## Advanced Calculus Homework Video

### Announcements

- The final exam has been scheduled on April 12 (Saturday), at 12:00 noon, in MATH 104.
- Math final exam packs (usually, 5 past final exams with solutions) can be purchased from the UBC Math Club. There are no exams packs for Math 227, but Math 317 exams should be similar.
- I will have office hours before the final exam on Friday, April 11, 11-1 pm.
**Syllabus for Chapter 17**(these are the topics that we actually covered in class)- Section 17.1: k-forms (all of it). Practice problems: 1-8.
- Section 17.2: differential k-forms and exterior derivative. Skip "1-forms and Legendre transformations" and "Maxwell's Equations Revisited." Practice problems: 1-13.
- Section 17.3: Manifolds and integration. We used a slightly different (but equivalent) definition of a manifold. The important parts are "Integration in n dimensions" and "Parametrizing and integrating over a smooth manifold." Practice problems: 5, 6.
- Section 17.4: Oriented manifolds. The main part is "Integrating a differential form over a manifold" (in class, I also showed how this extends the "usual" line and surface integrals). Practice problems: 5, 6.
- Section 17.5: Generalized Stokes's Theorem. We skipped the proof and focused on the special cases in Examples 3, 4, 5. Practice problems: 3-6. (Use Stokes's Theorem, that's what it's for :) )

- Homework #5 solutions are posted here.
**Update re: practice problems**: We will be skipping some of the more computational exercises from Sections 16.4. 1-15 are good practice problems (4,6,11 are HW problems, 12 was done in class). You can skip 16-18 and 21-30.**Midterm 2 was on Wednesday, March 12,**and covered:- Midterm 2 solutions are posted here
**Midterm 1 was on Wednesday, Feb. 5,**and covered the following:- Midterm 1 solutions are posted here

## Mathematics 227 (Advanced Calculus II), Winter/Spring 2014

**Section 201: MWF 12:00-12:50, MATH 103**

**Lecturer: Prof. I. Laba**

- Math Bldg 200, (604) 822 4457, ilaba@math.ubc.ca
- Office hours: Monday 1-2, Wednesday 3-4, Friday 11-12, in MATH 200.
- The best way to contact the instructor is by email. Please note that email received on evenings and weekends will be answered on the next business day.
- If you cannot attend regular office hours due to schedule conflict, please make an appointment in advance. Drop-ins and same-day requests for appointments cannot always be accommodated.

**Prerequisites:**A score of 68% or higher in MATH 226.

**Course web page:**http://www.math.ubc.ca/~ilaba/teaching/math227_S2014

**Homework assignments**will be posted here.

**Textbook:**Robert A. Adams and Christopher Essex, Calculus: Several Variables (or Calculus: A Complete Course), 8th ed. Pearson, 2013, ISBN 978-0-321-87741-3.

**Course topics:**

**Vector-valued functions and curves (Chapter 11)**: curves, velocity, acceleration, arc length, curvature, tangent, normal, binormal, planetary motion.**Vector fields and line integrals (Sections 15.1-15.4):**vector fields, field lines, conservative fields, line integrals.**Surface integrals (Sections 15.5-15.6):**surfaces, surface area, flux integrals.**Integral theorems (Chapter 16):**gradient, divergence and curl, vector identities, divergence theorem, Green's theorem, Stokes' theorem, applications.**Differential forms (Chapter 17):**differential forms, exterior derivative, generalized Stokes' Theorem (if time permits).

**Your course mark**will be based on homework (10%), two midterm exams (20% each), and the final exam (50%). The grades may be

**slightly**scaled at the end of the course.

**Examinations:**There will be two in-class 50-minute midterms, scheduled on Wednesdays, February 5 and March 12, and a 2.5 hour final exam in April. The date of the final examination will be announced by the Registar later in the term. Attendance at the final examination is required, so be careful about making other committments (such as travel) before this date is confirmed. All examinations will be strictly closed-book: no formula sheets, calculators, or other aids will be allowed.

**Homeworks:**There will be 5 homework assigmnents, due tentatively on Wednesdays, January 15, January 29, February 26, March 19, and Monday, March 31. Each homework will be announced and posted here at least a week in advance. The homeworks are to be handed in at the

**beginning**of class. If you cannot come to class, you may drop off your homework at your instructor's office prior to the start of class. Late assignments will not be accepted. Solutions will be posted on the course webpage immediately after the lecture. To allow for minor illnesses and other emergencies, the lowest homework score will be dropped.

**Academic concession:**Missing a midterm, or handing in a homework after the deadline, will result in a mark of 0. Exceptions may be granted in two cases: prior consent of the instructor, or a

**documented**medical reason. Your course mark will then be based on your remaining coursework.

Additional course related resources: General links:

- Please read the UBC policy on Student Conduct and Discipline.
- Mathematics Learning Centre: The Math Department runs a drop-in tutorial centre for undergraduate Math courses, staffed by Graduate Teaching Assistants. This centre is located in Rooms 300, 301, and 302 in the Leonard S. Klinck (LSK) Building, and is open Monday through Friday, 9:00am to 7:00pm. Check the website above for any changes to hours and announcements. All tutors provide assistance with first- and second-year calculus and linear algebra and will attempt to help with any undergraduate Math course. In addition to regular assistance, the MLC offers Quick Help for students who are looking for fast support for minor snags. There is no charge for the services MLC provides.
- Past final exam database
- UBC Math Club, located in Math Annex 1119, sells math exam packages (old exams together with solution sets) for a nominal price before each final exam session.

[Mathematics Department] [University of British Columbia]

## MAT25 Advanced calculus - Spring 2011

## Quick Links

## Homework assignments

All assignments are due at the beginning of your discussion section on the specified day. Late homework will not be accepted. If you are unable to come to the section, it is your responsibility to contact your TA to make an alternative arrangement for handing in the homework BEFORE the deadline.## News and announcements

- (6/8/11) Have a great summer!

- (6/8/11) Final grades have been uploaded to the system and should be visible soon on SmartSite/SIS. Here is an explanation of how the grades were computed: a total score (in the range 0-100) was computed as a weighted average of the midterms, final, and homework assignments, as described in the syllabus (this total score can be seen on the course SmartSite grades, under "Weighted average"). The lowest homework score was dropped when computing the homework component of the grade. The letter grades were then computed from the total score according to the following cutoff ranges:
A 81-100 A- 80-80.999 B+ 77-79.999 B 68-76.999 B- 65-67.999 C+ 63-64.999 C 58-62.999 C- 56-57.999 D+ 53-55.999 D 49-52.999 D- 48-48.999 F 0-47.999

The mean total score was 63.8, and the highest total score was 89.24. The following table shows the distribution of the letter grades:A range (A, A-) 17 students (18.7%) B range (B+, B, B-) 26 students (28.6%) C range (C+, C, C-) 27 students (29.7%) D range (D+, D, D-) 10 students (11.0%) F 11 students (12.1%) - (6/2/11) Click here for the solutions to the practice problems.
- (5/31/11) Click here for a set of practice problems for the final exam. Solutions will be posted later this week.
- (5/10/11) The grades for the midterm exam have been posted on SmartSite. The average grade was 63, the median grade was 65, and the standard deviation of the grades was 19. Here is a chart showing the distribution of the grades:

- (4/25/11) Here is some useful information about next week's midterm exam:
**Exam time and place:**Monday, May 2 at 9 a.m., Wellman 216. Come on time!**Exam duration:**45 minutes.**Exam type:**closed-book exam; no written material or electronic devices may be used. Definitions of important concepts such as convergence of a sequence to a limit, boundedness etc. will be given in the exam as needed.**Material to be covered:**all material covered in lectures, the homework and discussion section up to and including the lecture of Wednesday, April 27.**What to bring:**student ID and writing utensils (no need to bring an exam blue book).**Recommendations for studying:**Read the relevant sections in the textbook and in your class notes, with a focus on attaining a high level of understanding (as opposed to memorizing). Review the homework and its solutions. Solve the practice problems in homework assignment #5.

- The Student Disability Center asks that students interested in serving as paid notetakers for this course please contact Russ Zochowski at rjzochowski@ucdavis.edu. Notetakers are paid a stipend of $25 per unit. Students are asked to put notetaker, the course title and number, and instructorâ€™s name in the subject lines of their emails

## General Information

Instructor details: | Dan Romik |

Mathematical Sciences Building 2218 | |

tel: 530-554-1498 | |

email: | |

For more information go to my home page | |

Lectures: | MWF 9:00-9:50 at Wellman 216 |

Sections: | • Section A01 (Andrew Farris): T 4:10-5:00 at Olson 147 • Section A02 (Tim Wertz): T 5:10-6:00 at Wellman 115 |

Office hours: | F 10:30-12:30 (at my office, MSB 2218) |

TAs: | Andrew Farris (MSB 1111 -- office hours: M 2-4 at MSB 2117) |

Tim Wertz (MSB 2232 -- office hours: T 1-2, F 2-3) |

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