17 0 obj This book consists of all essential sections that students should know in the class, Analysis or Introduction of Real Analysis. << /S /GoTo /D (section.8.1) >> endobj QA300.T6672003 515-dc21 2002032369 Free Edition1.04, April 2010 This book was publishedpreviouslybyPearson (Functional Equations) In every chapter, it has used consistent letters and terminologies. xڍSM��0��+|t�M6���� XBB(�8x�����v���3������3����=�,ʒlI�>�t�8�^�~&�mw��IUw�6��E�"��`�t�?�7)t�3��#��ǝ0.�L:�c�p*��Z�pM� �Ozt����!�{�����5=�ݜ�9�T�Һ,��g����� �)xK�Ħ�i�#ׂ���o ���.�W��B��{�O}@=���$�m���8Zw?���i}h9 3ƒG!�[�ub�D���a$�[ѰTyRa�կIh����&�9��+V4M�&��2"(k��]KN�K�"�98�UK�%f�{ڬ��w>�A8 ^����.A@��R��"`�0.^r#��j;&=��-���$奂�����M���.���l�|��*� F�������o����>_t� �%w�cz�5n�bXVN�:c�Zz�� ^ ��T��. endobj << /S /GoTo /D (section.9.1) >> endobj Introduction to real analysis / William F. Trench p. cm. �M�Yo�R>����l��v:>�R�������[d���;G�?�w� ә�"xo]|�rF5�?��FξA�pVc�xQk�l5�+��ʣ����]A:X��џ\N� �J�n���!L*Z>�=���shKD��iLmI�G��bj[�[����C\̦@F���LHH 0I�;h�䷄�x�f�c�;��g�t�$ �CN,���S�s(��q��Ϻ۷��"�� �o�z 19 0 obj >> This book consists of all essential sections that students should know in the class, Analysis or Introduction of Real Analysis. 277.8 500] 69 0 obj This is a short introduction to the fundamentals of real analysis. (Solved Problems) FINAL EXAMINATION SOLUTIONS, MAS311 REAL ANALYSIS I QUESTION 1. ���w��-����;X�QU+�����hO> ��nd >> endobj 112 0 obj /FontDescriptor 26 0 R %���� 575 1041.7 1169.4 894.4 319.4 575] 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 272 761.6 462.4 (Functions) This textbook is for pure mathematics. >> endobj We get the relation p2 = 3q2 from which we infer that p2 is divisible by 3. read more. >> stream /FontDescriptor 11 0 R NORMED AND INNER PRODUCT SPACES Solution. endobj endobj (Solved Problems) The real numbers. endobj 129 0 obj Cowles Distinguished Professor Emeritus Departmentof Mathematics Trinity University San Antonio, Texas, USA wtrench@trinity.edu This book has been judged to (Supplementary Problems) (Supplementary Problems) (Solved Problems) 32 0 obj << /S /GoTo /D (section.6.1) >> All text is from the mathematics terminology that makes the writing lucid and readable. At least, I could not find them. /Type/Font %PDF-1.4 k��'a��Ez���ܪ�m�Z��^��dW�Ug���f����&~��f6zok�;u�>�*��˹K��H�S ��H�c9)���H�)I������o�l��1��1���O�_d��� 2 Real Analysis Use the alternative definition for continuity for sequences. 157 0 obj << 5 0 obj /Widths[249.6 458.6 772.1 458.6 772.1 719.8 249.6 354.1 354.1 458.6 719.8 249.6 301.9 endobj Please submit your solution to one of th email addresses below. (���n�b����]qJ��8֕�� �;���4J�|t���*�1b�6���т�v�q0���T)��c����@��o����"�xq��:�0�V�3 This free editionis made available in the hope that it will be useful as a textbook or refer-ence. << /S /GoTo /D (section.10.2) >> The set of all sequences whose elements are the digits 0 and 1 is not countable. endobj This book began in 1984 when the first author wrote a short set of course notes (120 pages) for a real analysis class at the University of Waterloo designed for students who came primarily from applied math and computer science. 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 We begin with the de nition of the real numbers. 5. 9!��8�� #�嘌�٣��A�� Gf@��(t�"4Q�T4H �fE"H�����a�(���� ����f:�j��K� Let f(x) = 1 and g(x) = 2x: Then kfk1 = Z 1 0 1:dx = 1; kgk1 = Z 1 0 j2xjdx = 1; while kf ¡gk1 = Z 1 0 j1¡2xjdx = 1 2; kf +gk1 = Z 1 0 j1+2xjdx = 2: Thus, kf ¡gk2 1 +kf +gk 2 1 = 17 4 6= 2( kfk1 +kgk2 1) = 4: ¥ Problem 3. 124 0 obj ��%�ݍ#�6�U�>���� endobj So, I believe it has no inclusive issues about races, ethnicities, and backgrounds at all. << /S /GoTo /D (section.3.2) >> 761.6 272 489.6] We show that the norm k:k1 does not satisfy the parallelogram law. The axiomatic approach. endobj /F3 15 0 R J�_�/ҾkKh�C�[�q)h�2�x�F���m�2�Π�9��6}��jg����2��:N�;4: |{3콺n��L�˂��QM@#��D����v���6� ���M������G��>+䃚� �7��C(��H_. 16 0 obj Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses, has had some exposure to the ideas of mathematical proof (including induction), and has an acquaintance with such basic ideas as equivalence relations and the elementary algebraic properties of the integers.