Calculus Problem Solver (REA) (Problem Solvers)
Average customer rating: 5 out of 5 stars
  • What you really want in a math text
  • One of the better calculus books
  • Forget this, if you want the best and most comprehensive TRY
  • This is exactly what the title says
  • Step by Step
Calculus Problem Solver (REA) (Problem Solvers)
The Staff of REA
Manufacturer: Research & Education Association
ProductGroup: Book
Binding: Paperback

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ASIN: 0878915052

Book Description

Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.

Here in this highly useful reference is the finest overview of calculus currently available, with hundreds of calculus problems that cover everything from inequalities and absolute values to parametric equations and differentials. Each problem is clearly solved with step-by-step detailed solutions.

DETAILS
- The PROBLEM SOLVERS are unique - the ultimate in study guides.
- They are ideal for helping students cope with the toughest subjects.
- They greatly simplify study and learning tasks.
- They enable students to come to grips with difficult problems by showing them the way, step-by-step, toward solving problems. As a result, they save hours of frustration and time spent on groping for answers and understanding.
- They cover material ranging from the elementary to the advanced in each subject.
- They work exceptionally well with any text in its field.
- PROBLEM SOLVERS are available in 41 subjects.
- Each PROBLEM SOLVER is prepared by supremely knowledgeable experts.
- Most are over 1000 pages.
- PROBLEM SOLVERS are not meant to be read cover to cover. They offer whatever may be needed at a given time. An excellent index helps to locate specific problems rapidly.

TABLE OF CONTENTS
Introduction
Chapter 1: Inequalities
Chapter 2: Absolute Values
Chapter 3: Limits
Chapter 4: Continuity
Chapter 5: Derivative ?-Method
Chapter 6: Differentiation of Algebraic Functions
Chapter 7: Differentiation of Trigonometric Functions
Chapter 8: Differentiation of Inverse Trigonometric Functions
Chapter 9: Differentiation of Exponential and Logarithmic Functions
Chapter 10: Differentiation of Hyperbolic Functions
Chapter 11: Implicit Differentiation
Chapter 12: Parametric Equations
Chapter 13: Indeterminate Forms
Chapter 14: Tangents and Normals
Chapter 15: Maximum and Minimum Values
Chapter 16: Applied Problems in Maxima and Minima
Chapter 17: Curve Tracing
Chapter 18: Curvature
Chapter 19: Related Rates
Chapter 20: Differentials
Chapter 21: Partial Derivatives
Chapter 22: Total Differentials, Total Derivatives, and Applied Problems
Chapter 23: Fundamental Integration
Chapter 24: Trigonometric Integrals
Chapter 25: Integration by Partial Fractions
Chapter 26: Trigonometric Substitutions
Chapter 27: Integration by Parts
Chapter 28: Improper Integrals
Chapter 29: Arc Length
Chapter 30: Plane Areas
Chapter 31: Solids: Volumes and Areas
Chapter 32: Centroids
Chapter 33: Moments of Inertia
Chapter 34: Double/Iterated Integrals
Chapter 35: Triple Integrals
Chapter 36: Masses of Variable Density
Chapter 37: Series
Chapter 38: The Law of the Mean
Chapter 39: Motion: Rectilinear and Curvilinear
Chapter 40: Advanced Integration Methods
Chapter 41: Basic Differential Equations
Chapter 42: Advanced Differential Equations
Chapter 43: Applied Problems in Differential Equations
Chapter 44: Fluid Pressures/Forces
Chapter 45: Work/Energy
Chapter 46: Electricity
Index

WHAT THIS BOOK IS FOR

Students have generally found calculus a difficult subject to understand and learn. Despite the publication of hundreds of textbooks in this field, each one intended to provide an improvement over previous textbooks, students of calculus continue to remain perplexed as a result of numerous subject areas that must be remembered and correlated when solving problems. Various interpretations of calculus terms also contribute to the difficulties of mastering the subject.

In a study of calculus, REA found the following basic reasons underlying the inherent difficulties of calculus:

No systematic rules of analysis were ever developed to follow in a step-by-step manner to solve typically encountered problems. This results from numerous different conditions and principles involved in a problem that leads to many possible different solution methods. To prescribe a set of rules for each of the possible variations would involve an enormous number of additional steps, making this task more burdensome than solving the problem directly due to the expectation of much trial and error.

Current textbooks normally explain a given principle in a few pages written by a calculus professional who has insight into the subject matter not shared by others. These explanations are often written in an abstract manner that causes confusion as to the principle's use and application. Explanations then are often not sufficiently detailed or extensive enough to make the reader aware of the wide range of applications and different aspects of the principle being studied. The numerous possible variations of principles and their applications are usually not discussed, and it is left to the reader to discover this while doing exercises. Accordingly, the average student is expected to rediscover that which has long been established and practiced, but not always published or adequately explained.

The examples typically following the explanation of a topic are too few in number and too simple to enable the student to obtain a thorough grasp of the involved principles. The explanations do not provide sufficient basis to solve problems that may be assigned for homework or given on examinations.

Poorly solved examples such as these can be presented in abbreviated form which leaves out much explanatory material between steps, and as a result requires the reader to figure out the missing information. This leaves the reader with an impression that the problems and even the subject are hard to learn - completely the opposite of what an example is supposed to do.

Poor examples are often worded in a confusing or obscure way. They might not state the nature of the problem or they present a solution, which appears to have no direct relation to the problem. These problems usually offer an overly general discussion - never revealing how or what is to be solved.

Many examples do not include accompanying diagrams or graphs, denying the reader the exposure necessary for drawing good diagrams and graphs. Such practice only strengthens understanding by simplifying and organizing calculus processes.

Students can learn the subject only by doing the exercises themselves and reviewing them in class, obtaining experience in applying the principles with their different ramifications.

In doing the exercises by themselves, students find that they are required to devote considerable more time to calculus than to other subjects, because they are uncertain with regard to the selection and application of the theorems and principles involved. It is also often necessary for students to discover those "tricks" not revealed in their texts (or review books) that make it possible to solve problems easily. Students must usually resort to methods of trial and error to discover these "tricks," therefore finding out that they may sometimes spend several hours to solve a single problem.

When reviewing the exercises in classrooms, instructors usually request students to take turns in writing solutions on the boards and explaining them to the class. Students often find it difficult to explain in a manner that holds the interest of the class, and enables the remaining students to follow the material written on the boards. The remaining students in the class are thus too occupied with copying the material off the boards to follow the professor's explanations.

This book is intended to aid students in calculus overcome the difficulties described by supplying detailed illustrations of the solution methods that are usually not apparent to students. Solution methods are illustrated by problems that have been selected from those most often assigned for class work and given on examinations. The problems are arranged in order of complexity to enable students to learn and understand a particular topic by reviewing the problems in sequence. The problems are illustrated with detailed, step-by-step explanations, to save the students large amounts of time that is often needed to fill in the gaps that are usually found between steps of illustrations in textbooks or review/outline books.

The staff of REA considers calculus a subject that is best learned by allowing students to view the methods of analysis and solution techniques. This learning approach is similar to that practiced in various scientific laboratories, particularly in the medical fields.

In using this book, students may review and study the illustrated problems at their own pace; students are not limited to the time such problems receive in the classroom.

When students want to look up a particular type of problem and solution, they can readily locate it in the book by referring to the index that has been extensively prepared. It is also possible to locate a particular type of problem by glancing at just the material within the boxed portions. Each problem is numbered and surrounded by a heavy black border for speedy identification.

Customer Reviews:

5 out of 5 stars What you really want in a math text.......2007-07-11

This is the single text you need to de-mystify calc. It's advantage is that it explains by demonstration... again and again and again... with increasing, but gradual, difficulty.

Keep in mind that most texts are pumped out by publishing houses to churn numbers and are authored by academic staff desiring a professional profile.
This REA text gives you the universal nuts and bolts of calculus without the publishing-house baggage.

4 out of 5 stars One of the better calculus books.......2007-05-11

This is a pretty good calculus help book, especially if you're looking for a book that will teach you how to do a lot of problems. This book gives step-by-step solutions to the problems it presents, so if you can't figure out what the next step is, you can just glance at the solution to figure it out.

This is exactly what a math student needs, a book that gives plenty of practice problems and solutions to the problems. This book does fall short in a few areas though. It doesn't cover everything in a calculus course (especially in the later levels of calculus), and at times, the things it does cover it doesn't cover enough (like it will give only one or two examples of a certain type of problem, which isn't very helpful). And sometimes the solutions seems to simplify too much or skip a step, leaving you pondering how they from one step to the next. However, this is a problem that seems to plague all solution-type of texts. And my final complaint is that the type of font they use in this book isn't exactly asthetically pleasing. They could have use a different font or do something else to make it nicer to look at.

Overall though, this book gets 4 stars from me because it is one of the better calculus help books I have seen, even if it does have a few short comings here and there.

4 out of 5 stars Forget this, if you want the best and most comprehensive TRY.......2006-08-18

THE KING OF ALL MATHEMATICAL PROBLEMS!!!!!!!!!

Problems in Mathematical Analysis (Hardcover)
by g. yankovsky (Translator), B. Demidovich (Author
Publisher: mir publisher; 4th Printing edition (1976)
ASIN: B000GTC2GA

5 out of 5 stars This is exactly what the title says.......2005-01-03

Even if you understand the principles, the handful of problems in the average textbook are too few to really drill you on the procedures. It's a little like the difference between understanding some music theory and being able to play an instrument. Practice, for those of us who are not math prodigies, is essential. If you are willing to put in the hours and hours, this hugh collection of solved problems is well worth the price.

5 out of 5 stars Step by Step.......2004-01-09

I have been out of college for 7 years. I began Grad school last quarter. This book gave me the basic steps to relearn and remember Calculus. It takes you through each kind of problem without skipping steps or assuming you already know what you are doing. A big crutch for understanding single and multivariable calculus. -I passed the placement exam and then used the book to assist in other engineering classes.
Advanced Calculus Problem Solver (REA) (Problem Solvers)
Average customer rating: 4 out of 5 stars
  • Excellent Service
  • Bad typesetting
  • Another fine resource from the folks at REA!
  • Upset College Student
  • salvation for Calculus I
Advanced Calculus Problem Solver (REA) (Problem Solvers)
The Staff of REA
Manufacturer: Research & Education Association
ProductGroup: Book
Binding: Paperback

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CalculusCalculus | Pure Mathematics | Mathematics | Science | Subjects | Books
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ASIN: 0878915338

Book Description

Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.

Here in this highly useful reference is the finest overview of advanced calculus currently available, with hundreds of calculus problems that cover everything from point set theory and vector spaces to theories of differentiation and integrals. Each problem is clearly solved with step-by-step detailed solutions.

DETAILS
- The PROBLEM SOLVERS are unique - the ultimate in study guides.
- They are ideal for helping students cope with the toughest subjects.
- They greatly simplify study and learning tasks.
- They enable students to come to grips with difficult problems by showing them the way, step-by-step, toward solving problems. As a result, they save hours of frustration and time spent on groping for answers and understanding.
- They cover material ranging from the elementary to the advanced in each subject.
- They work exceptionally well with any text in its field.
- PROBLEM SOLVERS are available in 41 subjects.
- Each PROBLEM SOLVER is prepared by supremely knowledgeable experts.
- Most are over 1000 pages.
- PROBLEM SOLVERS are not meant to be read cover to cover. They offer whatever may be needed at a given time. An excellent index helps to locate specific problems rapidly.
- Educators consider the PROBLEM SOLVERS the most effective and valuable study aids; students describe them as "fantastic" - the best books on the market.

TABLE OF CONTENTS
Introduction
Chapter 1: Point Set Theory
Sets and Sequences
Closed and Open Sets and Norms
Metric Spaces
Chapter 2: Vector Spaces
Definitions
Properties
Invertibility
Diagonalization
Orthogonality
Chapter 3: Continuity
Showing that a Function is Continuous
Discontinuous Functions
Uniform Continuity and Related Topics
Paradoxes of Continuity
Chapter 4: Elements of Partial Differentiation
Partial Derivatives
Differentials and the Jacobian
The Chain Rule
Gradients and Tangent Planes
Directional Derivatives
Potential Functions
Chapter 5: Theorems of Differentiation
Mean Value Theorems
Taylor's Theorem
Implicit Function Theorem
Chapter 6: Maxima and Minima
Relative Maximum and Relative Minimum
Extremes Subject to a Constraint
Extremes in a Region
Method of Lagrange Multipliers
Functions of Three Variables
Extreme Value in Rn
Chapter 7: Theory of Integration
Riemann Integrals
Stieltjes Integrals
Chapter 8: Line Integrals
Method of Parametrization
Method of Finding Potential Function (Exact Differential)
Independence of Path
Green's Theorem
Chapter 9: Surface Integrals
Change of Variables Formula
Area
Integral Function over a Surface
Integral Vector Field over a Surface
Invergence Theorem
Stoke's Theorem
Differential Form
Chapter 10: Improper Integrals
Improper Integrals of the 1st, 2nd, and 3rd Kind
Absolute and Uniform Convergence
Evaluation of Improper Integrals
Gamma and Beta Functions
Chapter 11: Infinite Sequences
Convergence of Sequences
Limit Superior and Limit Inferior
Sequence of Functions
Chapter 12: Infinite Series
Tests for Convergence and Divergence
Series of Functions
Operations on Series
Differentiation and Integration of Series
Estimates of Error and Sums
Cesaro Summability
Infinite Products
Chapter 13: Power Series
Interval of Convergence
Operations on Power Series
Chapter 14: Fourier Series
Definitions and Examples
Convergence Questions
Further Representations
Applications
Chapter 15: Complex Variables
Complex Numbers
Complex Functions and Differentiation
Series
Integration
Chapter 16: Laplace Transforms
Definitions and Simple Examples
Basic Properties of Laplace Transforms
Step Functions and Periodic Functions
The Inversion Problem
Applications
Chapter 17: Fourier Transforms
Definition of Fourier Transforms
Properties of Fourier Transforms
Applications of Fourier Transforms
Chapter 18: Differential Geometry
Curves
Surfaces
Chapter 19: Miscellaneous Problems and Applications
Miscellaneous Applications
Elliptic Integrals
Physical Applications
Index

WHAT THIS BOOK IS FOR

Students have generally found calculus a difficult subject to understand and learn. Despite the publication of hundreds of textbooks in this field, each one intended to provide an improvement over previous textbooks, students of advanced calculus continue to remain perplexed as a result of numerous subject areas that must be remembered and correlated when solving problems. Various interpretations of advanced calculus terms also contribute to the difficulties of mastering the subject.

In a study of calculus, REA found the following basic reasons underlying the inherent difficulties of advanced calculus:

No systematic rules of analysis were ever developed to follow in a step-by-step manner to solve typically encountered problems. This results from numerous different conditions and principles involved in a problem that leads to many possible different solution methods. To prescribe a set of rules for each of the possible variations would involve an enormous number of additional steps, making this task more burdensome than solving the problem directly due to the expectation of much trial and error.

Current textbooks normally explain a given principle in a few pages written by a mathematician who has insight into the subject matter not shared by others. These explanations are often written in an abstract manner that causes confusion as to the principle's use and application. Explanations then are often not sufficiently detailed or extensive enough to make the reader aware of the wide range of applications and different aspects of the principle being studied. The numerous possible variations of principles and their applications are usually not discussed, and it is left to the reader to discover this while doing exercises. Accordingly, the average student is expected to rediscover that which has long been established and practiced, but not always published or adequately explained.

The examples typically following the explanation of a topic are too few in number and too simple to enable the student to obtain a thorough grasp of the involved principles. The explanations do not provide sufficient basis to solve problems that may be assigned for homework or given on examinations.

Poorly solved examples such as these can be presented in abbreviated form which leaves out much explanatory material between steps, and as a result requires the reader to figure out the missing information. This leaves the reader with an impression that the problems and even the subject are hard to learn - completely the opposite of what an example is supposed to do.

Poor examples are often worded in a confusing or obscure way. They might not state the nature of the problem or they present a solution, which appears to have no direct relation to the problem. These problems usually offer an overly general discussion - never revealing how or what is to be solved.

Many examples do not include accompanying diagrams or graphs, denying the reader the exposure necessary for drawing good diagrams and graphs. Such practice only strengthens understanding by simplifying and organizing calculus processes.

Students can learn the subject only by doing the exercises themselves and reviewing them in class, obtaining experience in applying the principles with their different ramifications.

In doing the exercises by themselves, students find that they are required to devote considerable more time to advanced calculus than to other subjects, because they are uncertain with regard to the selection and application of the theorems and principles involved. It is also often necessary for students to discover those "tricks" not revealed in their texts (or review books) that make it possible to solve problems easily. Students must usually resort to methods of trial and error to discover these "tricks," therefore finding out that they may sometimes spend several hours to solve a single problem.

When reviewing the exercises in classrooms, instructors usually request students to take turns in writing solutions on the boards and explaining them to the class. Students often find it difficult to explain in a manner that holds the interest of the class, and enables the remaining students to follow the material written on the boards. The remaining students in the class are thus too occupied with copying the material off the boards to follow the professor's explanations.

This book is intended to aid students in advanced calculus overcome the difficulties described by supplying detailed illustrations of the solution methods that are usually not apparent to students. Solution methods are illustrated by problems that have been selected from those most often assigned for class work and given on examinations. The problems are arranged in order of complexity to enable students to learn and understand a particular topic by reviewing the problems in sequence. The problems are illustrated with detailed, step-by-step explanations, to save the students large amounts of time that is often needed to fill in the gaps that are usually found between steps of illustrations in textbooks or review/outline books.

The staff of REA considers advanced calculus a subject that is best learn...

Customer Reviews:

5 out of 5 stars Excellent Service.......2007-03-22

The book was received in good condition and on time. Very satisfied with the service.

4 out of 5 stars Bad typesetting.......2004-06-05

This book contains a wealth of useful information. My only complaint is that REA hasn't re-set the book in a decent type face. Instead, they continue to publish these books that look like they were typeset on a manual typewriter. Very hard on the eyes...

5 out of 5 stars Another fine resource from the folks at REA!.......2002-07-23

If you are taking a course covering the theory of Advanced Calculus or perhaps in introductory Real Analysis, this book is a great buy. There is alot of material covered, but make sure that you compare the syllabus of your couse and the contents of this book before buying. This book contains fully (and I mean fully) worked out solutions to very difficult problems that you may encounter in such courses. My only complaint is that there should have been included more of the proof-type questions for infinte suequences and series. However, if you taking merely an introductory calculus course, you would be better off buying REA's "Calulus Problem Solver", which is another great book.

2 out of 5 stars Upset College Student.......2001-02-26

All math students get stuck on a problem, while that maybe irritating enough, looking for the answer in this book doesn't make your situation any better. So if you're anyway like me, you don't want to spend 1 hour racking your brain on one math problem when you have billions of other things to do and another millenium looking for a problem that remotely resembles yours in this waste of paper. I'm not trying to be discouraging to anyone looking for help, but I suggest that you just continue your search. I bought this book and I am now sending it back. So be your own judge. If you don't believe me, then my second suggestion would be to find the book in a book store and check it out yourself before buying it. Just being honest.

4 out of 5 stars salvation for Calculus I.......2000-03-29

This book is great help for the university student. I have two books the problem solver REA and I sure that the exercises in this book will my salvation for Calculus I and I recommend shipp this book
Pre-Calculus Problem Solver (REA) (Problem Solvers)
Average customer rating: 4 out of 5 stars
  • Examples
  • disappointment
  • In a word: Excellent
  • If you're mathematically competent but lazy, get this book!
  • This book adheres to the highest editorial standards
Pre-Calculus Problem Solver (REA) (Problem Solvers)
The Staff of REA , and Dennis C. Smolarski
Manufacturer: Research & Education Association
ProductGroup: Book
Binding: Paperback

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ASIN: 0878915567

Book Description

Prepares students for calculus courses. Thorough coverage of first-year college math, including algebraic, trigonometric, exponential, and logarithmic functions and their graphs. Includes solutions of linear and quadratic equations, analytic geometry, elementary statistics, differentiation and integration, determinants, matrices, and systems of equations. Problem-solving strategies are included at the beginning of every chapter for each topic covered.

Customer Reviews:

5 out of 5 stars Examples.......2006-03-09

This book provides numerous examples that aid in understanding the complex world of precalculus.

2 out of 5 stars disappointment.......2005-10-13

sure it is somewhat helpful but in limited terms.I have come across solved algebra and precalculus books sold for Turkish college students. I recommend these excellent books written by Nesime Aydýn, Kerim Yeniay, Hasan Özer, Mevlut Gündoðdu, Emrullah Eraslan to math-lovers all around the world because the math language is universal and the books are written an easy fashion to follow the steps in any way.

5 out of 5 stars In a word: Excellent.......2004-03-08

This is the book to go to to remember how to do all those mathematical things, before calculus, we used to know but either forgot, took for granted, or shortcut and circumvented. Perfect example: solving inequalities involving absolute values -> the method I was using was producing right answers, however it was 'shotcutting' rather than solving the problem properly and robustly. Had a look inside...found an example...instant recollection and on my way again, the right way!

As far as I can tell there are not obvious mistakes (the review further down obviously has a really old copy or is just mistaken) and the coverage is quite comprehensive (though there are no problems for you to solve...as the title says, it is entirely solved problems and LOTS of them!). This isn't a book to teach you everything (though, I think if you worked through every example in whatever section, you would be a significantly better mathematician then when you started). As Einstein said, learng by example isn't just a way to learn...it's the only way to learn! It is a fine supplemental text and reference. The solutions are very clear, explicit and step by step. There are no logic jumps that can leave you wondering how the hell did they get from here to there? It is very systematic (even with explanations of what operation they are doing along the way- like a good teacher explaning how to do something without jumping steps).

Personally I regard the $18 as money well spent. It is an enormous book for the price, rich in content and extremely helpful. And given the price, what more could you want? It's a very useful addition to your library, if only as a reference work. There are basic attack strategies at the beginning of each chapter and masses of problems! Sure, the theory it covers is contained within the problems, not explicitly...hence you may need your course book along with this (or maybe as I said earlier: just try to learn from this book, which might be kinda weird and fun).

In all: well worth 5 stars! YOu can't expect a magical panacea for all your mathematical woes to be found within...but it tries! And it does deliver a great deal...

Happy Mathematics!

3 out of 5 stars If you're mathematically competent but lazy, get this book!.......2004-02-13

This book is not a tutorial or self-teaching guide, it's more of a reference book. If you are not familiar with intermediate algebra and trigonometry this book will not be useful to you. But if you know the basic concepts of alg/trig you will find this book useful for that one difficult problem that is in every workset of your textbook. So, if you don't want to spend time concentrating on one problem, you can spend time searching for a similar problem in this book that will get you started on the original problem. But if you need the entire problem worked out with explanations this is not the book for you.

5 out of 5 stars This book adheres to the highest editorial standards.......2003-06-26

With all due respect to the reviewer who found two errors in this book, these mistakes were corrected over 16 years ago. Our assumption is that he has a very outdated edition. The reviews of this book have been excellent and we are confident that it will help any student in pre-calculus.
Complex Variables Problem Solver (Problem Solvers)
Average customer rating: 5 out of 5 stars
  • You need this book for complex variables
  • Another Excellent Resource!
Complex Variables Problem Solver (Problem Solvers)
Emil G. Milewski
Manufacturer: Research & Education Association
ProductGroup: Book
Binding: Paperback

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ASIN: 0878916040

Book Description

For students in mathematics, engineering, and physics. Includes comprehensive coverage of complex numbers, set theory, mapping, functions, Cauchy-Riemann conditions, power series, Taylor series, Green's theorem, Laurent expansions, singularities, residues, transformations, and numerous scientific applications.

Customer Reviews:

5 out of 5 stars You need this book for complex variables.......2004-06-25

Text books on complex variables DO NOT HAVE ENOUGH WORKED PROBLEMS. This 900+ page softcover does. If you study "Visual Complex Analysis" by Needham (one of my favorites) this will help you do the exercises. The 24 chapters cover everything you would find in a one year course and then some. Each chapter is just one solved problem after another. I found a few misprints but nothing serious. You won't find a better resource and cheap too ! Highly recommended.

5 out of 5 stars Another Excellent Resource!.......2001-11-11

This book is essential for the study of Complex Variables, and it is compatible with other texts on the subject. The sections on how to solve complex contour integrals and Laurent Series are especially important since most texts do not provide enough worked examples to give the student an idea of the underlying patterns involved. The section on the use of Residue theory to solve real valued integrals is also very well done. "Complex Variables Problem Solver" is another fantastic product from the folks at REA.
Calculus of one variable (Problem solvers ; no. 5)
Average customer rating: 4 out of 5 stars
  • A source of robust examples and challenging exercises.
Calculus of one variable (Problem solvers ; no. 5)
Keith Edwin Hirst
Manufacturer: Allen and Unwin
ProductGroup: Book
Binding: Unknown Binding

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ASIN: 0045170045

Customer Reviews:

4 out of 5 stars A source of robust examples and challenging exercises........2007-08-21

Hirst's text does an effective job of introducing the techniques and applications of differential and integral calculus. Hirst does this by providing robust examples that enable the reader to develop the skills necessary to solve the quite complicated problems that he poses in the exercises. Since Hirst provides answers to nearly all of these exercises, the text lends itself to self-study. The text feels somewhat incomplete because it does not develop the underlying theory. It also does not cover sequences and series, which Hirst covers in his text Numbers, Sequences and Series (Modular Mathematics Series). While its scope is somewhat limited, working through the text is worthwhile since it helps you develop sophisticated problem solving skills.

This text is an introduction to college calculus for students who have been exposed to calculus while completing the A level course in pure mathematics. It would be appropriate for American students who have completed an Advanced Placement Calculus course and wish to develop their skills further. The prerequisites covered in the introductory chapter include functions and graphs, domain and range, odd and even functions, composite functions, inverse functions, and piecewise-defined functions. These prerequisites are discussed in the context of polynomial, rational, exponential, logarithmic, trigonometric, and hyperbolic functions and both trigonometric and hyperbolic identities.

The next chapter covers limits of functions, including the definition of limits and one-sided limits, algebraic techniques for finding them, properties of limits, infinite limits, limits at infinity, and the Squeeze Theorem. Since some exposure to differential calculus is assumed, Hirst also introduces L'Hopital's Rule here, although it could be deferred until later without interrupting the flow of the text.

Hirst then devotes several chapters to differentiation, covering the definition, properties of the derivative, the Chain Rule, higher derivatives, implicit differentiation, logarithmic differentiation, parametric differentiation, the differentiation of inverse functions, and Leibniz's Theorem. Once these skills have been introduced, Hirst shows you how to apply them to finding gradients and tangents, maxima and minima, optimization problems, linear motion problems, growth and decay problems, and the Newton-Raphson method of finding the roots of an equation. Related rates are not covered.

Hirst concludes his coverage of differentiation with a chapter on Taylor polynomials. The chapter begins with a discussion of linear approximation, the Mean Value Theorem, and quadratic approximation. He then demonstrates how to find the Taylor polynomial and the error associated with the Taylor polynomial approximation of a function. While I generally found this book to be fairly clear, I had to refer to Tom M. Apostol's text Calculus: Volume I in order to clarify the discussion in this chapter and to learn how to solve some of the problems.

The remainder of the text is devoted to integral calculus. After he introduces the anti-derivative (indefinite integral), Hirst discusses the logarithmic integral, integrals with variable limits, infinite integrals, and improper integrals before devoting chapters to integration by parts, integration by substitution, and integration by partial fractions. These chapters are particularly worthwhile since Hirst goes beyond the standard topics in order to cover reduction formulae, the Gamma function, inverse substitutions, trigonometric substitutions (including half-angle substitutions), hyperbolic substitutions, and partial fractions with repeated linear and quadratic factors. The text concludes with a chapter on applications of integration, including calculations of arc length, surface area of revolution, volume of revolution, density and mass, and center of mass.

This text would make a good companion to a more theoretical text such as Serge Lang's A First Course in Calculus (Undergraduate Texts in Mathematics), Tom M. Apostol's Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra (Second Edition), or Michael Spivak's Calculus.
Calculus of several variables (Problem solvers ; no. 2)
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    Calculus of several variables (Problem solvers ; no. 2)
    Leslie Marder
    Manufacturer: Allen and Unwin
    ProductGroup: Book
    Binding: Paperback

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    ASIN: 0045170010
    Calculus of variations (Problem solvers ; no. 9)
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      Calculus of variations (Problem solvers ; no. 9)
      James W Craggs
      Manufacturer: Allen and Unwin
      ProductGroup: Book
      Binding: Unknown Binding

      Mathematical AnalysisMathematical Analysis | Mathematics | Science | Subjects | Books
      MathematicsMathematics | Professional Science | Professional & Technical | Subjects | Books | Applied | Chaos & Systems | Geometry & Topology | Mathematical Analysis | Mathematical Physics | Number Systems | Pure Mathematics | Transformations | Trigonometry
      ASIN: 0045170096
      Optimal Control of Spatial Systems (Problem Solvers; No. 14)
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        Optimal Control of Spatial Systems (Problem Solvers; No. 14)
        K. C. Tan
        Manufacturer: Allen & Unwin Pty., Limited (Australia)
        ProductGroup: Book
        Binding: Hardcover

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        ASIN: 0045190186
        Problem Solver for Finite Mathematics and Calculus (Prindle, Weber & Schmidt Series in Mathematics)
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          Problem Solver for Finite Mathematics and Calculus (Prindle, Weber & Schmidt Series in Mathematics)
          Kenneth L. Wiggins
          Manufacturer: PWS Pub. Co.
          ProductGroup: Book
          Binding: Paperback

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          GeneralGeneral | Mathematics | Science | Subjects | Books
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          ASIN: 0534924395
          Advanced Calculus Problem Solver A Complete Solution Guide to Any Textbook
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            Advanced Calculus Problem Solver A Complete Solution Guide to Any Textbook
            M. Fogiel
            Manufacturer: NY
            ProductGroup: Book
            Binding: Paperback
            ASIN: B000N7IMEQ

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