Advanced Calculus

H1N1 policy

Homework

• Read 1.1, 1.2 for We, Sept 23
• No class Sept 25. Do problems 1, 2, 3, 4, 5
• Read 1.3, 1.4 for Mo, Sept 28. Turn in Ch1, problem 4 (all parts) ...
• Read 2.1 for We, Sept 30 Do Ch 1 problems 6, 7, 8, 9, 10. Turn in 7bde AND construct a one-to-one function from [0,1] onto [0,1)
• Fri, Oct 2: I will finish 2.1 and may start Section 2.2. Do Ch 2 problems 1, 2, 8
• Mo, Oct 5: I hope to finish 2.2 and start 2.3. Turn in Ch 2 #8, then work on inequalities: Ch 2: #3, 4, 5, 6, 7
• Turn in Ch 2: #3 and 5c for We, Oct 7 solution of 5c
• Fri, Oct 9: Do problems 9-15. Read Section 2.4
  
• For Mo, Oct 12: Read 3.1. Turn in Hw 5 | solution (TeX).
• For We, Oct 14: Read 3.2, do Ch 3 #1, 2. Turn in Hw 6 solution (TeX) [in class, or in my mailbox/office by Friday night].
• Fri, Oct 16: no class Do problems Ch 3 # 3-7, 20, 22
• Mo Oct 19: Open sets, closed sets, start Section 3.3 -- limits.
• We Oct 21: Section 3.3 (Limits) Turn in Hw 7 (TeX).
• Fri Oct 23: Limits, may start Section 3.4 (Completeness) Turn in Hw 7 Solution (TeX)
• Mo Oct 26 [limsup+Section 3.4] Turn in Hwk on limits: Hw 8 Solution (TeX)
• We Oct 28: [End of 3.4 + Recitation]
• Fri Oct 30: 12-1PM Q&A Then review 1PM-2PM

  Midterm 5:30PM-7++ in 804 Old Chem.
  Six questions from the material in Chapters 1, 2, 3 (up to and including Section 3.4) Check out rejected questions.

  
  
• Mo, Nov 2: Compact sets [Section 3.5]
• We, Nov 4: Compact sets ...
• Fri, Nov 6: Connected sets [Section 3.6]
• Mo, Nov 9: Continuous functions [Chapter 4, Section 4.1] Hwk 9: Turn in Ch 3 #37
• No class We, Nov 11 (UC closed)
• Fri, Nov 13: Section 4.2
• Mo, Nov 16: [4.3] Hwk 10: Turn in Ch 4 #2, 4 Sol of #4
• We, Nov 18: [4.4]
• Fri, Nov 20: [4.5]+ Normed Vector spaces: page 63 #22, page 93 # 22, 23
• Mo, Nov 23: Normed Vector Spaces+[4.6] Hwk 11: Ch 4 #9, 10, 11
• We, Nov 25: [4.6]
• No classes Fri, Nov 27 (UC closed)
• Mo, Nov 30: Review+ Hwk 12: Ch 4 #13, 14, 15, 16
• We, Dec 2: Review²
• Fri, Dec 4: Review³
• Final Exam: Wed, Dec. 9, 1:30-3:30 pm Chapters 1+2+3+4. (Four problems from Ch 4.) 1000%-e of questions

Material

Ordered sets, the real field, the complex field, Euclidean space, finite, countable and uncountable sets, metric spaces, compact sets, convergent sequences of numbers, Cauchy sequences, upper and lower limits, Bolzano-Weierstrass theorem, series, the number e, convergence tests for series, absolute convergence, addition and multiplication of series, rearrangements.

Limits and continuity of functions, continuity and compactness, connectedness and continuity, discontinuities, monotone functions, derivatives, the Mean Value theorem, l'Hopital's rule, higher order derivatives, Taylor's theorem, Riemann-Stieltjes integral, integration and differentiation of vector-valued functions, rectifiable curves.

Uniform convergence for sequences and series of functions, equi-continuous families of functions, the Stone-Weierstrass theorem, functions of several variables.

Important Dates

     Grade Cutoffs
     A  93% and higher
     A- 90% to 93%
     B- 80% to 83%
     C- 70% to 73%
     D- 60% to 63%