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5. ±³Àç ¹× ºÎ±³Àç

 

   ±³  Àç : Advanced Calculus (W. Fulks)

   ºÎ±³Àç : (1) Elementary classical analysis, J. E. Marsden & M.J.Hoffman-

           (2) The element of real analysis, R. G. Bartle

       

6. ÁÖº°¼ö¾÷°èȹ

 

   Á¦ 1ÁÖ: The Inversion Theorem

     Á¦ 1±³½Ã: Transformations. Inverse Transformations

     Á¦ 2±³½Ã: The Inversion Theorem

     Á¦ 3±³½Ã: Implicit Functions

 

  Á¦ 2ÁÖ : The Inversion Theorem

     Á¦ 1±³½Ã: Curvilinear Coordinates

     Á¦ 2±³½Ã: Extreme Values

     Á¦ 3±³½Ã: Extreme Values Under Constraints

 

  Á¦ 3ÁÖ : Multiple Integrals

     Á¦ 1±³½Ã: Integrals Over Rectangles

     Á¦ 2±³½Ã: Properties of the Integral   

     Á¦ 3±³½Ã: Classes of Integrable   

  

  Á¦4ÁÖ : Multiple Integrals

     Á¦ 1±³½Ã: Iterated Integrals

     Á¦ 2±³½Ã: Integration Over Regions. Area

     Á¦ 3±³½Ã: Integration Over Regions. Volume

 

  Á¦5ÁÖ: Line and Surface Integrals

     Á¦ 1±³½Ã: Line Integrals. Potentials

     Á¦ 2±³½Ã: Green's Theorem

     Á¦ 3±³½Ã: Surfaces. Area

 

  Á¦ 6ÁÖ : Line and Surface Integrals

     Á¦ 1±³½Ã: Surface Integrals. The Divergence Theorem

     Á¦ 2±³½Ã: Stokes' Theorem. Orientable Surfaces

     Á¦ 3±³½Ã: Change of Variables in Multiple Integrals

 

  Á¦ 7ÁÖ : Infinite Series  

     Á¦ 1±³½Ã: Convergence, Absolute and Conditional

     Á¦ 2±³½Ã: Series with Nonnegative Terms

     Á¦ 3±³½Ã: Series with Nonnegative Terms. Remainders

 

  Á¦ 8ÁÖ : Áß°£Æò°¡

 

  Á¦ 9ÁÖ : Infinite Series  

     Á¦ 1±³½Ã: Series with Variable Signs

     Á¦ 2±³½Ã: Rearrangements

     Á¦ 3±³½Ã: Improvement of Convergence  

  

  Á¦ 10ÁÖ : Sequnce and Series of Functions. Uniform Convergence

     Á¦ 1±³½Ã: Introduction

     Á¦ 2±³½Ã: Uniform Convergence

     Á¦ 3±³½Ã: Consequnces of Uniform Convergence

 

  Á¦ 11ÁÖ : Sequnce and Series of Functions. Uniform Convergence

     Á¦ 1±³½Ã: Consequnces of Uniform Convergence

     Á¦ 2±³½Ã: Abel's and Dirichlet's Tests

     Á¦ 3±³½Ã: A Theorem of Dini

 

  Á¦ 12ÁÖ : The Taylor Series

     Á¦ 1±³½Ã: Power Series. Interval of Convergence

     Á¦ 2±³½Ã: Properties of Power Series

     Á¦ 3±³½Ã: The Taylor and Maclaurin Series

 

  Á¦ 13ÁÖ : The Taylor Series

     Á¦ 1±³½Ã: The Arithmetic of Power Series

     Á¦ 2±³½Ã: Substitution and Inversion

     Á¦ 3±³½Ã: Real Analytic Functions

  

  Á¦ 14ÁÖ : Improper Integrals

     Á¦ 1±³½Ã: Improper Integrals. Conditional and Absolute Convergence

     Á¦ 2±³½Ã: Improper Integrals with Nonnegative Integrands

     Á¦ 3±³½Ã: The Cauch Principal Value. Alternation Test

 

  Á¦ 15ÁÖ : Improper Integrals

     Á¦ 1±³½Ã: Proper Integrals

     Á¦ 2±³½Ã: Uniform Convergence

     Á¦ 3±³½Ã: Consequences of Uniform Convergence

 

  Á¦ 16ÁÖ :   ±â¸»Æò°¡