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Math 411, Spring 2012

Course Title: Advanced Calculus II

General

Course and Section: Math411 - 0201
Class Time: MWF 12:00-12:50
Class location: Math 0409
Instructor: Matthias Goerner
Office: Math Building 4101
Email: matthias at umd dot edu
Office Hours: M 2:30-3:00, W 2:30-4:00
Course page: http://math.berkeley.edu/~matthias/math411/

Problem Solving and Help Sessions

Instructor: Manjit Bhatia
Location: Math Building 4408
Email: mbhatia at math dot umd dot edu
Math 411 Times: M 2:00, TuWTh 4:00
Time frame: February 1st until May 10th

Syllabus


Required text: Advanced Calculus, Patrick M. Fitzpatrick, Second Edition
WednesdayJanuary25th: Chapter 10.1 - Rn as vector space (Mike Boyle's notes)
FridayJanuary27th: Chapter 10.2 - Convergent sequences
MondayJanuary30th: Chapter 10.3 - Topology on Rn (Lecture Notes)
WednesdayFeburary1st: Chapter 11.1 - Continuous Functions (Lecture Notes)
FridayFebruary3rd: Chapter 11.2 - Compactness and uniform Continuity
MondayFebruary6th: Chapter 11.3 - Path-wise Connectedness
WednesdayFebruary8th: Chapter 11.4 - Connectedness and Intermediate Value Theorem
FridayFebruary10th: Chapter 12.1 - Metric spaces, induced topology, and the uniform metric on the space of continuous functions
MondayFebruary13th: Chapter 12.2 - Completeness and Contraction Mapping Principle
WednesayFebruary15th: Chapter 12.3 - Examples of Ordinary Differential Equations, some with Lipschitz condition violated resulting in non-uniqueness
FridayFebruary17th: Chapter 12.3 - Picard Lindelöf iteration to prove existence and uniqueness of solutions to Ordinary Differential Equations, see also wikipedia, Original Paper by Lindelöf
MondayFebruary20th: Solutions to selected homeworks Cheat sheat on Chapter 11.3 and 11.4, Notes on Chapter 11.1 and 11.2, Solutions to Problem 11 in 10.3, Solutions to Problem 5 in 11.4
WednesdayFebruary22nd: Chapter 13.1 - Limits of functions in several variables
FridayFebruary24th: Chapter 13.2 - Partial Derivatives
MondayFebruary27th: Chapter 13.3 - Directional Derivative
WednesdayFebruary29th: Chapter 14.1 - Linear approximations
FridayMarch2nd:Review for First Midterm (Sample problem)
WednesdayMarch7th: Chapter 14.2 - Quadratice Functions and Hessian Matrix
FridayMarch9th: Chapter 14.3 - Detecting local extrema through Hessian Matrix
MondayMarch12th: Review Linear Algebra, First and Second order approximations, chain rule
WednesdayMarch14th: Chapter 16.1 - Inverse Function Theorem
FridayMarch16th: Chapter 16.1 - Examples of the Inverse Function Theorem and Newton's Method
MondayMarch26th: Chapter 17 - Implicit Function Theorem: Examples
WednesdayMarch28th: Chapter 17 - Implicit Function Theorem: Statement
FridayMarch30th: Chapter 17 - Implicit Function Theorem: Proof
MondayApril2nd: Chapter 17 - Lagrange Multipliers
WednesdayApril4th: Examples of Lagrange Multipliers (Boltzman distribution, see here and Sakurai, "Modern Quantum Mechanics"), Implicit Surfaces (torus, see wikipedia), Computation of Volumes (sphere, see wikipedia)
FridayApril6th: Introduction to Integration, computation of Volumes of sphere, intersection of two cylinders, and torus
MondayApril9th:Integration Notes
WednesdayApril11th:Mock Midterm
MondayApril16th:Properties of the Riemann Integrals, Proofs
FridayApril20th:Properties of the Riemann Integrals, Proofs continued
MondayApril22nd:Axiomatic Characterisation and Upper-Lower-Darboux-Sum Definition of Riemann Integral
WednesdayApril24th:Riemann- and Lebesgue-measure zero. Theorem: Function is Riemann-integrable iff bounded, compact support and discontinuities have Lebesgue-measure zero.
FridayApril26th:Proof of Theorem (Notes)
MondayApril30th:Fubini's Theorem
WednesdayMay2nd:Change of Variables
FridayMay4th:Stoke's Theorem
MondayMay7th:Stoke's Theorem
WednesdayMay9th:Review of Final Exam Problems (Exam 1, Exam 2, Practice problems)

Grading

Gradesheet is here.
  • Final: 30%
  • Midterms: 20% each
  • Quizzes: 15% total
  • Homework: 15% total

Exams

To practice for the second midterm: Mock Midterm.

Topics for the final exam.

Quizzes

Quizzes will be biweekly.

Homeworks

Will be assigned weekly and posted here.
  • Homework 1 (due Wednesday, February 1st)
    in 10.1: 1, 2, 4, 5, 6, 7, 9, 10
    in 10.2: 1, 3, 5
  • Homework 2 (due Wednesday, February 8th)
    in 10.3: 1, 2, 7, 10, 11
    in 11.1: 4, 5d, 9, 10
    in 11.2: 3, 4, 6
  • Homework 3 (due Wednesday, February 15th)
    in 11.3: 1, 2 (and give a counterexample when replacing pathwise-connected by convex), 4, 6, 8
    in 11.4: 1, 3, 5
  • Homework 4 (due Wednesday, February 22nd)
    in 12.1: 1, 2a, 3, 10
    in 12.2: 1, 2, 6
    in 12.3: 6
    and these problems: HW4
  • Homework 5 (due Wednesday, February 29th)
    in 13.1: 1, 2, 4, 7, 10
    in 13.2: 1a, 1b, 3, 4, 11
  • Homework 6 (due Friday, March 9th)
    in 13.3: 1a, 1b, 2, 3, 4, 10, 11
    in 14.1: 1, 2, 6, 8, 9
  • Homework 7 (due Wednesday, March 14th)
    in 14.2: 1, 3
    in 14.3: 1a, 1c, 3, 5, 7, 8, 9, 10, 11c
  • Homework 8 (due Wednesday, April 4th): HW8
  • Homework 9 (due Wednesday, April 18th): HW9
  • Homework 10 (due Monday, April 30th): HW10
  • Homework 11 (due Monday, May 7th): HW11

Other

Missed Quiz/Homework/Midterm Policy: There will be no makeup quizzes in any circumstances, nor will late homework be accepted in any circumstances. However, the two lowest homework and quiz grades will be dropped at the end of the semester.
Permission to write a makeup midterm may be granted (or other arrangements made) if the absence is in accordance with the campus policy. The reason for absence must be unavoidable, documented, and reported to me as early as possible.

Students with disabilities: The University of Maryland provides upon request appropriate academic accommodations for qualified students with disabilities. Students who seek special accommodations due to disabilities must first set up an appointment with the Disability Support Services (DSS). Students should download the DSS registration forms and bring appropriate documentation to the DSS office (Shoemaker 0126) prior to the meeting.

Academic Integrity: You are expected to abide by the University's policy on academic integrity. All cases of academic dishonesty will be referred to the Office of Student Conduct. Academic dishonesty includes cheating on quizzes and exams. For the purposes of this course it is permissible (even encouraged) to work together on homework assignments, however all written assignments must be written entirely in your own words.

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