Applied Linear Algebra Olver Shakiban Pdf Compressor
Math 640 -- Linear Algebra with Applications Syllabus for Math 640-700 -- Linear Algebra with Applications General Description Linear Algebra is the study of linear equations in several variables and related topics. The word 'linear' here means the variables appear only with exponent 1 and do not appear inside other 'nonlinear' functions, such as exponentials or trigonometric functions. Indeed, a linear equation in two variables describes a straight line (hence the name 'linear').
Though this simple description makes the subject sound elementary, linear algebra is quite involved since typical applications require the solution of many equations with many unknowns (often numbering in the thousands). Thus, much of the subject involves finding efficient techniques for solving systems of linear equations, and other related tasks. The specific list of topics we will cover include the following: • Matrix Algebra (including matrix products, transpose, inverses and determinants); a matrix is an array which represents a set of linear equations and so the matrix is the basic object of study in this course. • Vector Spaces and subspaces (including spanning sets, linear independence and basis); a vector space can be thought of as the set spanned by all the variables used in a set of linear equations. • Linear Maps between vectors spaces and their matrix representations; understanding linear maps is the key to understanding what matrices mean and how they operate.
• Inner products and special 'orthogonal' bases; orthogonal is another name for perpendicular and such bases have nice computational properties in linear algebra. • Eigenvalues and Eigenvectors of a matrix (or linear map); finding a set of eigenvalues and eigenvectors can enormously simplify the description of a linear map and its matrix representation and thereby simplify many tasks. In particular, we'll cover the 'spectral theorem' on diagonalizing symmetric matrices (using eigenvalues and eigenvectors). • Applications - too numerous to mention all of them; we will concentrate on data representation topics including: least squares approximation (both linear and quadratic); approximation of functions by trigonometric polynomials (including the fast fourier transform); filtering of data and data compression. In terms of level of coverage of the topics, this course will be about a 50/50 mix between theory and computation. Certainly it is important to learn how to compute and manipulate matrices and related operations in linear algebra. You should also have access to the software package, Matlab from, either by purchasing the student version or having access to it from a university or library site.
Although you could use other forms of software (e.g. Maple), guidance will only be given for Matlab. Proofs of theorems will be covered and some proofs will be expected of you on assignments. Prerequisites The official prerequisite for the course is Math 304, which is an undergraduate linear algebra course. However, the assumption here is that many students enrolling in the distance section of Math 640 will not have had linear algebra for quite some time, and thus quite a bit of the material in Math 304 will be reviewed. Textbook The required textbook is Applied Linear Algebra by Olver and Shakiban, published by, 2005 (ISBN number is 0-13-147382-4).
We will cover most of chapters 1-5 and chapters 7 and 8. Format of the Class This is a 'distance class' which means there is no classroom or class meetings in the traditional sense.
All course materials, assignments and grades will be disseminated through starting the week before classes begin. There will be two types of lecture notes: 1) static notes in.pdf format 2) dynamic notes in the form of streaming videos. These lectures will be 'asynchronous', which means that you can view them anytime (i.e.
Applied Linear Algebra Olver Shakiban.pdf Free Download Here Applied Linear Algebra by Olver and Shakiban http://www.math.umaine.edu/~hiebeler/misc/olver-shakiban-06.
They are not live video cams that require you to be viewing them at any particular time). Assignments from the textbook will be posted on E-Learning (WebCT) and you will be required to send your assignments to me electronically through WebCT preferably in pdf, postscript or.doc format. I prefer you type your assignments, but neatly handwritten assignments which are scanned and then sent electronically will be accepted. Additional information on how to do this on WebCT (and other WebCT features pertaining to this course) will be given in the link to 'Use of WebCT in This Course' available from the course home page on WebCT. Course grades will be determined by homework (40%); a technology project/assignment (25%) and a final exam (35%). The technology project/assignment will require using computer software (Matlab is recommended) to solve various problems that are too difficult to solve by hand, and that relate to the course material (e.g. Least squares analysis, fast Fourier transform with data analysis, eigenvalues/eigenvectors, ill-conditioned matrices).
More details on the project will appear later. You may collaborate with other students on the homework. No collaboration with any humans is allowed on the final exam, but you may use books and notes. Grades will be made available through WebCT.
Use of Technology As mentioned above, you are recommended to purchase the Matlab software package from Mathworks. Many of the problems will be easier with this software package (at least as a check of your answers). The software will be essential for doing your technology/project. I will be giving you some instruction and hints on the use of Matlab, but not on the use of other software packages. When this course is loaded onto WebCT (the week before classes begin), you should be able to view the following three items from the course home page on WebCT: • Use of E-Learning (WebCT) in This Course (with some details on how to navigate WebCT • Course Content - this contains the 'guts' of the course - lecture notes, streaming video and assignments • Course Schedule - A week by week schedule will be kept here with reminders of assignment dates.
Description For in-depth Linear Algebra courses that focus on applications. This text aims to teach basic methods and algorithms used in modern, real problems that are likely to be encountered by engineering and science students—and to foster understanding of why mathematical techniques work and how they can be derived from first principles. No text goes as far (and wide) in applications. The authors present applications hand in hand with theory, leading students through the reasoning that leads to the important results, and provide theorems and proofs where needed.
Because no previous exposure to linear algebra is assumed, the text can be used for a motivated entry-level class as well as advanced undergraduate and beginning graduate engineering/applied math students. Some Quotes from Reviewers “The material on the concept of a general vector space, linear independence, basis, etc. Is always difficult for students in this course. Gujarati Tera Font Suraj Google Earth. This book handles it very well. It gives full, clear explanations. The style is very good, clear, and thorough. It should appeal to my students.
I like the book very much. It subscribes to the same philosophy of linear algebra as pioneered by Strang some 30 years ago (acknowledged in the introduction) and builds on the Strang books, making things even clearer and adding more topics. I would certainly like to use this book and would recommend it to my colleagues.” -Bruno Harris, Brown University “I like the book very much. We will consider it for our linear algebra courses.
This is the best new book to appear since the text by Gilbert Strang. It is really modern book, combining, in a masterful, core and applied aspects of linear algebra. This is a very good book written by a very good mathematician and a very good teacher.” -Juan J. Manfredi, University of Pittsburgh “In many, if not most, beginning texts of linear algebra, the applications may be collected together in a chapter at the end of the book or in an appendix, leaving any inclusion of this material to the discretion of the instructor. However, Applied Linear Algebra by Olver and Shakiban completely reverses this procedure with a total integration of the application with the abstract theory. The effect on the reader is quite amazing. The reader slowly begins to realize two main points: (1) how applications generally drive the abstract theory, and (2) how the abstract theory can illuminate the applications, and resolve solutions in very striking ways.
This text is easily the best beginning linear algebra text dealing with the applications in an integrated way that I have seen. There is no doubt that this text will be the standard to which all beginning linear algebra texts will be compared. Simply put, this is an absolutely wonderful text!” -Norman Johnson, University of Iowa “I lover the style of this book, especially the fact that you could feel the authors’ enthusiasm about the nice mathematics involved in the theory. The examples were very clear and interesting, and they always tried to approach the same problems over and over again as soon sas they had more weapons at their disposal to attack them. I thought this was great, this text introduces the notion of an abstract space very early (still, after Gaussian Elimination) and in a very natural way, then emphasizes along the way over and over again that tremendously. I would absolutely consider this text. I was really taken by the applications and the organization of the materials.
I also loved the abundance of exercises and problems.” -Tamas Wiandt, Rochester Institute of Technology “This text is very well-written, has lots of examples, and is easy to read and learn from. I’d use it in my Matrix Methods class. There is a good mixture of routine and more advanced examples.” -James Curry, University of Colorado-Boulder “I believe the writing style would appeal to my students because of the clarity and the examples, as well as the tone. I am going to consider its use, once I see its final form.” -Fabio Augusto Miner, Purdue University. • Abundant exercises—Appear after almost every subsection, in a wide range of difficulty.
• Starts each exercise set with straightforward computational problems to test and reinforce the new techniques and ideas. • Presents more advanced and more theoretical exercises later on in the set. • Includes numerous computer-based exercises and in-depth projects. • Discussion of the basics of matrices, vectors, and Gaussian elimination. • Coverage of less-familiar topics from linear systems theory—Includes the LU decomposition and its permuted versions. • Wide range of illustrative examples to explain essential concepts of vector space, subspace, span, linear independence, basis, and dimension—Addresses the difficulty students often have with these concepts.
• Concurrent development of the finite-dimensional and function space cases in Chapters 2 and 3 (Inner Products and Norms). • An entire chapter (Chapter 6) devoted to applications of the concepts of Minimization and Least Squares and Orthogonality. • Flexible presentation of Linear Functions, Linear Transformations, and Linear Systems (Chapter 7)—Can be covered or omitted as desired. • Coverage of eigenvalues and their applications in linear dynamical systems governed by ordinary differential equations and iterative systems, such as Markov chains and numerical solution algorithms. • Complete discussions of numerical linear algebra, including pivoting strategies, condition numbers, iterative solution methods such as Gauss- Seidel and SOR, singular value decomposition, the QR algorithm, and finite elements. • Unique chapter on Boundary Value Problems in One Dimension (Chapter 11). Presents topics from applied linear analysis such as delta functions, Green's function, and finite elements, as a completely natural development of linear algebra in function spaces.
• Text-specific website at a number of illustrative MATLAB problems the authors used in teaching the course.