Introduction to Calculus and Classical Analysis - Softcover

Hijab, Omar

Softcover

ISBN 10: 1441994890 ISBN 13: 9781441994899

Publisher: Springer, 2011

Synopsis

1 The Set of Real Numbers.- 1.1 Sets and Mappings.- 1.2 The Set R.- 1.3 The Subset N and the Principle of Induction.- 1.4 The Completeness Property.- 1.5 Sequences and Limits.- 1.6 Nonnegative Series and Decimal Expansions.- 1.7 Signed Series and Cauchy Sequences.- 2 Continuity.- 2.1 Compactness.- 2.2 Continuous Limits.- 2.3 Continuous Functions.- 3 Differentiation.- 3.1 Derivatives.- 3.2 Mapping Properties.- 3.3 Graphing Techniques.- 3.4 Power Series.- 3.5 Trigonometry.- 3.6 Primitives.- 4 Integration.- 4.1 The Cantor Set.- 4.2 Area.- 4.3 The Integral.- 4.4 The Fundamental Theorem of Calculus.- 4.5 The Method of Exhaustion.- 5 Applications.- 5.1 Euler's Gamma Function.- 5.2 The Number π.- 5.3 Gauss' Arithmetic-Geometric Mean (AGM).- 5.4 The Gaussian Integral.- 5.5 Stirling's Approximation of n!.- 5.6 Infinite Products.- 5.7 Jacobi's Theta Functions.- 5.8 Riemann's Zeta Function.- 5.9 The Euler-Maclaurin Formula.- A Solutions.- A.1 Solutions to chapter 1 .- A.2 Solutions to chapter 2.- A.3 Solutions to chapter 3.- A.4 Solutions to chapter 4.- A.5 Solutions to chapter 5.- References.- Index  

Edition details

• Publisher: Springer
• Publication date: 2011
• ISBN 10: 1441994890
• ISBN 13: 9781441994899
• Binding: Paperback
• Language: English