.
This text fills the gap between management science books lacking mathematical detail and rigor and graduate-level books on mathematical programming.
Author: Paul E. Fishback
Publisher: Chapman and Hall/CRC
Category: Business & Economics
Helps Students Understand Mathematical Programming Principles and Solve Real-World Applications Supplies enough mathematical rigor yet accessible enough for undergraduates Integrating a hands-on learning approach, a strong linear algebra focus, MapleTM software, and real-world applications, Linear and Nonlinear Programming with MapleTM: An Interactive, Applications-Based Approach introduces undergraduate students to the mathematical concepts and principles underlying linear and nonlinear programming. This text fills the gap between management science books lacking mathematical detail and rigor and graduate-level books on mathematical programming. Essential linear algebra tools Throughout the text, topics from a first linear algebra course, such as the invertible matrix theorem, linear independence, transpose properties, and eigenvalues, play a prominent role in the discussion. The book emphasizes partitioned matrices and uses them to describe the simplex algorithm in terms of matrix multiplication. This perspective leads to streamlined approaches for constructing the revised simplex method, developing duality theory, and approaching the process of sensitivity analysis. The book also discusses some intermediate linear algebra topics, including the spectral theorem and matrix norms. Maple enhances conceptual understanding and helps tackle problems Assuming no prior experience with Maple, the author provides a sufficient amount of instruction for students unfamiliar with the software. He also includes a summary of Maple commands as well as Maple worksheets in the text and online. By using Maple’s symbolic computing components, numeric capabilities, graphical versatility, and intuitive programming structures, students will acquire a deep conceptual understanding of major mathematical programming principles, along with the ability to solve moderately sized real-world applications. Hands-on activities that engage students Throughout the book, student understanding is evaluated through "waypoints" that involve basic computations or short questions. Some problems require paper-and-pencil calculations; others involve more lengthy calculations better suited for performing with Maple. Many sections contain exercises that are conceptual in nature and/or involve writing proofs. In addition, six substantial projects in one of the appendices enable students to solve challenging real-world problems.
ust like Mathematical Analysis, Linear Algebra too offers a number of tech3.1
Introduction The designers of the Maple ... also have occasion to preview some
advanced principles and methods you possibly have not been exposed to before.
Author: R.J. Stroeker
This unusual introduction to Maple shows readers how Maple or any other computer algebra system fits naturally into a mathematically oriented work environment. Designed for mathematicians, engineers, econometricians, and other scientists, this book shows how computer algebra can enhance their theoretical work. A CD-ROM contains all the Maple worksheets presented in the book.
All Maple commands are described ing on the central goal of linear algebra :
understanding in a precise , concise , and ... the existence of geodesics in
compact principle in mechanics and to introduce Pontjragin's numeric algorithms
, how to ...
Category: Computer software
Linear Algebra, Vector Calculus and Differential Equations James A. Carlson,
Jennifer M. Johnson. 1 1 1/12 7/24 7/241/12 1 2 ... The superposition principle
holds whenever the problem is a linear one , as is the case here . Equivalently ,
Author: James A. Carlson
Category: Algebras, Linear
By presenting side-by-side comparisons, this handbook enables Mathematica users to quickly learn Maple, and vice versa.
Author: Inna K. Shingareva
Publisher: Springer Science & Business Media
By presenting side-by-side comparisons, this handbook enables Mathematica users to quickly learn Maple, and vice versa. The parallel presentation enables students, mathematicians, scientists, and engineers to easily find equivalent functions on each of these algebra programs. The handbook provides core material for incorporating Maple and Mathematica as working tools into many different undergraduate mathematics courses.
Mathematics with computing ( Maple ) ; matrices , linear Course contact :
Admissions Tudor . ... dealing with linear algebra & multivariable modules worth
40 credit points in methods , principles & theories that calculus ; statistics ,
Category: Degrees, Academic
Modules for Interactive Learning Using MAPLE 6 Eugene A. Herman ... can find a
system of linear equations satisfied by the seven unknown flows Xı , ... , X , by
applying the " conservation of flow " principle : The number of vehicles that enter
Author: Eugene A. Herman
Publisher: Addison Wesley Publishing Company
New Interactive Linear Algebra Maple Modules. Linear Algebra: Modules for Interactive Learning Using Maple 6� is organized into a collection of twenty-nine extensive (and intensive) modules, which must be used in conjunction with Maple 6. Each module is divided into an interactive Tutorial followed by a rich and substantial collection of Problems. Linear Algebra: Modules for Interactive Learning Using Maple 6� has been carefully designed to help students develop their geometric intuition and deepen their understanding of linear algebra concepts and methods. These modules support both individual work and interactive collaboration. They can be used as a supplement in a traditional lecture course, or in a lab-only format. Due to the versatility of the modules, they can be easily adapted to a variety of curricula, institutions, and styles of teaching. The modules can be used on all the common hardware platforms Windows� PCs, Macintosh� computers, and Unix workstations.
The Decoupling Principle Lorenzo Adlai Sadun. Notes to the instructor The
readers of this book are assumed to have taken an introductory linear algebra
class , and hence to be familiar with basic matrix operations such as row
Author: Lorenzo Adlai Sadun
Preface 1 The Decoupling Principle 1 2 Vector Spaces and Bases 9 3 Linear Transformations and Operators 37 4 An Introduction to Eigenvalues 57 5 Some Crucial Applications 97 6 Inner Products 145 7 Adjoints, Hermitian Operators, and Unitary Operators 191 8 The Wave Equation 225 9 Continuous Spectra and the Dirac Delta Function 263 10 Fourier Transforms 287 11 Green's Functions 319 Index 346.
It mixes geometry , calculus , linear algebra , differential equations , complex
variables , the calculus of variations , and ... The Pontryagin Maximum Principle •
An Application to the Shape of a Balloon • The Caluclus of Variations and Maple
... Analysis Ritger and Rose : Differential Equations with Applications Robertson :
Engineering Mathematics with Maple ... Analysis Rudin : Principles of
Mathematical Analysis Rudin : Real and Complex Analysis Scheick : Linear
Algebra with ...
Author: John T. Scheick
Publisher: McGraw-Hill Science, Engineering & Mathematics
Designed for the second level course in linear algebra taken by your junior- or senior-level mathematics, engineering, or science majors, this text focuses on the fundamentals of linear algebra in a thematic framework which emphasizes concepts most important to applied mathematics, engineering, and science.
4 yr vector analysis ; variational analysis . course allows added breadth &
principles , complex analysis . ... Physics incl : statistical introduction to computing
( Maple ) ; mechanics ; computer devices ; matrices , linear algebra , geometry ...
Category: Universities and colleges
A comprehensive guide to full-time degree courses, institutions and towns in Britain.
The literature on numerical linear algebra is in relatively good shape and this
book certainly does not need to ... such as REDUCE or MACSYMA , which
operate on mainframe computers , and smaller versions such as mu MATH or
MAPLE that ...
Author: James P Keener
Publisher: Addison-Wesley Longman
Yr 2 : Mathematics : partial differential equations ; analysis ; vector analysis ;
variational principles ; complex analysis ... Mathematics & physics ; Yr 1 :
Calculus ; algebra ; foundations ; computing ( Maple ) ; matrices , linear algebra ,
geometry ; differential equations ; algebra . Physics ... Mathematics 1H ( geometry
; calculus ; mechanics ; analysis ; linear algebra ; Fourier series ; numerical
mathematics ) .
Category: Degrees, Academic
MAPLE performs algebraic manipulations , and the authors make directs the
reader to the specific functions within ... cover the local level and other linear
Gaussian models , the tedium , thus allowing more emphasis to be placed on
This step is necessary because arrays conform to the principle of last name
evaluation . This means that for an ... Maple ' s linear algebra tools are grouped
together in the Maple package linalg ( see ? linalg for more details ) . All or some
of the ...
Author: Christopher Tocci
Publisher: Artech House Publishers
Category: Technology & Engineering
Fast becoming the first choice in computer algebra systems (CAS) among engineers and scientists, Maple is easy-to-use software that performs numerical and symbolic analysis to solve complex mathematical problems. This book shows you how to tap the full power of Maple's latest version in solving real-world quantitative problems in circuit theory, control theory, curve-fitting, mechanics, and digital signal processing.
We feel it is important that others can in principle check the calculations , as we
were very much aware in setting up our initial data just how ... The computations
were done in Maple , using its polynomial handling and linear algebra routines .
Author: Igor Rivin
Category: Geometry, Hyperbolic
In particular , we identified weaknesses in library research skills and in using
software such as Maple , Excel and LaTeX . ... of sophistication which build upon
the fundamental concepts introduced in core major courses like Calculus , Linear
Algebra , Abstract Algebra , and Real Analysis . ... The principles of Imaging
Science are presented in the context of core concepts and the goals of the
Author: American Mathematical Society
Parallelizing Algorithms for Symbolic Computation using | | MAPLE | I * Kurt Sieg
) Research Institute for Symbolic ... involving non - linear equation Thus our goal
should be to reuse the huge library in existing computer algebra systems and ...
Category: Parallel programming (Computer science)