MTH 452/MTS 517,  Fall 2007

Advanced Calculus I

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Faculty: M. Shillor

Office: 554 SEB

Phone: 248-370-3439

email: shillor@oakland.edu

Class Time: TuTh 3:30- 5:17 PM

Room: 386 SEB

Section: 

Office Hours: Monday 2:00-3:30 PM and Thursday 2:15- 3:15 PM, and by appointment.

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Important Dates:

September 4 - First day of class

September 18 - Last day for no-grade drop and refund

November 6 - Last day for official withdrawal (W)

December 6 - Last day of class

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Discussion board and chat room

Click on MTH 452,  I will check it once a day or so.

You are encouraged to use the Book Swap organized by the OU Student Congress
for more info click here

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Text:
The main Textbook for the course:
"A Friendly Introduction to Analysis"
Witold A. J. Kosmala, 2nd Ed
Publisher: Pearson/Prentice Hall 2004

Office Hours:
Monday 2:00-3:30PM, Thursday 2:15--3:15 PM and by appointment.

Exams:

The grade in this course will be based on TWO 120 points midterm exams and a 160 points
final exam for 400 points in total.

The exams will be  on October 9 and November 15,
and will include all the material covered up to that time.

The Final Exam will be on  Thursday, December 13, 3:30-6:30 PM.

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The main topics of the course:

Tools for Analysis- one week
Convergent Sequences- three weeks
Continuous Functions- three weeks
Differentiation- three weeks
Integrations - three weeks

INTENDED SYLLABUS:

We will follow the schedule below.

We will cover parts of Chapters 2-8.
Make sure to read Chapter 1 carefully as a preparation.

Week of --- Sections / HW (this is the minimum, and the questions on the exams will be similar
                                                however the more of the problems at the end of the sections you do,
at least read the questions carefully and understand them, the better!)

September 3 ---  Sections 1.1 - 1.5

September 10 --- Sections 1.6  and 1.7,  2.1,
                         HW:   pp. 72-3 Q: 1, 2, 3, 7, 9, 11, 12

September 17 ---  Sections 2.2-2.4
                         HW:    pp. 79-80  Q: 3, 6, 9, 11, 12, 17, 19
pp. 86-87  Q: 3, 4, 5, 7, 10, 11, 14, 16
pp. 93-5    Q: 4, 5*, 6, 7, 10, 11*, 12*, 14, 16*  

Note: Questions with * are harder, but if you want the grade 4.0 in this course, you must know how to do them.

September 24 --- Sections 2.5 and 2.6,
                         HW:    pp. 103-5  Q: 1, 3, 7, 10*, 16, 17*, 18
p. 110  Q: 1, 2, 5, 8*
Read all the Review questions on page s 111-3, make sure you understand the questions,
                             and do some of them.


October 1 ---  Sections 3.1 and 3.2, Review on Thursday (bring whatever questions you have)
pp. 123-5    Q: 1, 2, 5, 6*, 7, 10, 11*, 13* 
pp. 131-2    Q: 1, 5, 6, 7, 8*, 9, 14

        There will be TWO Review sessions on Friday October 5 and Monday October 8, at 2-3:30 PM - location to be
        announced. Feel free to come and bring whatever questions you have.

October 8 ---  Tuesday Exam 1, Sections 3.2 and 3.3,
pp. 139-41    Q: 2, 4, 5, 10*, 11*, 15, 17*, 21

                        The material for the exam is:  Sections 2.1-2.6 and 3.1
                        The format of the exam is: solve 7 out of 10 questions, to total of 120 pts;
                        answer 5 out of questions 1-8, each is worth 20 pts;
                        questions 9 and 10 are mandatory, so you must answer them, and each one is worth 10 pts.

Exam #1 Median=98 (82%) (35 students).

Grade distribution for the exam:

95% - 100% grade 4.0	88% - 94% grades 3.5 - 3.9	80% - 87% grades 3.0 - 3.4	73% - 79% grades 2.5 - 3.0	65% - 72% grades 2.0 - 2.4	50% - 64% grades 1.0-1.8
4	12	7	7	4	1

Highest mark for the exam: 120 (100%)

The solution of Exam 1A
The solution of Exam 1B

October 15 ---  Sections 4.1 (very important), 4.2, and 4.3
pp. 153-5    Q: 1, 2, 3, 4, as many as you need in 6, 7, 10 - basic material for the rest
pp. 160-1    Q: 1(e)-(i), 2 as many as you want
pp. 167-8    Q: 3, 7*,  8, 9, 10*, 11* 12, 15 , 16*  - the main properties of continuous functions

October 22 --- Sections 4.4, 5.1, and 5.2
pp. 173-6    Q: 1, 2, 4*, 5, 7, 10, 12, 14*, 15* - basic material for the rest of calculus                     
pp. 190-2    Q: 2 (a)-(e), 5, 6, 7, 9*, 10 (a), (b), (d), (g), 12*, 13, 14, 15* -  basic derivatives                    

October 29 --- Sections 5.1, 5.2, 5.3, and some previous material
                       pp. 199-201    Q: 3, 4, 6, 8, 14            

November 5 --- Sections 5.3, and 5.4
pp. 205-9    Q: 1*, 2, 3*, 7, 8*, 10, 15 (a)-(c), (f), (k), 19, 20*, 28* 
pp. 216-20    Q: 2-6, 9, 12, 13 (b), 17, 19, 25, 27*, 30*             

November 12 ---  Tuesday- Review, Thursday Exam 2
                        There will be two review sessions out of class on Monday 2-4 and Wednesday 4-5.
                        The material for the exam:  Sections 3.2, 3.3, 4.1-4, 5.1-4
                        Theorems:  4.1.9;  4.3.4;  4.3.5;  4.3.6;  4.3.10;  4.4.6;  5.2.3;  5.2.8;  5.3.1;  5.3.3;  5.4.8
                               and Example 4.2.2

                        The format of the exam is: solve 7 out of 10 questions, to total of 120 pts;
                        answer 5 out of questions 1-8, each is worth 20 pts;
                        questions 9 and 10 are mandatory, so you must answer them, and each one is worth 10 pts.

Exam #2 Median=102 (85%) (34 students).

Grade distribution for the exam:

95% - 100% grade 4.0	88% - 94% grades 3.5 - 3.9	80% - 87% grades 3.0 - 3.4	73% - 79% grades 2.5 - 3.0	65% - 72% grades 2.0 - 2.4	50% - 64% grades 1.0-1.8
3	8	10	5	3	5

Highest mark for the exam: 114 (95%)

The solution of Exam 2A
The solution of Exam 2B

November 19 --- Sections 6.1, 6.2 and 6.3(a bit) (Tuesday)
pp. 245-6    Q: 1, 3, 4, 5*, 11 
pp. 249-50    Q: 1, 3*, 7, 11, 12
pp. 254-6    Q: 1, 2, 4(b)(c), 9*, 10, 13*,14*, 15* (The last three are hard, so just have a look.
                       They are very useful inequalities in analysis and are being used very often!)


Have a Good Thanksgiving Break!

November  26 ---  Sections 6.3 and 6.4. 
pp. 261-5    Q: 1, 2, 6, 8, 11, 12, 17-19

Thursday: Exit Exam for MATH Majors (if you are not a Math Major, skip class)

December 3 --- Sections 6.5 (a bit), 7.1 (a bit), and uniform convergence of sequences of functions.
                         Thursday is last class - Course Review!

       There will be TWO Review sessions on Friday, December 7, and Monday December 10, at 4-5:30 PM -
         location to be announced. Come and bring whatever questions you have.

The Final Exam will be on Thursday, December 13, 3:30-6:30 PM.

The material for the final:

        Chapter 2- Sections 2.1-6 Sequences
                    Convergence of a sequence, properties of the limits,  divergent sequences,
                    divergence to infinity, the ratio test, Cauchy sequences, subsequences
Chapter 3- Sections 3.1-3 Limits of Functions
                    Limits of functions as x approaches infinity, limits, the Dirichle's function,
                    limits from the right and the left
          Chapter 4- Sections 4.1-4 Continuity
                    Continuous functions and their properties, some discontinuous functions,
                    continuous functions on closed sets, Brouwer's fixed point theorem, uniform
                    continuity and extensions to closed interval, Lipschitz functions
          Chapter 5- Sections 5.1-3 Differentiation
                    The derivative, minima and maxima (local or global) of functions, Mean Value
Theorems
          Chapter 6- Sections 6.1-4 Integration
                    The Riemann Integral, integration of continuous functions, properties,
                    integration and differentiation, indefinite integrals, when the integral of the
derivative is the function.

Theorems:
                             2.4.4   Limits of increasing sequences.
                             2.5.9   Convergence of Cauchy sequences
                             4.3.6   Extreme Value Theorem
                             4.3.6   Bolzano's Intermediate Value Theorem
                             4.3.10 Brouwer's Fixed Point Theorem
5.2.5   If f has a relative extremum at x=c and is differentiable then f '(c)=0.
5.3.1   Rolle's Theorem
5.3.3   The Mean Value Theorem
                             6.3.8   The Mean Value Theorem for Integrals
                             6.4.2   The Fundamental Theorem of Calculus 

        The format of the final exam is:
          There are 15 questions for the total of 160 points.
          You need to answer 12 questions.
          Choose 10 questions out of questions 1-13 (14 points each);
          Questions 14 and 15 are mandatory (10 points each).

        ADVICE: Sleep well the night before the exam!
        You cannot do well if you are sleepy and unable to concentrate!

GOOD LUCK AND BE WELL!


The solution of the Final Exam in pdf format are: Final-A     and    Final-B
        The median was 83% (33 students), and the course median was 83% . 

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