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Real and Complex Analysis
Real and Complex AnalysisWalter Rudin1. Abstract Integration
2. Positive Borel Measures
3. L p -Spaces
4. Elementary Hilbert Space Theory
5. Examples of Banach Space Techniques
6. Complex Measures
7. Integration on Product Spaces
8. Differentiation
9. Fourier Transforms
10. Elementary Properties of Holomorphic Functions
11. Harmonic Functions
12. The Maximum Modulus Principle
13. Approximation by Rational Functions
14. Conformal Mapping
15. Zeros of Holomorphic Functions
16. Analytic Continuatio...
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Complex Analysis
Complex AnalysisLars V. AhlforsI. Complex Numbers
II. Complex Functions
III. Analytic Functions as Mappings
IV. Complex Integration
V. Series and Product Developments
VI. Conformal Mapping. Dirichlet's Problem
VII. Elliptic Functions
VIII. Global Analytic Functions
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Mathematical Analysis - A Modern Approach to Advanced Calculus
Mathematical Analysis - A Modern Approach to Advanced CalculusT.M. Apostol1. The Real and Complex Number Systems
2. Some Basic Notions of Set Theory
3. Elements of Point Set Topology
4. The Limit Concept and Continuity
5. Differentiation of Functions of One Real Variable
6. Differentiation of Functions of Several Variables
7. Applications of Partial Differentiation
8. Functions of Bounded Variation, Rectifiable Curves and Connected Sets
9. Theory of Riemann-Stieltjes Integration
10. Multiple Int...
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Ordinary Differential Equations
Ordinary Differential EquationsE.L. IncePart I. Differential Equations in the Real Domain
I. Introductory
II. Elementary methods of integration
III. The existence and nature of solutions of ordinary differential equations
IV. Continuous transformation-groups
V. The general theory of linear differential equations
VI. Linear equations with constant coefficients
VII. The solution of linear differential equations in an infinite form
VIII. The solution of linear differential equations by definite int...
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A Survey of Modern Algebra
A Survey of Modern AlgebraGarrett Birkhoff, Saunders Mac LaneI. The Integers
II. Rational Numbers and Fields
III. Polynomials
IV. Real Numbers
V. Complex Numbers
VI. Group Theory
VII. Vectors and Vector Spaces
VIII. The Algebra of Matrices
IX. Linear Groups
X. Determinants and Canonical Forms
XI. Algebra of Classes
XII. Transfinite Arithmetic
XIII. Rings and Ideals
XIV. Algebraic Number Fields
XV. Galois Theory
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Linear Algebra and Its Applications
Linear Algebra and Its ApplicationsGilbert Strang1. Matrices and Gaussian Elimination
2. Vector Spaces and Linear Equations
3. Orthogonality
4. Determinants
5. Eigenvalues and Eigenvectors
6. Positive Definite Matrices
7. Computations with Matrices
8. Linear Programming and Game Theory
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Geometric Transformations
Geometric TransformationsI.M. YaglomI. Displacements
1. Translations
2. Half Turn and Rotation
II. Symmetry
1. Refection and Glide Reflection
2. Directly Congruent and Oppositely Congruent Figures. Classification of Isometries of the Plane
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The cos πλ Theorem
The cos πλ TheoremMatts R. Essén1. The Hellsten-Kjellberg-Norstad inequality
2. The cos πλ -theorem
3. A generalization of the Ahlfors-Heins theorem
4. The Paley conjecture
5. A cos πλ -problem an da differential inequality
6. A counterexample
7. Proof of theorem 5.2
8. Two consequences of a theorem of A. Baernstein
9. On two theorems of A. Baernstein
10. References
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Diophantine Approximations and Value Distribution Theory
Diophantine Approximations and Value Distribution TheoryPaul Vojta1. Heights and Integral Points
2. Diophantine Approximations
3. A Correspondence with Nevanlinna Theory
4. Consequences of the Main Conjecture
5. The Ramification Term
6. Approximation to Hyperplanes
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Integral Operators in Potential Theory
Integral Operators in Potential TheoryJosef Král1. Weak normal derivatives of potentials
2. Double layer potentials
3. Contractivity of Neumann's operator
4. Fredholm radius of the Neumann operator
5. Boundary value problems
6. Comments and references
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