Advanced Calculus Problem Solver

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
Ch