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Problems and Theorems in Analysis
Part 5
The Location of Zeros
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5.1 · Rolle's Theorem and Descartes' Rule of Signs
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5.2 · The Geometry of the Complex Plane and the Zeros of Polynomials
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5.3 · Miscellaneous Problems
Chapter 5.1
Rolle's Theorem and Descartes' Rule of Signs
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Section 1
Zeros of Functions, Changes of Sign of Sequences
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Section 2
Reversals of Sign of a Function
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Section 3
First Proof of Descartes' Rule of Signs
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Section 4
Applications of Descartes' Rule of Signs
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Section 5
Applications of Rolle's Theorem
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Section 6
Laguerre's Proof of Descartes' Rule of Signs
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Section 7
What is the Basis of Descartes' Rule of Signs?
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Section 8
Generalizations of Rolle's Theorem
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Chapter 5.2
The Geometry of the Complex Plane and the Zeros of Polynomials
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Section 1
Center of Gravity of a System of Points with respect to a Point
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Section 2
Center of Gravity of a Polynomial with respect to a Point. A Theorem of Laguerre
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Section 3
Derivative of a Polynomial with respect to a Point. A Theorem of Grace
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Chapter 5.3
Miscellaneous Problems
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Section 1
Approximation of the Zeros of Transcendental Functions by the Zeros of Rational Functions
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Section 2
Precise Determination of the Number of Zeros by Descartes' Rule of Signs
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Section 3
Additional Problems on the Zeros of Polynomials
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