Mathematics Department and the Institute for Mathematical Sciences

Mathematics Department and the Institute for Mathematical Sciences

 
 
 
 
 
 
 
  XSXC

Week	Topics	Assignments
January 27-30	The Real Numbers - Part I Integers, rational and irrational numbers : 1.1 Construction of the real numbers : 1.2	Section 1.1: 4,5,8,9,16a  Section 1.2: 4,5,7,13,17  due February 3rd
February 3-6	The Real Numbers - Part II Axioms for the real numbers : 1.3 The Heine-Borel Theorem : 1.4	Section 1.3: 5b, 7 or 8, 16a, 20a  Section 1.4: 2ab, 4, 6, 7, 11, 12a  due February 10th
February 10-13	Limits Functions and limits : 2.1 and 2.2 Limit theory : 2.3	Section 2.1: 4ab, 7a  Section 2.2: 1acegh, 2, 4c, 8,9  Section 2.3: 1, 5a, 6  due February 17th
February 17-20	Continuity Other types of limits : 2.4 Continuity : 2.5	Section 2.4: 9, 11, 12  Section 2.5: 1, 4, 7, 9  due February 24th
February 24-27	Fundamental Theorems IVT and uniform continuity : 2.6 Compactness results : 2.6	Section 2.6: 4abc, 5a, 6a, 7b  Section 2.6: 9, 10ab, 12, 13  due March 2nd
March 2-5	Review and Midterm Exam Review of Chapters 1 and 2 MIDTERM 1 (Thursday March 4th)	Read section 3.1  Section 3.1:  due March 9th
March 9-12	Differentiation The derivative : 3.1 Rules of differentiation : 3.2	Section 3.1: 1a, 3, 5a, 7, 8a, 9  Section 3.2: 6, 8, 11ab, 12ac, 13  due March 16th
March 16-19	The Mean Value Theorem and Applications The Mean Value Theorem : 3.3 Intro. to Integration : 3.4.1	Section 3.3: 2, 3, 4, 5, 7, 9, 10, 11  Section 3.4: 1  due March 23rd
March 23-26	Integration The Riemann integral : 3.4 Properties of the integral : 3.5	Section 3.4: 5, 7, 10, 12  Section 3.5: 1, 2, 7, 11, 14  due March 30th
March 30 - April 2	The Fundamental Theorem of Calculus The Fundamental Theorem : 3.6 Taylors' Theorem : 3.7	Section 3.6: 1, 2, 5, 6, 8b, 10, 11  Section 3.7: 1cde, 3, 6a  due April 13th
April 13-16	Review and Midterm Review of Chapter 3 MIDTERM II (Thursday April 15th)	Read section 4.1  Section 4.1:  due April 20th
April 20-23	Sequences Sequences : 4.1 Cauchy sequences : 4.2	Section 4.1: 2, 4, 5, 9, 10  Section 4.2: 1, 2, 5, 9, (13 or 14 extra credit)  due April 27th
April 27-30	Series Infinite series : 4.3 Notions of convergence : 4.4	Section 4.3: 3 b c g h i j l, 4, 5, 6, 7  Section 4.4: 3  due May 4th
May 4-7	Sequences of functions Fundamental Theorems : 4.5 Power series representations : 4.6	Section 4.5: 1, 2, 4a, 5a, 8, 9, 12  Section 4.6: 3ad, 4b, 5  due May 7th
May 13	FINAL EXAM (Thursday, May 13) In Physics P116 Note the time: 1100-1:30 p.m. !!!

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