Math 140a: Foundations of Real Analysis I
نویسنده
چکیده
1. Ordered Sets, Ordered Fields, and Completeness 1 1.1. Lecture 1: January 5, 2016 1 1.2. Lecture 2: January 7, 2016 4 1.3. Lecture 3: January 11, 2016 7 1.4. Lecture 4: January 14, 2014 9 2. Sequences and Limits 13 2.1. Lecture 5: January 19, 2016 13 2.2. Lecture 6: January 21, 2016 15 2.3. Lecture 7: January 26, 2016 18 2.4. Lecture 8: January 28, 2016 21 3. Extensions of R: the Extended Real Numbers R and the Complex Numbers C 25 3.1. Lecture 9: February 2, 2016 25 3.2. Lecture 10: February 4, 2016 28 4. Series 32 4.1. Lecture 11: February 9, 2016 32 4.2. Lecture 12: February 11, 2016 37 4.3. Lecture 13: February 16, 2016 42 5. Metric Spaces 44 5.1. Lecture 14: February 18, 2016 47 5.2. Lecture 15: February 23, 2016 50 5.3. Lecture 16: February 25, 2016 52 5.4. Lecture 17: February 29, 2016 55 6. Limits and Continuity 57 6.1. Lecture 24: March 10, 2014 57
منابع مشابه
Math 140A Homework 2 (Solutions)
where the coefficients are real numbers and bm 6= 0. (i) Define addition and multiplication of two elements of F to be the usual addition and multiplication of functions. Show that with this addition and multiplication, F is a field. (ii) We can define an order on F as follows. A rational function like (1.1) is positive if and only if an and bn have the same sign, i.e., anbm > 0. Now given two ...
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