Math 2400 Lecture Notes: Differential Miscellany
نویسنده
چکیده
1. L’Hôpital’s Rule 1 1.1. The Cauchy Mean Value Theorem 1 1.2. L’Hôpital’s Rule 2 2. Newton’s Method 5 2.1. Introducing Newton’s Method 5 2.2. A Babylonian Algorithm 6 2.3. Questioning Newton’s Method 7 2.4. Introducing Infinite Sequences 7 2.5. Contractions and Fixed Points 8 2.6. Convergence of Newton’s Method 10 2.7. Quadratic Convergence of Newton’s Method 11 2.8. An example of nonconvergence of Newton’s Method 11 3. Convex functions 12 3.1. Convex subsets of Euclidean n-space 12 3.2. Goals 13 3.3. Epigraphs 14 3.4. Secant-graph, three-secant and two-secant inequalities 14 3.5. Continuity properties of convex functions 16 3.6. Differentiable convex functions 16 3.7. An extremal property of convex functions 17 3.8. Supporting lines and differentiability 17 3.9. Jensen’s Inequality 19 3.10. Some applications of Jensen’s Inequality 20 References 21
منابع مشابه
Reading List for Fall 2009 Seminar on Trace Formulas and Independence of `
[1] Deligne, P. Cohomologie étale. Séminaire de Géométrie Algébrique du Bois-Marie SGA 4 12 . Avec la collaboration de J. F. Boutot, A. Grothendieck, L. Illusie et J. L. Verdier. Lecture Notes in Mathematics, Vol. 569. Springer-Verlag, Berlin-New York, 1977. iv+312pp. [2] Deligne, P. La conjecture de Weil. II Inst. Hautes Études Sci. Publ. Math. No. 52 (1980), 137–252. [3] Freitag, E. and Kiehl...
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