MATH 402 Advanced Calculus II - MATH 402 002 CRN6016.

Hybrid Instructional Method: Face-to-Face Plus: 2:00 pm - 3:15 pm T SMLC B81, Remote Set Day/Time 2:00 pm - 3:15 pm R Remote Instruction Microsoft Teams.

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Please note the following information. You need to be registered for the course with a @unm.edu email. Any other email will disable features of Microsoft Teams. I will send you by email a link to join the MATH402 team. Please follow it in order to request access. You can find the link to join the team in Canvas as well. After you join the class MS Team. I will drop from the class all students who do not request access to Microsoft Teams by Friday, January 27. The remote class on Thursday will be through MS Teams. Homework, including submission, detailed topics list of the covered material and all remaining course information can be found in the class MS OneNote. This page contains only the basic information for the class, use the class MS Teams and OneNote for an up to date information throughout the semester.

 

Our classroom and our university should always be spaces of mutual respect, kindness, and support, without fear of discrimination, harassment, or violence. Should you ever need assistance or have concerns about incidents that violate this principle, please access the resources available to you on campus. Please note that, because UNM faculty, TAs, and GAs are considered "responsible employees" by the Department of Education, any disclosure of gender discrimination (including sexual harassment, sexual misconduct, and sexual violence) made to a faculty member, TA, or GA must be reported by that faculty member, TA, or GA to the university's Title IX coordinator. For more information on the campus policy regarding sexual misconduct, please see: https://policy.unm.edu/university-policies/2000/2740.html.

Support: LoboRESPECT Advocacy Center and the support services listed on its website, the Women's Resource Center and the LGBTQ Resource Center all offer confidential services and reporting.

 

Covid Policies

 

Instructor: Dimiter Vassilev     Office : SMLC 326  Email: vassilev@unm.edu  Phone Number: 505 277 2136 

 

Office Hours: I will have office hours through Microsoft Teams on T 10:00am-11:00am & Th 1:00pm-2:00pm. You can also send me an email to arrange a meeting or stop by my office if you have a quick question.

 

Student Attendance: Students are expected to attend all meetings of the classes in which they are enrolled. A student with excessive absences may be dropped from a course by the instructor with a grade of W or the student may receive a grade of F at the end of the semester. Absences due to illness, or to authorized University activity such as field trips, athletic trips, etc., are to be reported by the student to his/her instructor(s) and to the Dean of Students Office. If a student is unable to contact his/her instructor(s) the student should leave a message at the instructor's department. The reporting of absences does not relieve the student of responsibility for missed assignments, exams, etc. The student is to take the initiative in arranging with his/her instructor(s) to make up missed work, and it is expected that the faculty member will cooperate with the student in reasonable arrangements in this regard. Please, see https://pathfinder.unm.edu/campus-policies/class-absences-and-student-attendance.html for more details.

 

MATH402 Catalog Course Description. Generalization of 401/501 to several variables and metric spaces: sequences, limits, compactness and continuity on metric spaces; interchange of limit operations; series, power series; partial derivatives; fixed point, implicit and inverse function theorems; multiple integrals. Prerequisite: MATH401

 

Text: Introduction to Analysis, An, 4th edition, William Wade

 

Semester Deadline Dates: https://registrar.unm.edu/semester-deadline-dates/spring-2023.html

 

Collaboration.  I encourage you to work with your peers and me on the homework, provided you write up and submit your own solutions in your own words. I will have in-person office hour if you prefer to stop by my office. I will also have an office hour through Microsoft Teams.

 

Homework.  Homework is due every Thursday at the beginning of the class in MS Teams. I encourage you to work on the homework with your classmates, but you are required to write up your own solutions in your own words. To help the grader, please write your solutions neatly using correct grammar and mathematical notation (no points will be given for work that the reader cannot follow).   The ten best homework grades will be used in computing the homework score. Please do not turn-in late homework! The syllabus also lists recommended homework problems.  These are NOT to be handed in. Work as many as it takes for you to understand the material.  You should see me as early and as often as necessary if you are having difficulties with the homework problems.

 

Exams. The exam dates are given in the schedule posted in the class OneNote. The Final Exam date is set by UNM, see https://schedule.unm.edu/final-exams/final_exam/spring2023.pdf. No makeup exams will be given unless you contact me ahead of time with a documented “university authorized absence”, including, but not limited to illness, family emergency, active participation in scholarly or athletic events. Exams may include some multiple-choice questions testing very specific skills or concepts. The exams will be predominantly based on the homework and in-class problems. Students having conflicts with the examination schedule must notify me before TBD. Any student having more than three examinations scheduled in any one day may notify the instructor of the last examination listed. If notified before TBA, I shall make arrangements to give a special examination. Conflicts arising as a result of scheduling out of normal hours-pattern or day sequences must be resolved by the instructor of the off-pattern courses.        

 

Assessment (including grading). You should think of most of the work during the semester including homework and the midterm exams as means for feed-back and learning. This will be reflected in the grading policy where I will drop about 25%-30% of the lowest homework. The Final Exam will be an opportunity for a major grade change by  showing a cumulative  achievement of the course objectives. There will be some opportunities for bonus points. It is essential that you participate in class and keep tidy class notes in order to benefit from in-class opportunities on receiving bonus points. The final grade will be determined using the following weights: homework (30%), two midterms (35%), a final exam (35%), bonus points.  The Final Exam score will replace any of the midterm scores that is lower than the Final Exam score. Although a small curve might be used, 90%, 80% or 70% of the possible maximum points guarantees at least an A, B or C, respectively.

 

  Accommodations: UNM is committed to providing equitable access to learning opportunities for students with documented disabilities. As your instructor, it is my objective to facilitate an inclusive classroom setting, in which students have full access and opportunity to participate. To engage in a confidential conversation about the process for requesting reasonable accommodations for this class and/or program, please contact Accessibility Resource Center at arcsrvs@unm.edu or by phone at 505-277-3506.
Support: Contact me by email or in office hours and contact Accessibility Resource Center (https://arc.unm.edu/) at arcsrvs@unm.edu (505) 277-3506.

 

Topics and Schedule. Week of:

  1. 1/16/23 Chapter 6 Infinite series of real numbers - tests for convergence.
  1. 1/23/23 Chapter 7.1 Uniform convergence of sequences & begin 7.3 Power series.
  1. 1/30/23 Chapter end of 7.3 Power series & 7.4 Analytic functions.
  1. 2/6/23 Chapters: finish Analytic functions 7.4, Metric spaces 10.1 & Limits in Euclidean space 9.1.
  1. 2/13/23 Convex sets & functions, Jensen's inequality, (generalized) AM-GM, Young's, Holder's and Minkowski's inequalities. Continue 10.1 & 10.2, 8.1, 8.3, 9.1.
  1. 2/20/23 Exam 1 on 2/21/23. Adherent points and closure of a set. Compact metric spaces, sequential compactness, total boundedness. Lindelof's theorem.  Characterization of compactness. Separable spaces, dense sets. Ch's: 9.1, 9.5, 10.3, 10.4.
  1. 2/27/23 Subspaces, totally boundedness and subspaces, complete subspaces, compact spaces and subspaces. The Heine-Borel theorem in Euclidean space. Ch's: 9.2, 9.5. Application of compactness - contraction maps and fixed points; nowhere dense sets; Baire's category theorem. Connected spaces, Chapters 8.3, 10.5.
  1. 3/6/23 More on connected sets, Chapters 8.3, 10.5, path-connected sets.  Cluster points, limits of functions, Chapters 9.3, 10.2. Continuous functions, Chapters 9.4, 10.6. 
  • 3/13/23 Spring Break
  1. 3/20/23 Continuous functions defined on compact sets, homeomorphism theorem, uniform continuity, uniform convergence of series defined on a metric space, integrals depending on a parameter, Ch's 10.4, 10.6, 11.1. Differentiability of vector valued functions Ch's 11.1 and 11.2.
  1. 3/27/23 Continue Differentiability of vector valued functions Ch's 11.1, 11.2, 11.3 and 11.4: differentiability and partial derivatives, matrix and component expressions of the derivative, the chain and other rules for differentiation, continuously differentiable functions. 4/3/23 Exam 2 on April 4
  1. 4/10/23 The Mean Value Inequality (MVI), Derivatives of higher order, Taylor's formula, The inverse function theorem: Ch. 11.5, 11.6
  1. 4/17/23 Jordan regions Ch. 12.1; sets of (Lebesgue) measure zero, compact sets of Lebesgue measure zero and of (Jordan) volume zero; images of sets of measure zero under continuously differentiable functions Ch. 12.2 + notes.
  1. 4/24/23 The Riemann integral - definition and properties, relation to Jordan volume (content); Lebesgue's theorem Ch. 12.2 + notes.; Fubini's theorem 12.3; Change of variables Ch. 12.4.
  1. 5/1/23 Ch. 13 Integral formulas - surface integral over of a function over a piece-wise surface; orientable surfaces, flux of vector field; line integrals and circulation of vector field along a closed curve. The divergence theorem and the integration by parts formula; Stokes' theorem (13.6)

Final Exam, Tuesday, May 9, 10am - 12pm.