The Resource A Concise Approach to Mathematical Analysis, by Mangatiana A. Robdera, (electronic resource)

A Concise Approach to Mathematical Analysis, by Mangatiana A. Robdera, (electronic resource)

Label
A Concise Approach to Mathematical Analysis
Title
A Concise Approach to Mathematical Analysis
Statement of responsibility
by Mangatiana A. Robdera
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
A Concise Approach to Mathematical Analysis introduces the undergraduate student to the more abstract concepts of advanced calculus. The main aim of the book is to smooth the transition from the problem-solving approach of standard calculus to the more rigorous approach of proof-writing and a deeper understanding of mathematical analysis. The first half of the textbook deals with the basic foundation of analysis on the real line; the second half introduces more abstract notions in mathematical analysis. Each topic begins with a brief introduction followed by detailed examples. A selection of exercises, ranging from the routine to the more challenging, then gives students the opportunity to practise writing proofs. The book is designed to be accessible to students with appropriate backgrounds from standard calculus courses but with limited or no previous experience in rigorous proofs. It is written primarily for advanced students of mathematics - in the 3rd or 4th year of their degree - who wish to specialise in pure and applied mathematics, but it will also prove useful to students of physics, engineering and computer science who also use advanced mathematical techniques
http://library.link/vocab/creatorName
Robdera, Mangatiana A
Dewey number
515
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
Bg12w5oBZ9M
Image bit depth
0
Language note
English
LC call number
QA299.6-433
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/subjectName
  • Global analysis (Mathematics)
  • Mathematics
  • Functional equations
  • Fourier analysis
  • Sequences (Mathematics)
  • Analysis
  • Real Functions
  • Difference and Functional Equations
  • Fourier Analysis
  • Sequences, Series, Summability
Label
A Concise Approach to Mathematical Analysis, by Mangatiana A. Robdera, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
Numbers and Functions -- Real Numbers -- Subsets of ? -- Variables and Functions -- Sequences -- Definition of a Sequence -- Convergence and Limits -- Subsequences -- Upper and Lower Limits -- Cauchy Criterion -- 3. Series -- Infinite Series -- Conditional Convergence -- Comparison Tests -- Root and Ratio Tests -- Further Tests -- 4. Limits and Continuity -- Limits of Functions -- Continuity of Functions -- Properties of Continuous Functions -- Uniform Continuity -- Differentiation -- Derivatives -- Mean Value Theorem -- L'Hôspital's Rule -- Inverse Function Theorems -- Taylor's Theorem -- Elements of Integration -- Step Functions -- Riemann Integral -- Functions of Bounded Variation -- Riemann-Stieltjes Integral -- Sequences and Series of Functions -- Sequences of Functions -- Series of Functions -- Power Series -- Taylor Series -- Local Structure on the Real Line -- Open and Closed Sets in ? -- Neighborhoods and Interior Points -- Closure Point and Closure -- Completeness and Compactness -- Continuous Functions -- Global Continuity -- Functions Continuous on a Compact Set -- Stone—Weierstrass Theorem -- Fixed-point Theorem -- Ascoli-Arzelà Theorem -- to the Lebesgue Integral -- Null Sets -- Lebesgue Integral -- Improper Integral -- Important Inequalities -- Elements of Fourier Analysis -- Fourier Series -- Convergent Trigonometric Series -- Convergence in 2-mean -- Pointwise Convergence -- A. Appendix -- A.1 Theorems and Proofs -- A.2 Set Notations -- A.3 Cantor's Ternary Set -- A.4 Bernstein's Approximation Theorem -- B. Hints for Selected Exercises
Dimensions
unknown
Edition
1st ed. 2003.
Extent
1 online resource (XII, 362 p.)
File format
multiple file formats
Form of item
online
Isbn
9780857293473
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-0-85729-347-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000087505
  • (SSID)ssj0000805645
  • (PQKBManifestationID)11504539
  • (PQKBTitleCode)TC0000805645
  • (PQKBWorkID)10836652
  • (PQKB)10180980
  • (DE-He213)978-0-85729-347-3
  • (MiAaPQ)EBC3072160
  • (EXLCZ)993400000000087505
Label
A Concise Approach to Mathematical Analysis, by Mangatiana A. Robdera, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
Numbers and Functions -- Real Numbers -- Subsets of ? -- Variables and Functions -- Sequences -- Definition of a Sequence -- Convergence and Limits -- Subsequences -- Upper and Lower Limits -- Cauchy Criterion -- 3. Series -- Infinite Series -- Conditional Convergence -- Comparison Tests -- Root and Ratio Tests -- Further Tests -- 4. Limits and Continuity -- Limits of Functions -- Continuity of Functions -- Properties of Continuous Functions -- Uniform Continuity -- Differentiation -- Derivatives -- Mean Value Theorem -- L'Hôspital's Rule -- Inverse Function Theorems -- Taylor's Theorem -- Elements of Integration -- Step Functions -- Riemann Integral -- Functions of Bounded Variation -- Riemann-Stieltjes Integral -- Sequences and Series of Functions -- Sequences of Functions -- Series of Functions -- Power Series -- Taylor Series -- Local Structure on the Real Line -- Open and Closed Sets in ? -- Neighborhoods and Interior Points -- Closure Point and Closure -- Completeness and Compactness -- Continuous Functions -- Global Continuity -- Functions Continuous on a Compact Set -- Stone—Weierstrass Theorem -- Fixed-point Theorem -- Ascoli-Arzelà Theorem -- to the Lebesgue Integral -- Null Sets -- Lebesgue Integral -- Improper Integral -- Important Inequalities -- Elements of Fourier Analysis -- Fourier Series -- Convergent Trigonometric Series -- Convergence in 2-mean -- Pointwise Convergence -- A. Appendix -- A.1 Theorems and Proofs -- A.2 Set Notations -- A.3 Cantor's Ternary Set -- A.4 Bernstein's Approximation Theorem -- B. Hints for Selected Exercises
Dimensions
unknown
Edition
1st ed. 2003.
Extent
1 online resource (XII, 362 p.)
File format
multiple file formats
Form of item
online
Isbn
9780857293473
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-0-85729-347-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000087505
  • (SSID)ssj0000805645
  • (PQKBManifestationID)11504539
  • (PQKBTitleCode)TC0000805645
  • (PQKBWorkID)10836652
  • (PQKB)10180980
  • (DE-He213)978-0-85729-347-3
  • (MiAaPQ)EBC3072160
  • (EXLCZ)993400000000087505

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