Advanced Calculus Problem Solver A Complete Solution Guide to Any Textbook

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 CONTENTSIntroductionChapter 1: Point Set TheorySets and SequencesClosed and Open Sets and NormsMetric SpacesChapter 2: Vector SpacesDefinitionsPropertiesInvertibilityDiagonalizationOrthogonalityChapter 3: ContinuityShowing that a Function is ContinuousDiscontinuous FunctionsUniform Continuity and Related TopicsParadoxes of ContinuityChapter 4: Elements of Partial DifferentiationPartial DerivativesDifferentials and the JacobianThe Chain RuleGradients and Tangent PlanesDirectional DerivativesPotential FunctionsChapter 5: Theorems of DifferentiationMean Value TheoremsTaylor''s TheoremImplicit Function TheoremChapter 6: Maxima and MinimaRelative Maximum and Relative MinimumExtremes Subject to a ConstraintExtremes in a RegionMethod of Lagrange MultipliersFunctions of Three VariablesExtreme Value in RnChapter 7: Theory of IntegrationRiemann IntegralsStieltjes IntegralsChapter 8: Line IntegralsMethod of ParametrizationMethod of Finding Potential Function (Exact Differential)Independence of PathGreen''s TheoremChapter 9: Surface IntegralsChange of Variables FormulaAreaIntegral Function over a SurfaceIntegral Vector Field over a SurfaceInvergence TheoremStoke''s TheoremDifferential FormChapter 10: Improper IntegralsImproper Integrals of the 1st, 2nd, and 3rd KindAbsolute and Uniform ConvergenceEvaluation of Improper IntegralsGamma and Beta FunctionsChapter 11: Infinite SequencesConvergence of SequencesLimit Superior and Limit InferiorSequence of FunctionsChapter 12: Infinite SeriesTests for Convergence and DivergenceSeries of FunctionsOperations on SeriesDifferentiation and Integration of SeriesEstimates of Error and SumsCesaro SummabilityInfinite ProductsChapter 13: Power SeriesInterval of ConvergenceOperations on Power SeriesChapter 14: Fourier SeriesDefinitions and ExamplesConvergence QuestionsFurther RepresentationsApplicationsChapter 15: Complex VariablesComplex NumbersComplex Functions and DifferentiationSeriesIntegrationChapter 16: Laplace TransformsDefinitions and Simple ExamplesBasic Properties of Laplace TransformsStep Functions and Periodic FunctionsThe Inversion ProblemApplicationsChapter 17: FouriResearch and Education Association Staff is the author of 'Advanced Calculus Problem Solver A Complete Solution Guide to Any Textbook' with ISBN 9780878915330 and ISBN 0878915338.