Problems and Theorems in Analysis

[1809/99%]

G. Pólya, G. Szegő

Part 1Infinite Series and Infinite Sequences[237/100%]

Chapter 1.1Operations with Power Series[85/99%]

Chapter 1.2Linear Transformations of Series. A Theorem of Cesàro[34/100%]

Chapter 1.3The Structure of Real Sequences and Series[44/100%]

Chapter 1.4Miscellaneous Problems[74/100%]

Part 2Integration[248/100%]

Chapter 2.1The Integral as the Limit of a Sum of Rectangles[70/100%]

Chapter 2.2Inequalities[42/98%]

Chapter 2.3Some Properties of Real Functions[55/100%]

Chapter 2.4Various Types of Equidistribution[48/100%]

Chapter 2.5Functions of Large Numbers[33/100%]

Part 3Functions of One Complex Variable[347/100%]

Chapter 3.1Complex Numbers and Number Sequences[54/100%]

Chapter 3.2Mappings and Vector Fields[53/100%]

Chapter 3.3Some Geometrical Aspects of Complex Variables[42/100%]

Chapter 3.4Cauchy's Theorem. The Argument Principle[64/100%]

Chapter 3.5Sequences of Analytic Functions[59/98%]

Chapter 3.6The Maximum Principle[75/100%]

Part 4Functions of One Complex Variable: Special Part[217/97%]

Chapter 4.1Maximum Term and Central Index, Maximum Modulus and Number of Zeros[77/99%]

Chapter 4.2Schlicht Mappings[88/100%]

Chapter 4.3Miscellaneous Problems[52/88%]

Part 5The Location of Zeros[212/100%]

Chapter 5.1Rolle's Theorem and Descartes' Rule of Signs[107/100%]

Chapter 5.2The Geometry of the Complex Plane and the Zeros of Polynomials[56/100%]

Chapter 5.3Miscellaneous Problems[49/100%]

Part 6Polynomials and Trigonometric Polynomials[113/100%]

Section 6.1Tchebychev Polynomials[7/100%]

Section 6.2General Problems on Trigonometric Polynomials[8/100%]

Section 6.3Some Special Trigonometric Polynomials[13/100%]

Section 6.4Some Problems on Fourier Series[10/100%]

Section 6.5Real Non-negative Trigonometric Polynomials[5/100%]

Section 6.6Real Non-negative Polynomials[6/100%]

Section 6.7Maximum-Minimum Problems on Trigonometric Polynomials[12/100%]

Section 6.8Maximum-Minimum Problems on Polynomials[5/100%]

Section 6.9The Lagrange Interpolation Formula[10/100%]

Section 6.10The Theorems of S. Bernstein and A. Markov[7/100%]

Section 6.11Legendre Polynomials and Related Topics[19/100%]

Section 6.12Further Maximum-Minimum Problems on Polynomials[11/100%]

Part 7Determinants and Quadratic Forms[84/100%]

Section 7.1Evaluation of Determinants. Solution of Linear Equations[20/100%]

Section 7.2Power Series Expansion of Rational Functions[18/100%]

Section 7.3Generation of Positive Quadratic Forms[11/100%]

Section 7.4Miscellaneous Problems[17/100%]

Section 7.5Determinants of Systems of Functions[18/100%]

Part 8Number Theory[317/100%]

Chapter 8.1Arithmetical Functions[111/100%]

Chapter 8.2Polynomials with Integral Coefficients and Integral-Valued Functions[46/100%]

Chapter 8.3Arithmetical Aspects of Power Series[65/98%]

Chapter 8.4Some Problems on Algebraic Integers[54/100%]

Chapter 8.5Miscellaneous Problems[41/100%]

Part 9Geometric Problems[34/94%]

Section 9.1Some Geometric Problems[34/94%]