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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.
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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: 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: 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
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 additi...