- Instructor: Dr. Mathias Schulze
- E-mail: mschulze@math.okstate.edu
- Phone: (405) 744-5773
- Office: MSCS 406
- Office Hours: MWF 9:00-10:00am and by appointment

- Class Meeting: MWF 10:30-11:20am, MSCS 422
- Textbook:
*Advanced Calculus*by R. Creighton Buck, 3rd Edition, Waveland Press, Inc. (2003) - Prerequisites:
- Course Web Page: http://www.math.okstate.edu/~mschulze/teaching/09F-MATH5043
- OSU Syllabus Attachment: http://osu.okstate.edu/acadaffr/aa/syllabusattachment-Fall.htm

You are expected to attend class on a regular basis and participate in class discussion. Because of the high correlation between poor attendance and low grades, attendance will be taken at the beginning of each lecture. I expect you to inform me about your reason for each unattended lecture. Attendance can influence the final grade in borderline cases. You are responsible to know the material covered in class and that in the corresponding sections in your textbook.

Working on example problems is the key to understand abstract concepts. Therefore there will be a homework assignment for each lecture in the course schedule. You turn in your solutions at the end of the lecture at the given due date. If there is no lecture at this day, you put your solutions in the drop box at the math office MS401 before noon. Make sure that you write your and my name and the course and section number on the front page. Late submissions will not be accepted. Your homework score is part of your final grade. Example solutions for selected problems can be found in the solutions section after the due date. Feel free to ask me for solutions for specific problems you could not solve.

Be prepared for 5-minutes in-class quizzes that count toward your final grade. These quizzes will not be announced and there are no make-up quizzes. Books, notes, and electronic devices are not permitted during quizzes.

There will be 2 midterm exams and a final exam which contribute to your final grade. Each exam will be announced in class and appear online in the course schedule. Make-up exams will be given only under exceptional circumstances and if you contact me in advance. Books, notes, and electronic devices are not permitted during exams. Example solutions for the exams can be found in the solutions section after each exam.

To gain credit your answers must be clearly presented. Your work must show how you proceeded to find the answer or why your answer is correct. Scratch work should be clearly separated from what is to be graded and the final result should be marked by drawing a rectangle around it.

The contributions to your total score will be weighted as follows.

Contribution | Homework + Quizzes | 2 Midterm Exams | Final Exam |
---|---|---|---|

Weight (final grade) | 30% | 2 x 20% | 30% |

Weight (6-week grade) | 50% | 1 x 50% | NA |

Your total score will be truncated to an integer percentage and determines your final grade as follows.

Total Score | 0-59% | 60-69% | 70-79% | 80-89% | 90-100% |
---|---|---|---|---|---|

Letter Grade | F | D | C | B | A |

Curving may be applied in form of a linear adjustment to all scores on a particular exam. I reserve the right to decide borderline cases based on class attendance and subjective impressions such as effort and conscientiousness.

Your starting points are the textbook and the lecture. It is easier to follow the lecture if you have seen the material before and presented from a slightly different point of view. I strongly recommend that you read each section in your textbook at home before it is covered in class. Try to isolate what you do not understand and be prepared to ask questions during the lecture.

Do not hesitate to ask questions. If something is unclear to you in class, just ask. You can be sure that many of the other students have the same question but do not dare to ask. If you let me know what your problems are, I can adapt the lecture and make it easier for you to follow. There are no stupid questions. On the contrary, asking the right question is often an important step in the process of solving a problem.

The importance of working on example problems can not be overemphasized. Try to work on the homework problems intensively and pick additional similar problems from your textbook.

Discussion is crucial to understand mathematics. I strongly encourage you to discuss both the material covered in class and your solutions of the homework problems with other students in your section. The best way to check your own understanding of a subject is to explain it to someone else.

Ideally you solve the homework problems on your own or working with other students. If you realize that you do not understand the homework problems, seek help immediately. With a backlog of not understood material it extremely difficult to catch up with the class again.

Free tutoring and other services for this and similar mathematics courses are provided by the Mathematics Learning Resource Center (MLRC). For more information, see http://www.math.okstate.edu/mlrc.

You are always welcome to see me in my office hour or contact me by email if you have any questions or problems. If my office hours do not fit your schedule, please contact me by email for an appointment.

The following course schedule is preliminary.

Class Meeting |
Date | Sections from Textbook |
Subject | Homework Assignment |
Due Date |
---|---|---|---|---|---|

1 | 08/17 | 1.2 | Real n-space | 4,5,6,9,10,12,19,23 | 08/19 |

2 | 08/19 | 1.3 | Distance | 1,5,6,9,10,13,17 | 08/21 |

3 | 08/21 | 1.4 | Functions | 1,2,3,7,10,16 | 08/24 |

4 | 08/24 | 1.5 | Topology | 1,2,5,6,9,14,16,17 | 08/28 |

5 | 08/26 | 1.5 1.6 | Topology Sequences | ||

6 | 08/28 | 1.6 | Continued | 2,7,11,12,21(b),32 | 08/31 |

7 | 08/31 | 1.7 | Monotonic-Sequence Property | 1,3,4,7,9,10 | 09/02 |

8 | 09/02 | 1.8 | Compactness | 1-6 | 09/04 |

9 | 09/04 | 2.2 | Continuity | 2,4,5,7,10,13 | 09/09 |

09/07 | Holiday | ||||

10 | 09/09 | 2.2 | Continued | ||

11 | 09/11 | 2.3 | Uniform Continuity | 1,5,6,7 | 09/14 |

12 | 09/14 | 2.4 | Implications of Continuity | 3,5,8,9 | 09/16 |

13 | 09/16 | 2.4 | Continued | ||

14 | 09/18 | Review for Midterm 1 | |||

15 | 09/21 | MIDTERM 1 | |||

16 | 09/23 | 2.5 | Limits of Functions | ||

17 | 09/25 | 2.6 2.7 | Discontinuities Inverses of Univariate Functions | ||

18 | 09/28 | 3.2 | Mean Value Theorems and L'Hospital's Rule | 1,3,5,9,23,24,25 | 09/30 |

19 | 09/30 | 3.3 | Derivatives of Multivariate Functions | ||

20 | 10/02 | 3.3 | Continued | 1,3,4,7,8,11 | 10/05 |

21 | 10/05 | 3.4 | Differentiation of Composite Functions | ||

22 | 10/07 | 3.4 | Continued | 8,10,11,12,16,18 | 10/12 |

10/09 | Students' Fall Break | ||||

23 | 10/12 | 3.5 | Taylor's Theorem | 4,5,6,7,17,18 | 10/14 |

24 | 10/14 | 3.6 | Extremal Problems | ||

25 | 10/16 | 3.6 | Continued | X1,X2,4,5,9,10, | 10/19 |

26 | 10/19 | 4.2 | Definite Integrals | ||

27 | 10/21 | 4.2 | Continued | 3,5,8,9,10,14 | 10/23 |

28 | 10/23 | 4.3 | Evaluation of Definite Integrals | ||

29 | 10/26 | 4.3 | Continued | 2a,5,6,13,16,23 | 10/28 |

30 | 10/28 | Review for Midterm 2 | |||

31 | 10/30 | MIDTERM 2 | |||

32 | 11/02 | 4.4 | Substitution in Multiple Integrals | ||

33 | 11/04 | 4.5 | Improper Integrals | ||

34 | 11/06 | 4.5 | Continued | 2,4,6,9 | 11/11 |

35 | 11/09 | 4.5 | Continued | ||

36 | 11/11 | 5.2 | Infinite Series | 2,3a,5ab,6,9 | 11/13 |

37 | 11/13 | 5.3 | Conditionally Convergent Series | 2cdfijm,3,6bc,9 | 11/16 |

38 | 11/16 | 5.4 | Double Series | ||

39 | 11/18 | 6.2 | Series and Sequences of Functions | ||

40 | 11/20 | 6.2 | Continued | 1,4,7,9,10,11,12,14 | 11/30 |

41 | 11/23 | 6.2 | Continued | ||

42 | 11/25 | Thanksgiving Break | |||

11/27 | Thanksgiving Break | ||||

43 | 11/30 | 6.3 | Power Series | ||

44 | 12/02 | Review for the Final Exam | |||

45 | 12/04 | Review for the Final Exam | |||

46 | 12/09, 10:00-11:50am | FINAL EXAM |

**X1** Apply a coordinate change to f(x,y)=xy+x^{2}y+y^{3} that diagonalizes the Hessian at 0.
What type of critical point is 0?

**X2** Apply Sylvester's theorem to make a statement about the eigenvalues of the Hessian at 0 of f(x,y,z)=2x^{2}-2xy+2y^{2}+2yz+z^{2}.
What type of critical point is 0?

- Assignment 1.7
- Assignment 1.8
- Assignment 2.2
- Assignment 2.4
- Assignment 3.2
- Problem 3.3.7
- Assignment 4.3
- Midterm 1
- Midterm 2
- Final Exam

I will respect OSU's commitment to academic integrity and uphold the values of honesty and responsibility that preserve our academic community. For more information, see http://academicintegrity.okstate.edu.

This syllabus may be subject to future changes and it is your responsibility to be informed. Any change of the syllabus will be announced in class and appear online.