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Advanced Calculus (3rd Edition) by Angus E. Taylor, W. Robert Mann

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Advanced Calculus (3rd Edition) by Angus E. Taylor , University of California and W. Robert Mann , University of North Carolina. Outlines theory and techniques of calculus, emphasizing strong understanding of concepts, and the basic principles of analysis. Reviews elementary and intermediate calculus and features discussions of elementary-point set theory, and properties of continuous functions.

Advanced Calculus (3rd Edition) by Angus E. Taylor and W. Robert Mann cover the following topics.

  • 1. Fundamentals of Elementry Calculus
    2. The Real Number System
    3. Continuous Functions
    4. Extensions of the low of the mean
    5. Functions of Several Variables
    6. The element of Partial Differentiation
    7. General Theorems of Partial Differentiation
    8. Implicit Function Theorems
    9. The Inverse Function Theorem with Applications
    10. Vectors and Vector Fields
    11. Linear Tranformations
    12. Differential Calculus of Functions from the Rn to Rm
    13. Double and Triple Integrals
    14. Curves and Surfaces
    15. Line and Surface Integrals
    16. Point set Theory
    17. Fundamental Theorems of Continuous Functions
    18. The Theory of Integration
    19. Infinite Series
    10. Uniform Coverage
    11. Power Series
    12. Improper Integrals

  • Answer to selected Exercises

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