MATH 417
-- Fall 2017:Advanced Calculus I |

Time: MWF 12-12:50 pm - Location: Engineering B105

Instructor: Gerhard Dangelmayr, WB 116; 491-3332; e-mail: gerhard@math.colostate.edu

Office Hours: WRF 1:10pm to 2:00pm in Weber 116

Required Text:Patrick M. Fitzpatrick, Advanced Calculus, 2nd edition, Thomson Brooks/Cole 2006, ISBN 0534376037

Catalog Description:Topology of Euclidean spaces, limits, derivatives and integrals on Euclidean spaces. Implicit functions and the implicit function theorem.

Prerequisites:MATH 369 and MATH 317.

Course Contents:This course extends real analysis of one variable, taught in MATH 317, to the case of several variables. The course material is similar to that of Calculus 3, MATH 261, but will be based on rigorous definitions and theorems with carefully formulated proofs and an abstract framework of understanding. While in one-variable analysis the basic number system is the real number line,

R, our basic number system will be now the Euclidean spaceR, where^{n}nis the number of variables on which a function may depend. Accordingly, the concepts of open and closed intervals need to be generalized to open and closed subsets ofR, which will provide the natural framework for generalizing the definition of convergence along with the continuity of functions and mappings. The study of differentiability of mappings between Euclidean spaces will lead to the derivative matrix together with the corresponding linear mapping called the differential, which generalize the concept of the tangent-line of one-variable analysis. Therefore, a first course in linear algebra (MATH 369 or equivalent) is the second prerequisite for MATH 417. The final subjects of the course are the multivariable version of the inverse function theorem and its generalization to the implicit function theorem. The foundation of multivariable integration theory and related topics will be the subject of MATH 418.^{n}

Tentative weekly schedule:(numbers refer to section numbers in the text):

WeekSectionsWeekSectionsWeekSectionsAug 21-25 10.1-2 Sep 25-29 14.1-2 Oct 30-Nov 3 16.2-3 Aug 28-Sep 1 10.3, 11.1 Oct 2-6 14.2-3, 15.1 Nov 6-10 17.1-2 Sep 4-8 11.1-2 Oct 9-13 15.1, RE Nov 13-17 17.3, RE Sep 11-15 13.1-2 Oct 16-20 15.1-2 Nov 27-Dec 1 17.3-4 Sep 18-22 13.2-3 Oct 23-27 15.3, 16.1 Dec 4-8 Review Thanksgiving Break: Nov 20 – 24; RE: Exam-Review on Wednesday and Exam on Friday

Homework:There will be seven homework assignments, due roughly every two weeks. Four selected problems from the homework assignment will be graded. Please formulate your solutions so that one can clearly understand the logic and line of reasoning. Include appropriate explanations and comments and avoid "Math-Steno". Please write neatly and state every problem number and the problem itself.

No late homework assignments will be graded. See theHomework Pagefor assignments and due dates.

Exams:There will be two in-class midterm exams and one final exam on the following dates:Midterm Exam 1: Friday, Oct 13, Engineering B 105

Midterm Exam 2: Friday, Nov 17, Engineering B 105

Final Exam: Wednesday, Dec 13, 4:10-6:10 pm in Engineering B 105

Allowed in Midterm Exams: 1 handwritten page(letter size)of notes;Allowed in Final:2 handwritten pages(letter size)of notes;

Not allowed in all exams: calculators, cell phones, tablets, laptops, books, typed notes.

Grading:

Homework assignments: 35% • Midterm Exam 1: 15% • Midterm Exam 2: 15% • Final Exam: 35%

Letter grades; A: 90 - 100, B: 80 - 89, C: 70 - 79, D: 60 - 69, F: 0 - 59

Important Remarks:

(1) Scores will be posted on Canvas.

(2) Do not expect exam, quiz, or homework assignment scores to be curved or dropped.

(3) There will be no exam or quiz retakes.

(4) Homework must be turned in on the date it is due, in class. It may also be turned in earlier. No late homework will be graded.

(5) No early examinations will be given.

(6) Do not take an exam if you are sick. Let your instructor know of your situation right away.

(7) No late examinations will be given, except in the case of a documented emergency (e.g. sickness) or university sponsored events.

Important Dates(see http://registrar.colostate.edu/faculty-staff/important-dates/):

Aug 21 First day of classes for Fall 2017

Aug 25 Restricted Drop Deadline

Aug 28 Add With Override Begins

Sept 6 Registration Closes for Most Courses

Oct 16 Course Withdrawal Period Ends

Oct 16 Repeat/Delete Requests due

Dec 8 Classes End; Last Day to Process a University Withdrawal (from all courses)