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This section contains free e-books and guides on Calculus, a number of the resources on this section can be looked at online and a variety of them can be downloaded.
This book covers the subsequent topics: Field of Reals and Beyond, From Finite to Uncountable Sets, Metric Spaces and Some Basic Topology, Sequences and Series, Functions on Metric Spaces and Continuity, Riemann Stieltjes Integration.
This lecture note covers these topics: General linear homogeneous ODEs, Systems of linear coupled first order ODEs, Calculation of determinants, eigenvalues and eigenvectors as well as their use in the perfect solution is of linear coupled first order ODEs, Parabolic, Spherical and Cylindrical polar coordinate systems, Introduction to partial derivatives, Chain rule, change of variable, Jacobians with examples including polar coordinate systems, surfaces and Sketching simple quadrics.
This lecture note explains Differential and Integral calculus of functions of just one variable, including trigonometric functions.
This lecture note explains the next topics: Methods of integration, Taylor polynomials, complex numbers plus the complex exponential, differential equations, vector geometry and parametrized curves.
James Callahan, David Cox, Kenneth Hoffman, Donal OShea, Harriet Pollatsek, Lester Senechal
Calculus in Context will be the product with the Five College Calculus Project. Besides the introductory calculus text, the item includes computer programs and a Handbook for Instructors.
This is advantageous notes for Calculus. This notes contain Real numbers, Functions, Derivatives, Integration theory and Sequences
This notes has the details about The untyped lambda calculus, The Church-Rosser Theorem, Combinatory algebras, The Curry-Howard isomorphism, Polymorphism, Weak and strong normalization, Denotational semantics of PCF
This notes contain Complex numbers, Proof by induction, Trigonometric and hyperbolic functions, Functions, limits, differentiation, Integration, Taylors theorem and series
This notes contains these subcategories Calculus, Introduction to Number Theory and Vector Calculus
This book emphasizes the essential concepts from calculus and analytic geometry and also the application of these concepts to selected parts of science and engineering. Topics covered includes: Sets, Functions, Graphs and Limits, Differential Calculus, Integral Calculus, Sequences, Summations and Products and Applications of Calculus.
Calculus Made Easy is certainly the most popular calculus primer, and also this major revision from the classic math text definitely makes the subject taking place still more comprehensible to readers coming from all levels. This is really a book that explains the philosophy in the subject in a really simple manner, which makes it easy to understand even for people who find themselves not familiar with math.
This book is really a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus comprehensive, which is rich with applications.
David Cox, Amherst College
Kenneth Hoffman, Hampshire College
Donal OShea, Mount Holyoke College
Harriet Pollatsek, Mount Holyoke College
Lester Senechal, Mount Holyoke College
Support to the different aspects of Calculus in Context is here from several sources. Primary funding for curriculum development and dissemination was supplied by the National Science Foundation in grants DMS-14004 1988-95 and DUE-9153301 1991-97, awarded to Five Colleges, Inc. Other curriculum development funding has been supplied by NECUSE New England Consortium for Undergraduate Science Education, funded through the Pew Charitable Trusts to Smith College 1989 and Mount Holyoke College 1990. Five Colleges, Inc. also provided start-up funds.
Equipment and software for computer classrooms continues to be funded by NSF grants from the ILI program: USE-8951485 to Smith College and DUE/EHR-9551919 to Mount Holyoke College. The Hewlett-Packard Corporation contributed equipment to Mount Holyoke and Smith Colleges, along with other equipment was contributed to Mount Holyoke College by IBM along with the Sloan Foundation.
Any opinions, findings, and conclusions or recommendations expressed within this material are those from the authors , nor necessarily reflect those with the National Science Foundation.
Calculus in Context will be the product with the Five College Calculus Project. Besides the introductory calculus text, this product includes software applications and a Handbook for Instructors described below. The story with the Five College Calculus Project began almost 40 years ago, if your Five Colleges were only Four: Amherst, Mount Holyoke, Smith, plus the large Amherst campus with the University of Massachusetts. These four resolved to produce a new institution that will be a site for educational innovation with the undergraduate level; by 1970, Hampshire College was enrolling students and enlisting faculty. Early in their academic careers, Hampshire students grapple with primary sources to all fields-in economics and ecology, plus in history and literature. And journal articles dont shelter their readers in your own home truths: when a mathematical argument is necessary, it can be used. In this way, students within the life and social sciences found, sometimes thus to their surprise and dismay, that they can needed to know calculus whenever they were to master their chosen fields. However, the calculus they needed hasn't been, in general, the calculus which was actually being taught. The journal articles dealt directly together with the relation between quantities along with their rates of change-in simple terms, with differential equations.
Confronted having a clear need, those students wanted help. By the mid-1970s, Michael Sutherland and Kenneth Hoffman were teaching training for those students. The core with the course was calculus, but calculus as it really is used in contemporary science. Mathematical ideas and techniques grew outside of scientific questions. Given an activity, students were forced to recast it a model; generally, the model was obviously a set of differential equations. To solve the differential equations, they used numerical methods implemented on the computer.
The course evolved and prospered quietly at Hampshire. More than a decade passed before a few of us with the other four institutions paid some awareness of it. We liked its fundamental premise, that differential equations belong with the center of calculus. What astounded us, though, was the revelation that differential equations could really be in the center-thanks on the use of computers.
This book will be the result of our own efforts to translate the Hampshire course for any wider audience. The typical student in calculus hasn't been driven to review calculus as a way to come to grips together with his or her scientific questions-as those pioneering students had. If calculus is usually to emerge organically from the minds with the larger student population, an easy method must be found to involve that population inside a spectrum of scientific and mathematical questions. Hence, calculus in context. Moreover, those contexts has to be understandable to students without having special scientific training, as well as the mathematical issues they raise must lead to your central ideas in the calculus-to differential equations, in reality.
Coincidentally, the continent turned its focus on the undergraduate science curriculum, also it focused on the calculus course. The National Science Foundation developed a program to back up calculus curriculum development. To carry out our plans we requested funds to get a five-year project; we had arrived fortunate to get the only multi-year curriculum development grant awarded within the first year with the NSF program. The text and software would be the outcome in our effort.
We feel that calculus may be for students exactly what it was for Euler along with the Bernoullis: a language along with a tool for studying the whole fabric of science. We also believe much with the mathematical depth and vitality of calculus depends on connections along with other sciences. The mathematical questions that arise are compelling partially because the answers matter with other disciplines. We began our work using a clean slate, not by asking what parts with the traditional course to incorporate or discard. Our starting points are thus our breakdown of what calculus is actually about. Our curricular goals are that which you aim to convey concerning the subject from the course. Our functional goals describe the attitudes and behaviors produce your own . our students will adopt in making use of calculus to approach scientific and mathematical questions. Calculus is fundamentally a method of working with functional relationships that exist in scientific and mathematical contexts. The techniques of calculus should be subordinate for an overall view from the questions that provides rise to the telltale relationships.
Technology radically enlarges all the different questions we are able to explore along with the ways we can easily answer them. Computers and graphing calculators tend to be more than tools for teaching the standard calculus.
The thought of a dynamical strategy is central to science. Therefore, differential equations belong with the center of calculus, and technology makes this possible for the introductory level.
The procedure for successive approximation can be a key tool of calculus, even if the outcome from the process-the limit-cannot be explicitly shown in closed form.
Develop calculus within the context of scientific and mathematical questions.
Treat systems of differential equations as fundamental objects of study.
Construct and analyze mathematical models.
Use the tactic of successive approximations to define and solve problems.
Develop geometric visualization with hand-drawn and computer graphics.
Give numerical methods an even more central role.
Encourage collaborative work.
Enable students to utilize calculus like a language along with a tool.
Make students comfortable tackling large, messy, ill-defined problems.
Foster an experimental attitude towards mathematics.
Help students appreciate the price of approximate solutions.
Teach students that understanding grows from working on problems.
Differential equations is now able to solved numerically, to enable them to take their rightful place inside the introductory calculus course.
The chance to handle data and perform many computations makes exploring messy, real-world problems possible.
Since we are able to now handle credible models, the role of modelling becomes additional central for the subject.
The text illustrates how you have pursued the curricular goals. Each goal is addressed in the first chapter which starts off with questions about describing and analyzing the spread of an contagious disease. A model was made: a model which can be actually a system of coupled non-linear differential equations. We then set up a numerical exploration on those equations, as well as the door is opened into a solution by successive approximations. Our implementation on the functional goals can be evident. The text has lots of more words than the standard calculus book-it is often a book being read. The exercises make unusual demands on students. Most are besides variants of examples which were worked from the text. In fact, the written text has rather few template examples.
It may also become apparent for your requirements that the words reflects substantial shifts in emphasis in comparison for the traditional course. Here are many of the most striking: Since all of us value elegance, we will explain might know about mean by brute force. Eulers method is usually a good example. It is usually a general approach to wide applicability. Of course if we use it to fix a differential equation like
we are choosing a sledgehammer to compromise a peanut. But at the very least the sledgehammer works. Moreover, it functions with coconuts like
also it will even knock down a property like
Students also understand the elegant special methods that is usually invoked to resolve
separation of variables and partial fractions are discussed in chapter 11, but they also understand which they are fortunate indeed whenever a real problem will succumb to such methods.
Our curriculum is just not aimed at its own clientele. On the contrary, the world thinks that calculus is one in the great bonds that unifies science. All students needs to have an opportunity to find out how the language and tools of calculus help forge that bond. We emphasize that this just isn't a service course or calculus with applications, but rather a training course rich in mathematical ideas that will assist all students well, including mathematics majors. The student population inside first semester course is specially diverse. In fact, because so many students take only 1 semester, the primary six chapters stand alone being a reasonably complete course. We have also experimented with present the contexts of broadest interest first. The increased exposure of the physical sciences increases from the second half in the book.
We have prepared a Handbook for Instructors a PDF file dependant on our experiences, and that relating to colleagues at other schools, with specific recommendations for use from the text. We urge prospective instructors to talk it, because this course differs substantially on the calculus courses most people have learned from and taught inside past. These are QuickBasic versions from the Basic programs that appear inside the text; you may also get QuickBasic itself.
sarah-marie belcastro has produced an amount of notebooks to accompany the written text. They are designed in both Mathematica and Sage ; the latter is usually a free open source substitute for Magma, Maple, Mathematica and Matlab.
David Cox, Amherst College
Kenneth Hoffman, Hampshire College
Donal OShea, Mount Holyoke College
Harriet Pollatsek, Mount Holyoke College
Lester Senechal, Mount Holyoke College
Calculus I Chapters 1-6, plus front matter and full index
Calculus II Chapters 7-12, plus front matter and full index
Support for that different aspects of Calculus in Context originates from several sources. Primary funding for curriculum development and dissemination was furnished by the National Science Foundation in grants DMS-14004 1988-95 and DUE-9153301 1991-97, awarded to Five Colleges, Inc. Other curriculum development funding has been given by NECUSE New England Consortium for Undergraduate Science Education, funded with the Pew Charitable Trusts to Smith College 1989 and Mount Holyoke College 1990. Five Colleges, Inc. also provided start-up funds.
Equipment and software for computer classrooms may be funded by NSF grants within the ILI program: USE-8951485 to Smith College and DUE/EHR-9551919 to Mount Holyoke College. The Hewlett-Packard Corporation contributed equipment to Mount Holyoke and Smith Colleges, along with other equipment was contributed to Mount Holyoke College by IBM plus the Sloan Foundation.
Any opinions, findings, and conclusions or recommendations expressed on this material are those from the authors and don't necessarily reflect those with the National Science Foundation.
Calculus in Context may be the product from the Five College Calculus Project. Besides the introductory calculus text, the item includes computer programs and a Handbook for Instructors described below. The story in the Five College Calculus Project began almost 4 decades ago, in the event the Five Colleges were only Four: Amherst, Mount Holyoke, Smith, along with the large Amherst campus with the University of Massachusetts. These four resolved to make a new institution that you will find a site for educational innovation with the undergraduate level; by 1970, Hampshire College was enrolling students and enlisting faculty. Early in their academic careers, Hampshire students grapple with primary sources to all fields-in economics and ecology, and history and literature. And journal articles dont shelter their readers in your own home truths: in case a mathematical argument is essential, it truly is used. In this way, students within the life and social sciences found, sometimes thus to their surprise and dismay, how they needed to know calculus whenever they were to master their chosen fields. However, the calculus they needed has not been, generally, the calculus that has been actually being taught. The journal articles dealt directly using the relation between quantities as well as their rates of change-in plain english, with differential equations.
Confronted having a clear need, those students wanted help. By the mid-1970s, Michael Sutherland and Kenneth Hoffman were teaching training for those students. The core in the course was calculus, but calculus as it can be used in contemporary science. Mathematical ideas and techniques grew away from scientific questions. Given a procedure, students were required to recast it as a a model; frequently, the model would have been a set of differential equations. To solve the differential equations, they used numerical methods implemented over a computer.
The course evolved and prospered quietly at Hampshire. More than a decade passed before a number of us with the other four institutions paid some care about it. We liked its fundamental premise, that differential equations belong with the center of calculus. What astounded us, though, was the revelation that differential equations could really be for the center-thanks on the use of computers.
This book would be the result of our own efforts to translate the Hampshire course for any wider audience. The typical student in calculus will not be driven to review calculus as a way to come to grips in reference to his or her very own scientific questions-as those pioneering students had. If calculus is always to emerge organically inside the minds with the larger student population, a means must be found to involve that population within a spectrum of scientific and mathematical questions. Hence, calculus in context. Moreover, those contexts have to be understandable to students without having special scientific training, along with the mathematical issues they raise must lead on the central ideas in the calculus - -to differential equations, in truth.
Coincidentally, america turned its focus on the undergraduate science curriculum, plus it focused on the calculus course. The National Science Foundation designed a program to guide calculus curriculum development. To carry out our plans we requested funds for the five-year project; we had been fortunate to get the only multi-year curriculum development grant awarded inside first year on the NSF program. The text and software will be the outcome of the effort.
We think that calculus could be for students exactly what was for Euler and also the Bernoullis: a language as well as a tool for checking whole fabric of science. We also feel that much in the mathematical depth and vitality of calculus depends on connections for some other sciences. The mathematical questions that arise are compelling partly because the answers matter with other disciplines. We began our work that has a clean slate, not by asking what parts from the traditional course to feature or discard. Our starting points are thus our introduction to what calculus is very about. Our curricular goals are might know about aim to convey in regards to the subject within the course. Our functional goals describe the attitudes and behaviors hopefully our students will adopt with calculus to approach scientific and mathematical questions. Calculus is fundamentally a means of working with functional relationships that happen in scientific and mathematical contexts. The techniques of calculus need to be subordinate in an overall view from the questions that provides rise to the telltale relationships.
Technology radically enlarges the plethora of questions we can easily explore and also the ways we could answer them. Computers and graphing calculators tend to be more than tools for teaching the conventional calculus.
The idea of a dynamical strategy is central to science. Therefore, differential equations belong in the center of calculus, and technology makes this possible for the introductory level.
The technique of successive approximation is usually a key tool of calculus, even if your outcome on the process-the limit-cannot be explicitly caved closed form.
Develop calculus inside the context of scientific and mathematical questions.
Treat systems of differential equations as fundamental objects of study.
Construct and analyze mathematical models.
Use the tactic of successive approximations to define and solve problems.
Develop geometric visualization with hand-drawn and computer graphics.
Give numerical methods an even more central role.
Encourage collaborative work.
Enable students make use of calculus to be a language along with a tool.
Make students comfortable tackling large, messy, ill-defined problems.
Foster an experimental attitude towards mathematics.
Help students appreciate the need for approximate solutions.
Teach students that understanding grows away from working on problems.
Differential equations is now able to solved numerically, just for them to take their rightful place inside the introductory calculus course.
The capability to handle data and perform many computations makes exploring messy, real-world problems possible.
Since we could now take care of credible models, the role of modelling becomes additional central to your subject.
The text illustrates the way we have pursued the curricular goals. Each goal is addressed in the first chapter which starts off with questions about describing and analyzing the spread of an contagious disease. A model was made: a model that is actually a system of coupled non-linear differential equations. We then take up a numerical exploration on those equations, plus the door is opened into a solution by successive approximations. Our implementation with the functional goals can be evident. The text has several more words than the original calculus book-it is usually a book to become read. The exercises make unusual demands on students. Most are besides variants of examples which have been worked inside the text. In fact, the written text has rather few template examples.
It can even become apparent to you personally that the writing reflects substantial shifts in emphasis in comparison on the traditional course. Here are a number of the most striking: Since all of us value elegance, let's explain whatever we mean by brute force. Eulers method is often a good example. It is usually a general means of wide applicability. Of course after we use it to resolve a differential equation like
we are employing a sledgehammer to break into a peanut. But a minimum of the sledgehammer works. Moreover, it truly does work with coconuts like
and yes it will even knock down a residence like
Students also start to see the elegant special methods that may be invoked to unravel
separation of variables and partial fractions are discussed in chapter 11, nonetheless they understand they are fortunate indeed every time a real problem will succumb to such methods.
Our curriculum will not be aimed at an exclusive clientele. On the contrary, the world thinks that calculus is one with the great bonds that unifies science. All students really should have an opportunity to find out how the language and tools of calculus help forge that bond. We emphasize that this isn't a service course or calculus with applications, but rather an application rich in mathematical ideas that will aid all students well, including mathematics majors. The student population from the first semester course is specially diverse. In fact, as a general rule students take only 1 semester, the very first six chapters stand alone as being a reasonably complete course. We have also attemptedto present the contexts of broadest interest first. The focus on the physical sciences increases inside second half on the book.
We have prepared a Handbook for Instructors a PDF file according to our experiences, and that regarding colleagues at other schools, with specific ideas for use from the text. We urge prospective instructors to refer to it, because course differs substantially from your calculus courses many of us have learned from and taught from the past. There are also software packages are available at totally free for use with this particular text.
These are QuickBasic versions on the Basic programs that appear within the text; also you can get QuickBasic itself.
sarah-marie belcastro has produced an amount of notebooks to accompany the words. They are designed in both Mathematica and Sage ; the latter can be a free open source option to Magma, Maple, Mathematica and Matlab.
School math, multimedia, and technology tutorials.
The list listed here are free Calculus and Analysis Ebooks for Undegraduate and Graduate students. Please report if you will discover links who are not working.
Advanced Calculus and Analysis, by Ian Craw
These text selections are outstanding!!!! great work compiling doing this great and useful information.
September 5, 2014 at 7:30 pm
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This new edition, with the well-known calculus text, is ideal for college kids majoring in physical sciences, engineering, computer science or mathematics. As with earlier editions, the written text fits a three-semester 4 to 5 quarter introductory calculus of merely one and several variables. It can also be used for the one-year course in single-variable calculus.
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Communicating: A Social, Career, and Cultural Focus 12th Edition
Professor Robert Ellis received his undergraduate degree at Miami University in Oxford, Ohio and his awesome from Duke University. Since 1966 he has become on the faculty in the University of Maryland, teaching both undergraduate and graduate courses and doing research in the regions of functional analysis and operator theory. In 1972 he received a Senior Scientist award in the Alexander Von Humboldt Foundation.
Professor Denny Gulick received his undergraduate degree at Oberlin College, with the exceptional from Yale University. He has taught in the University of Maryland since 1965. His interests were formerly in abstract functional analysis, and much more recently his interests ventured into chaos and fractals. He is additionally involved in issues of mathematics education. In 2000 he received the Campus Kirwan Prize for Undergraduate Education.
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Publisher: Thomson Custom Publishing; 6th edition July 2, 2003
Shipping Weight: 5.6 pounds
I used the second Edition within the mid 80s for that three-semester calculus sequence for engineers and the majority science majors within big Midwestern land-grant university, in order that is what I am reviewing here. And I analyze it mainly relative to your usual tastes of an mathematician. But the people inside my calc classes were mostly engineers, and I dont remember hearing any grumbling concerning the textbook.
I find that this first half with the book has thorough mathematical rigor and completeness. Just about everything from the single-variable calculus is proven, some inside the appendix. The multivariable material to the third semester is often additional relaxed, and most of the time doesnt conclude deltas and epsilons, as it were. So I was sometimes left wondering precisely how things worked. Im guessing they've already beefed inside the multivariable theory in later editions.
The theorems are stated concisely and followed immediately by proofs, the many chat, motivation, and examples being separate. That makes it beneficial to quick reference if you want to refresh the main points of some theorem.
In three semesters, we had been assigned about 1800 problems. The accompanying solutions manuals two volumes were extremely valuable. I could be working inside the wee hours and do not get stuck, and never was required to ask questions from the profs. I worked virtually every problem assigned and do not found over a few errors in the solutions or the link. I remember finding some stupid systematic round-off errors inside the solutions coping with exponential decay. I may are finding a couple errors besides, but not enough to increase anybodys ire. And you can believe me-I did grind the content to dust. Read more
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Many on the explanations within this book usually are not written clearly. I was required to spend a large amount of time deciphering the fabric, as it had not been clearly explained in college, either. This book in conjunction having a prof who is often a good teacher will be find, but when you are in your own for learning in the book, it can be not very efficient.
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Firstly, I attend the University of Maryland, where both authors in this book teach.
This book is difficult, but only as this material is hard. This book is actually only suitable for engineering and physics majors, several examples are suited to just these kinds of problems. As a computer science major, such example problems only confuse and baffle me. However, example problems involving as an example the Manelbrot set make the information fun to digest.
The book itself is amazing. The University of Maryland uses this book for 3 courses: Calc I, II, and III, and contains done so for many years. Theres a superb reason because of this: it covers EVERYTHING you need to be familiar with basic to advanced scientific calculus.
I am just completing Calculus II using this type of book. Honestly, im wanting to destroy it and do not see it again. But this regards the pad taught, not the novel itself, and that is top-notch. If youre looking for an easy calculus book, this isnt it. However, if you are serious around the material and carry out the example exercises, this book does a fantastic job teaching you the pad.
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I have got courses in Calculus at three different times - 1974, 1979-1980 and also this year 2012 to be a review of Calculus 3 multi-variable. Of the three textbooks I used, the most beneficial was this by Robert Ellis and Denny Gulick, which I found in 1979-1980. I liked it since I remember the ability to learn through the book without depending upon the professors, tutors or, this coming year on the internet. The explanations and examples were east to understand and problems were great. True I was utilizing a much earlier version but I would guess the most up-to-date version can be as good or better. In contrast, the Calculus textbook by Deborah Hughes-Hallett, which I used in 2010 retaking Calculus 3, is awful see my review while others.
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I used this text when I attended The University of Maryland, College Park UMCP. In fact, I had a class with one from the authors. Since then, I have graduated together with a quite successful technological career. I have tutored a lot of people from other schools in calculus and I took an associated class at MIT during one semester.
Therefore, I have seen many textbooks and also have a fair grounds for comparison.
In my view, the textbook has little value in accordance with texts used at other schools perhaps thats why it isn't more widely used. The primary value with this textbook is that it packs three semesters of stuff into one volume. That being said, perhaps the Calculus for Dummies book could be better when you get you through enough material that may be the equivalent in the first 2/3 on the Gulick text.
Further, can you think that in class, one in the authors had us carry out the unanswered problem sets any problem had solutions, but wouldnt hand back the graded work? All we have back would be a letter grade. There was little feedback in any respect as to that which you did or didn't understand. I neednt describe how happy students werent this.
To excel, it is advisable to find another text and do many extra problems in your own with solution sets provided.
Having seen the texts used at other schools, I did feel a lttle bit cheated.
Dont take my word correctly. Definitely COMPARE other texts on this one before buying borrow a replica from a math or engineering library somewhere and judge yourself.
If, however, you take calculus at UMCP, well, I guess you happen to be stuck buying The Brick. Just do numerous extra problems as you're able.
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I passed my class with this particular book. Its fairly detailed in explaining calculus 1, 2, and 3.
The book would have been a requirement for an academic course. It was used frequently during the semester. I failed to have strong mathematical skills when I used the publication. Read more
Published on July 24, 2013 by Henry C
of course, calculus with analytic geometry was delivered on time and yes it was packed, the external cover on the book is exchanged. Read more
Published on June 28, 2012 by Ambesaw
I heavily depend on textbooks for my classes. I read James Stewarts book Single Variable Calculus practically cover to hide, and might get an A while missing 50% of Read more
Published on February 1, 2012 by Josh Gross
Very well-written book: it offers real world examples and clear explanations and proofs. I also employ a solutions manual because of this book, which can be very helpful.
Published on September 28, 2010 by RuBun
When this book is bought, can it come which has a webassign purchase code?
Published on September 13, 2010 by lala
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