1512-Honor Calculus II  (Fall 2005)

MATH 1512   Instructor
Jean Bellissard
Professor of Mathematics and Physics
School of Math, Skiles 132 , Physics Howey W511
Phone: (404) 385-2179 (Math), 404-385-2509 (Phys)
Fax: (404) 894-4409
e-mail: jeanbel@math.gatech.edu
Lectures
Recitations::		 Skiles  146  Tuesday-Thursday 9:35-10:55AM
Monday-Wednesday 10:05-10:55am

Teaching Assistant Room Office hours
Robert Pruvenok 
Sang-Ho Shim
Skiles  168
Skiles  108B
 Tuesday 1-3pm Skiles 153




Office Hours: Skiles  132  Tuesday 4:30-6pm


Dates: August 22nd till December  8th, 2005


Final Exam on Tuesday December 13th , 2005,
2:50-5:40 pm, Skyles 146


 Homework November 21st pdf file
 Homework November 30th pdf file

Training exercises

Honor Calculus is intended to introduce Mathematics as a Science in itself,
rather than just giving rules of calculus for practical purposes.
Honor Calculus II will emphasis on reasoning, use of abstraction and proofs
as much as learning practical rules of Calculus.

Course Outline
Topic Text Sections # of Lectures

Approximation byPolynomials Functions

 20 in Spivak  2
Infinite Sequences  I, II
 22 in Spivak. 3
Infinite Series  I, II
 23 in Spivak 3
Uniform Convergence and Power Series 24 in Spivak 2
Review: Analysis
 20-24 in Spivak
 1
Matrices and Linear Equations  I, II
 1. in Helson
 3
Vector Spaces I, II, III
 2. in Helson 6
Linear Transformations I, II,
3. in Helson 3
Determinants I, II,
4. in Helson 3
Reduction of Matrices I, II, III,
 5. in Helson
 5

Textbooks   Spivak, Calculus, Chapter IV sections 20-24
(The book used in 1502 is Calculus, by Salas, Hille and Etgen, 9th edition, Sections 8 & 10-11)
Henry Helson, Linear Algebra,
15 The Crescent, Berkeley CA 94708, helson@socrates.berkeley.edu, (510) 848-8629
 For exercises and problems look also at
Eric Carlen, Maria Conceição  Carvalho,  Beginning with Linear Algebra
Homework & Quizzes Students are required to do the homework every week. The weekly quiz on Wednesday will be a test on the homework that has been done. The homework will NOT be graded, but students needing some feedback are advised to turn it in at the Monday recitation
class and to ask the TA to grade it. There should be about 12 quizzes during the Fall
semester but only the 10 best ones will be counted in the final grade. An absence on
a quiz will be graded 0 (zero)
 (so that only if the student is absent less than twice, it will not affect the final grade).
One-Hour Test There will be twice a 1-Hour test during the Fall semester.
The first one after the end of the Analysis  course,
The other one in the middle of the Algebra course
Final Exam  December 12-16th 2005.

Final Grade

Grade Distribution:

Quizzes
One Hour Tests
Final		 25%
35%
40%
90% for an A
80% for a   B
70% for a   C
60% for a   D

Calendar (updated on September 12, 2005)

Preliminary test:    click here (pdf-file)  (ps-file) 

August 23rd & 25th: Approximation by polynomials, Spivak Chapter 20
Reading: Spivak Chapter 20
Brook Taylor was an English Mathematician (1685-1731)I
Joseph-Louis Lagrange was an Italian-French mathematician (1736-1813)
who proposed to consider Taylor's expansion as the basic principle of Calculus.

Homework 1 :  Spivak p. 427-433, Problems 1, 2, 3, 6, 8, 10, 16, 19
Due date :  Monday August 29th, 10:00AM
Quiz 1 :  Wednesday August 31st, 15-20 minutes, during the recitation 10:00AM

 August 30th & September 1st: Infinite Sequences I, Spivak Chapter 22
Reading: Spivak Chapter 21 & 22

Homework 2 : Spivak p. 453-462, Problems 1, 2, 3, 4, 6, 7, 8,  9, 12, 13, 14, 20, 27, 30
Due date :  Tuesday September 6th, 10:00AM  (Sept. 5th is a school holiday)
Quiz 2 :  Wednesday September 7th, 15-20 minutes, during the recitation 10:00AM

 September 6th & 8th: Infinite Sequences II, Spivak Chapter 22  and
Infinite Series I, Spivak Chapter 23
Reading: Spivak Chapter 23

Homework 3 : Spivak p. 482-490, Problems 1, 2, 3, 4, 5, 7, 9, 10, 12, 13, 15, 18, 21, 25, 26, 27
Due date :  Monday September 12th, 10:00AM
Quiz 3 :  Wednesday September 14th, 15-20 minutes, during the recitation 10:00AM , on homeworks #2 & 3
(The quiz will treat the parts of the homework related to the courses taught on Sept 6-8)

 September 13th & 15th: Infinite Series II, Spivak Chapter 23
Reading: Spivak Chapter 23

Homework 4 : Spivak p. 482-490, Problems 6, 8, 11, 14, 15, 17, 19, 20, 22, 24, 25 (again)
Due date :  Monday September 19th, 10:00AM
Quiz 4 :  Wednesday September 21th, 15-20 minutes, during the recitation 10:00AM , on homework #4
(The quiz will treat the parts of the homework related to the courses taught on Sept 13-15)


 September 20th & 22th: Uniform Convergence and Power Series, Spivak Chapter 24
Reading: Spivak Chapter 24

Homework 5 : Spivak p. 508-516, Problems 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 19, 21, 25, 27, 31
Due date :  Monday September 26th, 10:00AM

September 27th: Reviewing Chapters 20-24 in Spivak's book
One hour test #1: Wednesday September 28th, during the recitation 10:00AM,  on Spivak Chapters 20-24

 September 29th: Matrices and Linear Equations I, Helson Chapter 1.1-1.2 pages 1-12
Reading: Helson Chapter 1

Homework 6 : Helson p. 5-6, Problems 1, 2, 3, 4, 5, 6,  Helson p.13-14: Problems 1, 2, 3, 4, 5, 6, 7
Due date :  Monday October 3rd, 10:00AM
Quiz 5 :  Wednesday October  5th, during the recitation 10:00AM , on homework #6

 October 4th & 6th: Matrices and Linear Equations II, Helson Chapter 1.3,1.4,1.5,1.6 pages 6-32
Reading: Helson Chapter 1.3, 1.4, 1.5, 1.6

Homework 7 : Helson p. 17-18, Problems 1, 2, 3, 4, 5,  p. 23-24: Problems 1, 2-3-42, 3, 4;
p.32-33  Problems 1,3,4,5,7,8,9,10,
Due date :  Monday October 10th, 10:00AM
Quiz 6 :  Wednesday October  12th, during the recitation 10:00AM , on homework #7

 October 11th & 13th: Vector Spaces I, Helson Chapter 2.1-2.2-2.3-2.4 pages 37-5889-
Reading: Helson Chapter 2.1-2.2-2.3-2.4

Homework 8 : Helson p. 34-35, Problems 1, 2, 3, 4, 5, 6, 7; p. 41-42: Problems 1, 2, 3, 4, 5, 6;
p.46-47 Problems 1,3,4,5,8,9,
Due date :  Thursday October 20th, 10:00AM

 October 20 th (Fall recess on 17-18th) : Vector Spaces II, Helson Chapter 2.5-2.6 pages 59-67
Reading: Helson Chapter 2.5-2.6

Homework 9 : Helson p. 52, Problems 1, 2, 3, 4, 5; p. 58: Problems 3, 4, 5, 6;
p.60-61  Problems 1,2,3,4;   p.67-68 Problems 1,5,6,8,9
Due date :  Monday October 24th, 10:00AM
Quiz 7 :  Wednesday October  26th, during the recitation 10:00AM , on homework #8 & 9

October 25th & 27th Vector Spaces III, Helson Chapter 2.7-2.8-2.9 pages 68-86
Reading: Helson Chapter 2.7- 2.8-2.9

Homework 10 : Helson p. 75-76, Problems 1,4,5,7,11,12; p. 81: Problems 1,3,4; p.86 Problems 1,2,3,6;
p.87-88 Problems 1,4,6,7,8,11
Due date :  Monday October 31st, 10:00AM
Quiz 8 :  Wednesday November 2nd, during the recitation 10:00AM , on homework #10

 November 1st & 3rd : Linear Transformation I, Helson Chapter 3.1-3.2-3.3 pages 89-107
Reading: Helson Chapter 3.1-3.2-3.3

Homework 11 : Helson p. 94, Problems 1, 2, 3, 4, 5, 6; p. 98: Problems 1, 2, 3, 4, 5, 6;
p.106  Problems 1, 2, 3, 4, 5, 6, 7, 8, 9; p.107 Problems 11, 12, 13
Due date :  Monday November 7th, 10:00AM
One Hour Test #2:  Monday November 7th, 50 minutes during the recitation 10:00AM,
                                        on Helson Chapters 1, 2 and Sections 3.1-3.3-


 November 8th & 10th : Linear Transformation II, Helson Chapter 3.4-3.5 pages 107-119
and  Determinants I  4.1-4.2 pages 123-130
Reading: Helson Chapter 3.4-3.5 & 4.1-4.2

Homework 11 : Helson p. 113, Problems 1, 2, 3, 4, 5, 6, 7, 8; p. 120: Problems 1, 2, 3, 4, 5, 6;
p.120-121  Problems (Problems for Chapter 3) 1, 2, 3, 4, 5, 6, 7, 8, 11; p.126 Problems 1, 2, 3, 4
Due date :  Monday November 14th, 10:00AM
Quiz 9 :  Wednesday November 16th, during the recitation 10:00AM , on homework #11

 November 15th & 17th : Linear Transformation , Helson Chapter 3
Reading: Helson Chapter 3

Homework 12 : Helson p. 130, Problems 1, 2, 3, 4, 5, 6; p. 134-135: Problems 1, 2, 3, 4, 5;
p.138-139  Problems 1, 2, 3, 4, 5, 6; p.146 Problems 1, 2, 3, 4; p 148 Problems 1, 2, 3, 4;
Due date :  Monday November 21st, 10:00AM
Quiz 10 :  Monday November 21st, during the recitation 10:00AM , on homework #12

 November 22nd (24-25th are Thanksgiving holidays) : Reduction of Matrices I,
Helson Chapter 5.1-5.2 pages 151-163
Reading: Helson Chapter 5.1-5.2

Homework 13 : Helson p.148-149  Problems (Problems for Chapter 4) 3, 4, 5, 6;
p. 156-157 Problems 1, 2, 3, 4, 5, 6, 7, 8,  9,  10, 11; p.163  Problems 1, 2, 3, 4;
Due date :  Monday November 28th, 10:00AM
Quiz 11 :  Wednesday November 30th, during the recitation 10:00AM , on homework #13

 November 29th & December 1st : Reduction of Matrices II, 
Helson Chapter 5.3-5.4-5.5-5.6 pages 164-186
Reading: Helson Chapter 5.3-5.4-5.5-5.6

Homework 14 : p. 173 Problems 1, 2, 3, 4, 5, 6; p.175-176  Problems 1, 2, 3, 4, 5;
p. 186 Problems 1, 2, 3, 4, 5, 6;
Due date :  Monday December 5th, 10:00AM
No quiz

December 6th & 8th : Reduction of Matrices III, 
Helson Chapter 5.7-5.8-5.9-5.10 pages 186-199
Reading: Helson Chapter 5.7-5.8-5.9-5.10

Homework 15 : p. 190 Problems 1; p.192  Problems 1, 2, 3;  p. 195  Problems 1, 2, 3;  p. 199  Problems 1, 2, 3;
p. 200-201 (Problems for Chapter 5) Problems 1-13;
No quiz

Final exam: Tuesday December 13th, 2005  2:50-5:40pm  (see Calendar)




Training exercises click here (back)
          August 25 2004 (15min quiz)
          September 1  2004 (15min quiz)
          September 8 2004 (15min quiz)
          September 22 2004 ( 1/2 hour test)