Spring 2008, MATH 317, Section 2
Adavanced Calculus of One Variable

Lectures
Tue.01/22: Overview, Some typical problems in analysis
Wed.01/23: Section 1:  Math induction
Fri.01/25: Section 2:  Irrational numbers.  Rational Zeros Theorem
Mon.01/28: Section 3:  Associative/commutative/distributive laws.  Ordering/inequalities
Tue.01/29: Discussion session
Wed.01/30: Section 4: The Completeness Axioms
Fri.02/01: Sections 5 and 6: Infinity, Development of R
Mon.02/04: Section 7: Sequences and limits
Tue.02/05: Discussion session. Quiz 1
Wed.02/06: Section 8: Formal proofs of sequence limits
Fri.02/08: Section 9: Rules of sequence limits
Mon.02/11: Section 9: (Cont'd)
Tue.02/12: Discussion session
Wed.02/13: Section 10: Monotone and Cauchy sequences
Fri.02/15: Section 11: Subsequences, Bolzano-Weierstrass Theorem
Mon.02/18: Section 11: (Continued)
Tue.02/19: Discussion session. Quiz 2
Wed.02/20: Section 10,11,12: lim inf's and lim sup's
Fri.02/22: Section 14: Series
Mon.02/25: Section 14: Series
Tue.02/26: Section 15: Alternating series
Wed.02/27: Discussion session
Fri.02/29: Section 17: Continuous functions
Mon.03/03: Section 17: Continuous functions
Tue.03/04: Section 18: Properties of continuous functions
Wed.03/05: Section 18: Properties of continuous functions
Fri.03/07: Discussion session
Mon.03/10: Section 19: Uniform continuity
Tue.03/11: Section 19: Uniform continuity
Wed.03/12: Review for the Midterm Test
Fri.03/14: Midterm Test (in class)
Mon.03/24: Discussion session
Tue.03/25: Sections 19, 20:
Wed.03/26: Section 23: Power series
Fri.03/28: Section 24: Uniform convergennce of function sequences
Fri.03/31: Section 24: (cont'd)
Tue.04/01: Discussion session
Wed.04/02: Section 24: (cont'd)
Fri.04/04: Section 25: More on uniform convergennce
Mon.04/07: Section 26: Differentiation and integration of power series
Tue.04/08: Section 26: (cont'd)
Wed.04/09: Discussion session (problems on the extra worksheet)
Fri.04/11: Section 28: Derivatives
Mon.04/14: Section 28: (cont'd) Chain rule
Tue.04/15: Discussion session
Wed.04/16: Section 29: Mean value theorem
Fri.04/18: Section 30: L'Hospital Rules
Mon.04/21: Section 31: Taylor theorem
Tue.04/22: Section 29: Discussion session
Wed.04/23: Section 32: Riemann integral: Riemann sums
Fri.04/25: Section 32: Riemann integral: Darboux sums
Mon.04/28: Section 33: Properties of Riemann integral
Tue.04/29: Section 33: (cont'd)  and Discussion session
Wed.04/30: Section 34: Fundamental Theorem  of Calculus
Fri.05/02: Section 34: Subsitution and Integration by parts
Mon.05/05--Fri.05/09: Review
Mon. 05/12/2008, 11:20am-1:20pm, Engrg E205  Final Exam


Homeworks

ExtraCreidts (Updated)
The extra homework problems

HW1: Due Fri. 02/01 before class
(Wed.01/23) Section1: p5 #1,7,11
(Wed.01/23) An extra problem
(Fri.01/25) Section 2: p12 #3,5,6
(Mon.01/28) Section 3: p18 #1,5,6

HW2: Due Wed. 02/13 before class
(Wed.01/30) Section 4: pp25-26 #7(a),11,12,16
(Fri.02/01) Section 5: p28 #2,5,6 and p30 #2
(Mon.02/04) Section 7: pp36-37 #3(a-s)odd, 4, 5(a,b)
(Tue.02/05) An extra problem (click the link above)
(Wed.02/06) Read Section 8 p40Ex.5.  Do Section 8 pp42-43 #2(c,e),3,8(a,b),10

HW3: Due Mon. 02/25 before class
(Fri.02/08) Read Section 9 Theorem 3&5 proofs.  Do Section 9 pp52-53 #3,5,6,7
(Mon.02/11) Section 9: pp53-54 #8,13,15
(Tue.02/12) An extra problem (click the link above)
(Wed.02/13) Section 10: p63 #8,9,11
(Fri.02/15) Section 11: pp73-74 #2(a,b,e),3(a,b,e),7

HW4: Due Mon. 03/10 before class
(Mon.02/18) Section 11: Read p72 Thm 11.8 proof, Do p73 #5
(Wed.02/20) Section 12: pp78-79 #3(a,b,d,g),14
(Fri.02/22) Section 14: pp98-99 #1,3,7,8
(Mon.02/25) Section 14: pp98-99 #4,6,13
(Tue.02/26) Section 15: pp104-105 #1,3,6

HW5: Due Tue. 03/25 before class
(Fri.02/29) Section 17: Read p119 Ex3, Do pp123-125 #4,9(a,c),10(a,b)
(Mon.03/03) Section 17: pp123-125 #3(a,c,e,g),13(a)
(Mon.03/03) Bonus problem (5points) Section 17: p125 #14
(Tue.03/04) Section 18: pp131-132 #5(a),7,8,9
(Wed.03/05) Section 18: p132 #10
(Mon.03/10) Section 19: Read Ex.1,2; p144 #1(a,c,e,g),3

HW6: Due Fri. 04/04 before class
(Tue.03/25) Section 20: p155 #3,4,11(b,c)  Read Corollary 7&8
(Wed.03/26) Section 23: p176 #1(a,c,e,g),2,7
(Fri.03/28) Section 24: pp182-183 #1,2,3
(Mon.03/31) Section 24:

HW7: Due Mon. 04/14 before class
(Wed.04/02) Section 24: pp182-184 #9,10,13,15,17
(Fri.04/04) Section 25: pp190 #3,5,7
(Mon.04/07) Section 26: pp199 #2,3,4
(Tue.04/08) Section 26: pp199-120 #6,7,8

HW8: Due Fri. 04/25 before class
(Fri.04/11) Section 28: pp211-213 #2, 3(a,b), 7
(Mon.04/14) Section 28: pp211-213 #1(a,c,e,f),5,9,15
(Wed.04/16) Section 29: pp220-222 #1,4,5,11,12,16,18
(Fri.04/18) See above

HW9&10: Due Mon. 05/09 before 5pm
(Mon.04/21) Sections 30-31: p229 #1,3  p240 #1,2,5
(Wed.04/23) Section 32: pp252-253 #1,3,7
(Mon.04/28) Section 33: pp260-261 #4,5,8,9,13
(Wed.04/30) Section 34: pp267-268 #2,3,5,6,7,8,11