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Honors Multi­variable Calculus (110.211) Spring 2015

Instructor:Carl McTague
Lectures:MW 12–1:15pm in Krieger 304
Office Hours:T 3–5pm in Krieger 212
TA:Apurva Nakade
Recitation:F 12–12:50pm in Krieger 308
Text:SJ Colley, Vector Calculus, 4th Ed., Pearson, 2012 (Amazon).

Announcements

27 JanThere is an inexorable force in the cosmos where time and space converge. A place beyond man’s vision but not his reach. It is the most mysterious and awesome point in the universe.

Schedule

LectureDateTopicReadingAssignmentDue Date
1Jan 26Vector operations§1.1:
§1.2:
§1.3:
§1.4:

12, 16.
16, 25.
4, 17, 18, 20.
228Matrix multiplication§1.5:
§1.6:
2, 20, 34, 39.
10, 18, 30–32.
Feb 2
3Feb 2Spherical & Cylindrical coordinates§1.7:
§2.1:
24, 32.
4, 18, 42, 44.
44Limits, Derivative§2.2:6, 18, 46, 53.Feb 9
59Derivatives, cont’d§2.3:
§2.4:
10, 16, 24, 30, 36, 59.
2, 6, 22.
611Chain rule§2.5:2, 8, 22, 24, 28.Feb 16
716Implicit function theorem
Paths
§2.6:
§3.1:
§3.2:
§3.3:
8, 12, 20, 26, 40, 44.
10.
6, 10, 14, 18.
2, 22, 28.
818Curvature, div, curl§3.4:5, 8, 12, 14, 31.Feb 23
923Taylor’s formula in several variables§4.1:8, 12, 16, 32.
1025ReviewMar 9
Mar 2FIRST MIDTERM (lectures 1–8)
114Extreme values§4.2:12, 18, 20, 28, 36.Mar 9
129Lagrange multipliers§4.3:4, 8, 12, 22, 38.
1311Double integrals
Changing the order of integration
§5.1:
§5.2:
2, 4, 8.
6, 12, 20, 28.
Mar 23
16–22Spring Break
1423Order of integration
Triple integrals
§5.3:
§5.4:
4, 14, 16, 18.
8, 14, 20.
1525Change of variables§5.5:2, 4, 8, 16, 26, 34.Apr 6
1630Path & line integrals
Conservative vector fields
§6.1:
§6.3:
4, 14, 24, 34.
2, 6, 18, 22.
Apr 6
17Apr 3Green’s theorem§6.2:8, 10, 14, 16.
186Parametrized surfaces§7.1:2, 10, 12, 24, 26, 28.
198Surface integrals§7.2:4, 6, 8, 10, 16, 22, 28.Apr 20
13SECOND MIDTERM (lectures 9–16)
2015Stokes’s and Gauss’s theorems§7.3:4, 6, 10, 12, 16, 18, 22, 27, 31, 34.
2120Introduction to differential forms§8.1:4, 10, 14, 18.
2222Manifolds, integration of k-forms§8.2:2, 6, 10, 12.Apr 27
2327Generalized Stokes’s theorem§8.3:2, 4, 6, 8, 10, 12.
2429Loose ends
May 12FINAL EXAM (lectures 1–24)

Syllabus

Key topics will include:

Vectors and the geometry of Euclidean space, differentiation in several variables, vector-valued functions, maxima and minima in several variables, multiple integration, line integrals, surface integrals and vector analysis, and vector analysis in higher dimensions.

Grading: The grading scheme will be:

Homework 30%Midterm Exams 30%Final Exam 40%

Homework: Your assignments will be posted above. They will be collected in lecture on Mondays and returned in recitation. Late homework will not be accepted except in extraordinary circumstances, agreed to in writing with the instructor in advance. You are encouraged to discuss homework problems with one another. However, each of you must write up your solutions independently, in your own words, without supervision or well-meaning influence from anyone else.

Midterm Exams will be in class on Mon 2 Mar and Mon 13 Apr.

The Final Exam will be in class 2–5pm Tues 12 May, further details nearer the time.

Absence: You are expected to attend class and take exams as scheduled. If you miss a midterm exam then you will get a zero for that exam. If you miss the final exam then you will automatically fail the course.

Disability: Any student with a disability who may need accommodations in this class must obtain an accommodation letter from Student Disability Services, 385 Garland, (410) 516-4720, studentdisabilityservices@jhu.edu.

Ethics: Don’t get it WRONG, like Kant! Seriously though, cheating & other forms of academic dishonesty are corrosive & harmful to our university:

The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition.

Report any violations you witness to the instructor. You may consult the associate dean of student affairs and/or the chairman of the Ethics Board beforehand. See the guide on “Academic Ethics for Undergraduates” and the Ethics Board Web site for more information.


Copyright © 2015 by Carl McTague