MAT 371 TENTATIVE SYLLABUS*

FALL 2012

Text: Introduction to Analysis by Edward Gaughan, 5th edition

Instructor:  Prof. H. Kuiper 

Office: PSA 625    phone: 965-5004,   email:kuiper@asu.edu

URL: http://math.asu.edu/~kuiper

Objectives:  To become acquainted with the mathematical foundations of Calculus.  To understand some of the key concepts in Analysis, such as real number, convergence, sequence, limit, continuity, compactness, derivative, and Riemann integral  (this requires the precise knowledge of the definitions and terminology),  and to learn and  understand some of the most important theorems of Calculus.  You will also be expected to learn how to write proofs. This is a skill that is acquired by reading proofs, learning some “tricks”, and by practicing.  On each exam there will be one or more questions that will ask you to prove something. 

Grading: Grades will be based on 2 exams, a final exam, homework and quizzes.  Quizzes should be expected each Tuesday and will typically consist of having to give definitions of terms and (rarely) a short problem very similar to homework problems that you have done.  You may also be asked to give the precise statements of theorems that have names.   See the link Definitions to know exactly what you will be responsible for on quizzes.  Homework will be collected each Thursday.  The homework will count for the equivalent of an exam.  To pass the course you will probably need to earn at least 75% on your homework.  The quizzes may count up to the equivalent of an exam, depending on the number of quizzes given during the semester. To pass the course you will probably need to earn at least 70% on your quizzes. 

Important:  Since you are expected to be able to give precise definitions of the terms that are introduced.  I suggest that you use 3x5 note cards with the term on one side and the definition on the other.  It is much like learning a foreign language.  If you don’t learn the vocabulary you will neither be able to understand nor to speak (translate: write proofs).  You should take this assignment very seriously, for failure to do so will surely mean that you will not be able to pass this class.  You should also conscientiously attempt to learn how to use the terminology and the statements of the main results to write out simple proofs.  This is probably the hardest part of the course and is learned by carefully reading the proofs in the book and by practice on the homework.

Syllabus:   The schedule is only an approximation.  When the material gets difficult we may allow ourselves to take more time.  If we run out of time we will omit less important material.  After a very brief and superficial look at Chapter 0, we will carefully do all of chapters 1 through 5. Homework problems A1-X11 are from old exams that are found at

  http://math.la.asu.edu/~kuiper/370files/371OldExams.pdf    

Class Attendance:  You are allowed 3 unexcused absences.  Further unexcused absences will be penalized.    Homework assignments are due on Thursdays.  On Tuesdays there will be quizzes on definitions and statements of main theorems.  The total quiz grade will have the same weight as an exam and will be subject to the scale: A=90%, B=80%, C=70%, D=60%. 

Location of Exams.   If we fall behind and need to make up time, there is a small chance that some exams might be given in the Math Testing Center in the basement of PSA (Wexler Hall).  

Be sure you have your Sun Card – no exam will be given without this ID.  Make sure you know the hours that the testing center is open

Week

of

Read

Topics

Sec

 

#

Homework Assignment

Due

Aug 19

pp1-20

Sets, relations.

0.1 –0.2

1

Ch 0 : 7,8,10,12,14 ; J3

Aug 30

Aug 26

pp21-27

Cardinality, the real numbers, rational powers

0.3-0.5

2

Ch 0: 22, 37, 44; G3

Sep 6

Sep 2

pp33-49

Sequences, neighborhoods, limits, Bolzano-Weierstrass Theorem

1.1-1.3

3

Ch 1: 3,5,7,9,10, 11,18,19, 21,22; A4, F11, G5, J4, P3, P5, S3

Read the file

http://math.la.asu.edu/~kuiper/370files/sequences&accpoints.pdf

Sep 13

Sep 9

pp49-69

Algebra of limits, subsequences, monotone sequences,

1.4,2.1

4

Ch 1: 23,25,26,27,32;  A6, D6, G7, J2, M4, P4, P6

Sep 20

Sep 16

pp69-86

Theorems on limits of functions

2.2-2.4

5

Ch 1: 35, 36, 38, 39, 45, 46; B4, H3, M5, M6

Sep 27 Exam1 Oct 2

Sep 23

pp83-89

Continuity, the algebra C[a,b]

3.1-3.2

6

Ch 2: 2, 6, 7, 8, 11,12,19, 22;

Oct 4

Sep 30

pp89-96

Uniform continuity, compactness, Heine-Borel Theorem

3.3

7

Ch3:2,6,14;15,19,20;B1, B6, B7, E2,H2, T6

Read the file

http://math.la.asu.edu/~kuiper/370files/interior&closure.pdf

Oct 11

Oct 7

3.3

8

Ch3 :26-29, 31,32, 35,36;  C7, D7, E6,H4, I10,L3, Q6, T5, U12

Oct 25

Oct 14

Fall Break

Oct 21

pp96-104

Properties of continuous functions

3.4

9

Ch3 : 41, 43 ; Ch 4: 3,5,6 ; E5, F7, K5, Q4, T7

Nov    1

Exam 2, Nov 6

Oct 28

pp111-119

Derivatives, algebra of derivatives, Rolle’s Theorem

4.1-4.2

10

Ch4: 12, 15,18,19,21, 23,32,33; O7

Nov

8

Nov 4

pp119-129

Mean Value Theorem, Cauchy MVT, L’Hôpital’s rule,

4.3,4.4

11

Ch4:40;  E7, H6, K2.

Nov

15

Nov 11

Inverse Function Theorem, Trig functions ,Riemann Integral

12

Ch 5: 1,3,9; C3, C5, F8, I11, H0, R7

Read the file

 http://math.la.asu.edu/~kuiper/370files/Riemann_1.pdf

Nov

22

Nov 18

pp137-148

Riemann sums, Fundamental Thm of Calculus, Leibnitz’s rule Integration by parts

5.1-5.2

13

Ch5 : 11, 12, 14, 16; C9, C10, F3, F4, I2, L1

Read the file

 http://math.la.asu.edu/~kuiper/370files/Riemann2.pdf

Nov

29

Nov 25

pp148-155

Algebra of integrable functions,

5.3-5.6

14

Ch 5: 19,26,28,29,30, 32, 33, 34;  R10

Dec  

4

Dec  2

pp155-165

MVT for integrals, Taylor’s Thm, Change of variables,Exponential and log functions, irrational powers

5.7

 

Ch 5: 33,44; F12, I4, I9, L6,O10

Dec

11

(last day

of class)

Dec 9

 

Review

15

 

 

 

Final Exam:  See ASU Final Exam Schedule