Free Linear Algebra textbook
Linear Algebra
A Free text for a standard US undergraduate course
jhefferon at smcvt.edu
Linear Algebra is a text
for a first US undergraduate Linear Algebra course.
You can use it as a main text,
as a supplement, or for independent study.
It is Free.
The book with
the answers to all exercises,
as well as beamer slides for classroom use and a lab manual using
Highlights
The coverage is standard:
linear systems and Gauss's method,
vector spaces, linear maps and matrices, determinants,
and eigenvectors and eigenvalues.
It is Free.
The book is ,
including its source.
The approach is developmental.
Although it covers the requisite
material by proving things,
it does not assume that
students are already able at abstract work.
Instead, it proceeds with a great deal of
motivation, many computational examples,
and exercises that range from
routine verifications to a few challenges.
The goal is,
in the context of developing the material of an
undergraduate linear algebra course, to help raise
each student's level of
mathematical maturity.
Extensive exercise sets, with worked answers to all exercises.
Sometimes material described on the web as a
book is really someone's lecture notes.
That's fine but from notes to a book is a long way.
That includes things like figures and an index,
but most importantly means exercises.
Each subsection here has many,
spanning a range of difficulty,
each with a worked answer, including proofs.
This book has been downloadable since 1996 and has been used
in hundreds of classes at many schools, as well as by many individuals
for independent study.
Applications.
Each chapter finishes with four or five short
supplemental topics.
These are good for reading or projects, or for
small group work.
You can get beamer slides to use in class, and a lab manual
using Sage.
Prerequisite:
one semester of calculus.
Here are some:
Download Linear Algebra
Here is the latest version of
Save these files in the same directory
clicking on an exercise sends you to its answer and
clicking on an answer sends you to the exercise.
(Of course you must use a PDF reader that supports this,
such as Adobe Reader.)
If you prefer a paper copy then you can buy an official
one from a number of
sources using ISBN-13:&978-, including
the price there is $20.
If you are teaching a class then
have a look at the
for classroom presentation.
These draw
for instance, theorems appear referenced with their number from the text.
But they use different examples so students see twice as many.
(Those slides omit some proofs in favor of i
there is also a version that includes
that supplements
the text material
(I don't know anyone who has class-tested the lab.
If you use it then please let me know.)
Material of less interest.
If you are into LaTeX then you can
You could also get
if for some reason you are keen.
Additional material
Prof&Harold W.&Ellingsen of SUNY&Potsdam has shared
You can also
that I assigned for take home work when I taught the class in the Fall of
This text is Free.
Use it under either the
or the , at your discretion.
For bookstores: thank you for being concerned about my rights.
I give instructors permission
to make copies of this material, either electronic or paper,
and give or sell those copies to students.
Easier than making your own is getting a print on demand copy
from Amazon, or NACSCORP, or
directly from Ingram via LightningSource,
ISBN-13:&978-.
Please avoid ordering used or unofficial copies since they can be outdated
or have significantly different content and pagination&& with
an up to date copy at pretty much the price of printing, any
dollar savings from old versions are tiny compared to
the cost of confusion, particularly confusion to me since I get
contacted about already-fixed bugs.
The current version is 2014-Dec-25; see
the printed copy's title page or the last page of the Preface.
If you have any questions, don't hesitate to contact me.
For instructors who want to modify the text:
please, feel free.
If you can
then I'd be glad to see them, but if not that is fine.
However, as a favor, I ask that you make clear which material
is yours and which is from the main version of the text.
I often get questions or bug reports
and working out what is going on gets frustrating all
around unless authorship is clear.
In particular, one approach that would help is
changing the cover to include a statement about your modifications.
Something like this would be great: & \fbox{The material in the second appendix on induction is not from the main version of the text but has been added by Professor Jones of UBU.
For this material contact \url{}.}&
Can You Help With Linear Algebra?
Feel free to write me with any comments.
I enjoy hearing about the experience that instructors have
and I find suggestions helpful,
especially bug reports.
I save these and periodically revise.
has some material that you are able to share back,
such as the ,
then I'd be delighted to see it.
(For instance, if you could write a 3-5 page Topic illustrating eigenvalues
and eigenvectors by using normal modes of coupled pendulums,
perhaps by descretizing the problem, and perhaps with video,
why then that'd be great.
Also great would be a topic on dimension reduction for Machine Learning.)
Of course, I reserve the ability to choose whether to edit or include it.
I gratefully acknowledge all the contributions that I use,
or I can keep you anonymous.
In particular, I would welcome exams or problem sets.
Some instructors have reservations about using a text
where the answers to the exercises are downloadable.
(I can't resist noting here that this objection is misguided:
anyone college student can
get copies of the answers to
all widely-available texts off the Internet in seconds.
I'll also say that in the past I tried witholding the answers and
asking class instructors to email me for copies but
that left me trying to determine identity via email,
which is just not practical.)
Thus additional sets of exercises without answers would answer the requests
of some instructors.
If you could contribute
your TeX or LaTeX source that'd be great because then
instructors could cut and paste.
I would also welcome contrbutions related to the emerging electronic
For instance, if you have sets of questions that are suitable for
and that you could
share with other users of this book then
write me and we can see about making them available.
The same holds for
My email is jhefferon at smcvt.edu.
Related work
You may also like my
text, also Freely available.
It is for a proofs course taught using Moore method, which
is known in other fields as Inquiry-Based or the Discovery Method.
Site Information
is located in the
in Colchester, Vermont
Joshua runs under Linux
Open Source software is a great idea.
This project would not have gotten done without it.
(Credit for the logo to Matt Ericson.)Linear Algebra and Multivariable Calculus
The standard prerequisite for most linear algebra and multivariable calculus courses is two semesters of calculus. The exception is MATH 2310, which requires only one semester of calculus.
MATH -: Linear Algebra and Multivariable Calculus
is taught at a higher theoretical level than MATH . For example, in 2210 certain abstract concepts such as vector spaces are introduced, theorems are carefully stated, and many of these theorems are proved. MATH 2210 is primarily a linear algebra course, but it also provides an introduction to linear ordinary differential equations. Some of the linear algebra in MATH 2210 is then used to develop multivariable and vector calculus in MATH 2220. MATH 2210 does not provide adequate preparation for MATH 2240.
MATH -: Theoretical Linear Algebra and Calculus
is “integrated” in the sense that both linear algebra and multivariable calculus are taught in each semester, rather than covered in separate semesters (as in ). MATH
is taught at a higher level of mathematical sophistication than MATH , particularly the portion dealing with vector calculus. Students who have been extremely successful in their previous calculus courses are encouraged to try this sequence. Those who find MATH 2230 too challenging or time-consuming may drop down to MATH 2210 at the beginning of the term or continue with MATH 2220 instead of 2240.
MATH --: Engineering Mathematics
The defining characteristic of this sequence is its rapid and utilitarian coverage of a wide variety of mathematical topics important in engineering and the physical sciences. Although MATH 30-2940 covers more topics than other programs, the courses in the sequence cover those topics in somewhat lesser depth and with less attention to theoretical background, particularly when compared to MATH
and MATH . MATH 1920 covers multivariable calculus, MATH 2930 is a course in ordinary and partial differential equations, and MATH 2940 is a linear algebra course. MATH 2930 and 2940 are indep MATH 1920 is the prerequisite for both. MATH 1920 and 2940 are sufficient prerequisites for most higher-level math courses. In fact, some engineering programs do not require 2930.
MATH : Calculus III – MATH : Linear Algebra with Applications
MATH 2130 is a course with many different topics, including differential equations and multivariable calculus. MATH 2310 is an applied linear algebra course that is less theoretical than 2210. The only prerequisite for MATH 2310 is MATH 1110, but it is also a good option for students who have taken MATH 2130 and want to learn some linear algebra. Both courses are intended for students who do not expect to take more advanced math courses.
Transfer Credit and Placement
Mathematically advanced high school students who have taken a linear algebra or multivariable calculus course will not receive transfer credit if the course was taught in a high school to high school students (even if the college provides a transcript) or if the course is used to satisfy high school graduation requirements. Repeating the material at Cornell may be necessary if the student’s college
otherwise, more advanced courses with a linear algebra or multivariable calculus prerequisite may be attempted if the student is confident in his/her mastery of the material. When in doubt, speak with the course instructor or the director of undergraduate studies in math.您所在位置： &
&nbsp&&nbsp&nbsp&&nbsp
Study Guide to Linear Algebra and Its Applications.3rd Ed.教材.pdf349页
本文档一共被下载：
次 ,您可全文免费在线阅读后下载本文档。
文档加载中...广告还剩秒
需要金币：160 &&
你可能关注的文档：
··········
··········
GUIDE LINEAR ALGEBRA
ITS APPLICATIONS THIRD EDITION UPDATE David C. Lay University of Maryland C College Park Copyright ? 2006 Pearson Addison-Wesley. All rights reserved.
Reproduced by Pearson Addison-Wesley from electronic files supplied by the author.
Copyright ? 2006 Pearson Education, Inc.
Publishing as Pearson Addison-Wesley, 75 Arlington Street, Boston, MA 02116.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or
transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or
otherwise, without the prior written permission of the publisher. Printed in the United States of
ISBN 0-321-28066-0
1 2 3 4 5 6 BB 08 07 06 05 Copyright ? 2006 Pearson Addison-Wesley. All rights reserved. Brief Contents INTRODUCTION HOW TO STUDY LINEAR ALGEBRA
C H A P T E R
1 LINEAR EQUATIONS IN LINEAR ALGEBRA
C H A P T E R
2 MATRIX ALGEBRA
C H A P T E R
3 DETERMINANTS
C H A P T E R
4 VECTOR SPACES
C H A P T E R
5 EIGENVALUES AND EIGENVECTORS
C H A P T E R
6 ORTHOGONALITY AND LEAST SQUARES
C H A P T E R
7 SYMMETRIC MATRICES
A P P E N D I C E S
TECHNOLOGY INDEX OF PROCEDURES AND TERMS INTRODUCTION TO MATLAB NOTES FOR THE MAPLE COMPUTER ALGEBRA SYSTEM NOTES FOR THE MATHEMATICA COMPUTER ALGEBRA SYSTEM NOTES FOR THE TI-83+/86/89 GRAPHIC CALCULATORS NOTES FOR THE HP-48G GRAPHIC CALCULATOR Copyright ? 2006 Pearson Addison-Wesley. All rights reserved. Contents INTRODUCTION vii Technology Support vii Review Materials on the Web viii HOW TO STUDY LINEAR ALGEBRA ix Strategies for Success in Linear Algebra ix
C H A P T E R
1 LINEAR EQUATIONS IN LINEAR ALGEBRA 1.1
Systems of Linear Systems 1-1 1.2
Row Reduction and Echelon Forms 1-7 1.3
Vector Equations 1-10 1.4
The Matrix Equation Ax
b 1-15 Mastering Linear Algebra Concepts: Span 1.5
Solution Sets of Linear Systems 1-20 1.6
Applications of Linear Systems 1-25 1.7
正在加载中，请稍后...