MAT 370   SYLLABUS*

FALL 2009

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/terminology.  To learn and to understand some of the most important theorems of Calculus.  You will be expected to read proofs and you will be asked to write some short proofs.  Exams will, however, be based primarily on knowledge of definitions, statements of theorems, and applications to specific computations.

Grading: Grades will be based on 2 exams, a final exam, homework and quizzes.  Quizzes should be expected each class period and will typically consist of having to give definitions of terms and/or short problems very similar to homework problems that you have done.  You may also be asked to give the precise statements of theorems that have names.   Total points for homework and quizzes will be scaled and count the equivalent of between 1 and 2 exams, depending on the number of quizzes given during the semester and the number of homework problems graded.

Important:  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.  In order to pass this class you should conscientiously learn the terminology and the statements of the main results, and use these to write out simple proofs.

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. 

Since we will, from time to time, diverge from the text, and since there will be unannounced quizzes, it is important for you to attend all classes. 

Location of Exams.   Exams will 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

 

Weekof

Reading

Topics

Sections

to read

Homework Assignment

HW due

Note

Aug 23

pp1-20

Sets, relations.

0.1 –0.2

Ch 0 : 6,10,14,17

Sep 3

Aug 30

pp21-27

Cardinality, the real numbers, rational powers

0.3-0.5

Ch 0: 21,29,37,38,45

Sep 10

Sep 6

pp33-49

Sequences, neighborhoods, limits, Bolzano-Weierstrass Theorem

1.1-1.3

Ch 1: 3,4,7,8,9,10,11,14,18,19,21,22

Sep 17

Sep 13

pp49-69

Algebra of limits, subsequences, monotone sequences,

1.4,2.1

Ch 1:25,26,27,31,32,36,38,39,44,45,46

Sep 24

Sep 20

pp69-86

Theorems on limits of functions

2.2-2.4

Ch 2: 2,4,5,6,7,11,12

Oct 1

Exam1 (Ch0-1) 

Sep 27

pp83-89

Continuity

3.1-3.2

Ch 2: 16,19,20,22,24

Ch 3: 2,4,6,8,10,12,14

Oct 8

Oct 4

pp89-96

Uniform continuity, compactness, Heine-Borel Theorem

3.3

Ch3: 15,19,20,21,26,27,28

Oct 15

Oct 11

pp96-104

Properties of continuous functions

3.4

Ch3 : 29,30, 31,32,33,35,36,40

Oct 22

Oct 18

pp111-119

Derivatives, algebra of derivatives

4.1-4.2

Ch 4: 3,5,6,14

Oct 29

Oct 25

pp119-121

Rolle’s Theorem, Mean Value Theorem,

4.3

Ch 4: 18,19,20,21,26,27,31 

Nov 5

Exam 2 (Ch 2,3)

Nov 1

pp121-129

Cauchy MVT, L’Hôpital’s rule, Inverse Function Theorem, Trig functions

4.4

Ch 4: 32,33,36,37,39

Nov 12

Nov 8

pp137-148

Riemann Integral

5.1-5.2

Ch 5: 1,3,7,9

Nov 19

Nov 15

pp148-155

Riemann sums, Fundamental Thm of Calculus

5.3-5.4

Ch5 : 11, 12, 13, 14,15

Dec 1

Tues!

Nov 22

Leibnitz’ s rule

Supplementary practice exercises

Nov 29

pp155-165

Algebra of integrable functions,  integration by parts,  MVT for integrals, Taylor’s Theorem, Change of variables theorem

5.5-5.7

Ch 5: 16,18,19,26,28,29,30, 32,34

Dec 8

 

Tues!

Dec 6

Exponential and log functions, irrational powers

Supplementary practice exercises

Dec 8

Last

class

 

Dec  10

(Thursday)

7:30-9:20 am

Final Exam

*This syllabus is subject to changes.  Changes will be announced in class.