1512 D-Honor Calculus II  (Fall 2006)

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  169  Tuesday-Thursday 9:35-10:55AM
Monday-Wednesday 10:05-10:55am Skiles 153

Teaching Assistant Room Office hours

Yongfen Li

Skiles  144
Tuesday  8:30-9:30 am
            11:00-12:00 am




Office Hours: Skiles  132  Tuesday 1:30-2:30pm & 5-6pm


Dates: August 21st till December  7th, 2006

Final exam Thursday December 14th, 2006 at 8:00-10:50 am Room 169

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  I  II 

20 in Spivak  2
Infinite Sequences  I  II  III 
22 in Spivak. 3
Infinite Series  I  II  III 
23 in Spivak 3
Uniform Convergence and Power Series  I  II 
24 in Spivak 2
Review: Analysis
20-24 in Spivak
1
Introduction to Vectors and Matrices I  II  III  IV 1.1-1.6 in C2 4
Systems of Linear Equations & Row Reduction I  II 2.1-2.4 in C2 2
Kernel, Image, Subspaces, & Least Squares I  II  III 3.1-3.4 in C2 3
  Review  Algebra Part I Chap.1-3.3 in C2 1
Orthogonal Projections, Gram-Schmidt  I  II   3.5-3.8 in C2 2
Determinants & Cross Product I  II 
4.1-4.3 in C2 2
Eigenvectors &  Applications  I   II   III   IV   V 
5.1-5.6 in C2 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)
  Eric Carlen, Maria Conceição  Carvalho,  Beginning with Linear Algebra, (called C2 here)
    
Solutions Manual for Linear Algebra from the Beginning
Homework & Quizzes Students are required to do the homework every week. The weekly quiz on Wednesday will be a test based on the homework of the week. 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 will be 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 a student is absent less than twice, it will not affect his final grade).
1-Hour Test There will be twice a 1-Hour test (50') during the Fall semester.
The first one on   Wednesday September 27th   after the end of the Analysis  course,
The other one on Wednesday November 1st      in the middle of the Algebra course
Final Exam  Thursday December 14th 2006, 8:00-10:50


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 (to be updated )

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

August 22rd & 24th: Approximation by polynomials, Spivak Chapter 20  (back to Course Outline)
Reading: Spivak Chapter 20
Brook Taylor was an English Mathematician (1685-1731)

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 28th, 10:00AM
Quiz 1 :  Wednesday August 30th, 15-20 minutes, during the recitation 10:00AM


August 29th & 31st: Infinite Sequences I, Spivak Chapter 22  (back to Course Outline)
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 5th, 9:35AM  (Sept. 4th is a school holiday)
Quiz 2 :  Wednesday September 6th, 15-20 minutes, during the recitation 10:00AM

September 5th : Infinite Sequences II, Spivak Chapter 22  and  (back to Course Outline)
September 7th : Infinite Series I, Spivak Chapter 23  (back to Course Outline)
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 11th, 10:00AM

Quiz 3 :  Wednesday September 13th, 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 5-7)

September 12th & 14th: Infinite Series II, Spivak Chapter 23  (back to Course Outline)
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 18th, 10:00AM

Quiz 4 :  Wednesday September 20th, 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 12-14)


September 19th & 21st: Uniform Convergence and Power Series, Spivak Chapter 24  (back to Course Outline)
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 25th, 10:00AM


September 26th: Reviewing Chapters 20-24 in Spivak's book    (back to Course Outline)
One hour test # 1: Wednesday September 27th, during the recitation 10:00AM,  on Spivak Chapters 20-24
                                      (back 1-Hour Test)



September 28th: Introduction to Vectors and Matrices I,   C2 Chapter 1 Sections 1 & 2  (back to Course Outline)
Reading:
C2 Chapter 1 Sections 1 & 2

Homework 6 :
C2    p.13           Exercises: 1.1 to 1.14 and
                              p.28-33      Exercises: 2.1, 2.2, 2.3, 2.4, 2.6, 2.7, 2.10, 2.11,2.12, 2.13, 2.14,
                                                               2.16, 2.19, 2.22, 2.28, 2.29, 2.32
,
Due date :   
Monday October 2nd, 10:05AM
Quiz 5 : Wednesday October 4th, 15-20 minutes, during the recitation 10:00AM , on homework #6

October 3rd & 5th: Introduction to Vectors and Matrices II-III,  C2 Chapter 1 Sections 3-4-5  (back to Course Outline)
Reading:
C2 Chapter 1 Sections 3-4-5

Homework 7 : 
C2    p.44-49      Exercises: 3.1, 3.2, 3.3, 3.9, 3.10, 3.11, 3.12, 3.13,
                                                               
3.14, 3.15, 3.16, 3.17, 3.18, 3.19, 3.20,
                              p.58-61      Exercises: 4.4, 4.5 4.6, 4.8, 4.9, 4.14
                              p.70-73      Exercises: 5.4, 5.6, 5.10, 5.11, 5.14, 5.17, 5.20, 5.25, 5.26
Due date :   
Monday October 9th, 10:05AM
Quiz 6 :  Wednesday October 11th, , 15-20 minutes, during the recitation 10:00AM , on homework #7

October 10th: Introduction to Vectors and Matrices IV,  C2 Chapter 1 Sections 5-6  (back to Course Outline)
October 12th: Systems of Linear Equations & Row Reduction I,  C2 Chapter 2 Sections 1-2  (back to Course Outline)
Reading:
C2 Chapter 1 Sections 5-6 & Chapter 2 Sections 1-2

Homework 8 :
C2    p.83-84      Exercises 6.2, 6.3, 6.5, 6.6, 6.7,
                              p.94-98      Exercises 1.2, 1.3, 1.5,  1.8, 1.10, 1.11, 1.13, 1.17, 1.18, 1.22, 1.24, 1.27
                              p.104-105  Exercises 2.1, 2.2, 2.3, 2.4
Due date :    Wednesday October 18th, 10:05AM
Quiz 7 :  Thursday
October 19th, 15 minutes, during the lecture 9:35AM on homeworks #8
(Due to the Fall recess the quiz #7 will take place on Thursday instead of Wednesday)

October 19th (Fall recess Oct 16-17): Systems of Linear Equations & Row Reduction II,   (back to Course Outline)
C2 Chapter 2 Sections 3-4
Reading:
C2 Chapter 2 Sections 3-4

Homework 9 :
C2    p.116-118  Exercises from 3.1 to 3.15
                              p.134-135  Exercises 4.1 to 4.11
Due date :    Monday October 23th, 10:05AM
Quiz 8 :  Wednesday
October 25th, 15-20 minutes, during the recitation 10:05AMon homeworks #9

October 24th& 26th  Kernel, Image, Subspaces, & Least Squares I & II, C2 Chapter 3 Section 1-2-3  (back to Course Outline)
Reading:
C2 Chapter 3 Section 1-2-3

Homework 10 :
C2  p.157         Exercises 1.2, 1.3, 1.5, 1.7, 1.8, 1.10, 1.11, 1.12
                              p.174-175  Exercises 2.1, 2.2, 2.3, 2.5, 2.6, 2.8
                             
p.185-187  Exercises 3.2, 3.5, 3.8, 3.10, 3.13, 3.15
Due date :    Monday October 30th, 10:05AM

October 31st : Reviewing Chapters 1 & 2 & 3.1-3.3     (back to Course Outline)
One hour test # 2: Wednesday November 1st, during the recitation 10:00AM,  on C2  Chapters 1 & 2 & 3.1-3.3
                                      (back 1-Hour Test)



 
November 2nd: Kernel, Image, Subspaces, & Least Squares III, C2 Chapter 3 Section 4-5  (back to Course Outline)
Reading:
C2 Chapter 3 Section 4-5

Homework 11 :
C2  p.196-198  Exercises 4.2, 4.3, 4.6, 4.9, 4.11, 4.14, 4.19, 4.20
                             
p.207  Exercises 5.1, 5.2, 5.3, 5.5, 5.6, 5.7,
Due date :    Monday November 6th, 10:05AM
Quiz 9 :  Wednesday
November 8th, 15-20 minutes, during the recitation 10:05AM on homeworks #11

November 7th & 9th: Orthogonal Projections, Gram-Schmidt I & II,  C2 Chapter 3 Section 5-6-8  (back to Course Outline)
Reading:
C2 Chapter 3 Section 5-6-7-8 (read also section 7, even if it is not taught in class).

Homework 12 :
C2  p.219  Exercises 6.1 to 6.13
                             
p.232  Exercises 8.1 to 8.7
Due date :    Monday November 13th, 10:05AM
Quiz 10 :  Wednesday
November 15th, 15 minutes, during the recitation 10:05AM on Section 3.3-3.4-3.5


November 14th & 16th: Determinants  C2 I & II Chapter 4 Section 1-2-3-4   (back to Course Outline)
Reading: C2 Chapter 4 Section 1-2-3-4

Homework 13 :
C2  p.247-248  Exercises from 1.1 to 1.5
                              
p.259-260  Exercises 2.1, 2.2, 2.3, 2.4, 2.5
                               p.270-271  Exercices 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.9
                               p.281         Exercices 4.1 to 4.3
Due date :    Monday November 20th, 10:05AM
Quiz 11 :     
Tuesday November 21st, 15 minutes, during the lecture 9:35AM on homeworks #13 
(Due to Thanksgiving the quiz #11 will take place on Tuesday instead of Wednesday)



November 21th: (Thanksgiving is on the 23th)
Eigenvalues, Eigenvectors I  C2 Chapter 5 Section 1   (back to Course Outline)  
Reading:
C2 Chapter 5 Section 1

Homework 14 :
C2  p.293-296 Exercices 1.1 to 1.22
Due date :       Monday November 27th, 10:05AM
Quiz 12 :  Wednesday Nov
ember 29th, 15 minutes, during the recitation 10:05AM on homeworks #14


November 28th & 30th: Eigenvalues, Eigenvectors II & III  C2 Chapter 5 Section 2-3    (back to Course Outline)
Reading: C2 C
hapter 5 Section 2-3

Homework 15 :
C2  p.301-303 Exercices 2.1, 2.2, 2.3, 2.6, 2.7, 2.11
                             
p.313-315 Exercices 3.1, 3.2, 3.3, 3.9, 3.10
Due date :      
Monday December 4th, 10:05AM
Quiz : No quiz     


December 5th & 7tht: Eigenvalues, Eigenvectors IV&V C2 Chapter 5 Section 4-5  (back to Course Outline)
Reading:
C2 Chapter 5 Section 4-5

Homework 16 :
C2  p.325-327 Exercices 4.1 to 4.12 
                              
p.342-343 Exercices 5.1, 5.2, 5.3, 5.5, 5.7, 5.10
(Since this is the last week of teaching before the final exam, this homework is strongly recommended
 but there is no possibility to turn it in. However the Chapters 4 & 5 will be part of the final exam)

 
Final exam : Thursday December 14th, 2006  8:00-10:50am  (see Calendar)

Training exercises click here (back)

          August 25 2004 (15min quiz)
       
  September 1  2004 (15min quiz)
       
  September 8 2004 (15min quiz)
       
  September 21 2005 (15 min quiz)
       
  September 28 2005 (50 min test)
          September 22 2004 ( 1/2 hour test)
 

© 2006  Jean Bellissard