The Calculus Problem Solver: A Complete Solution Guide to Any Textbook (Paperback)

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Product Summary

Format: Paperback

ISBN: 9780878915057

Publisher: Research and Education Association

Publish Date: 12/1/1984

Buy.com Sku: 30217595

Item#: RK7Q4W

Buy.com Sales Rank: 106388

Dimensions (in Inches) 9.75H x 6.75L x 2T

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 locatespecific 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 DifferentialEquations
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 ofapplications 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 inclass, obtaining experience in applying the principles with their different ramifications.
In doing the exercises by themselves, students find that

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