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). |

27 Jan | There 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. |

Lecture | Date | Topic | Reading | Assignment | Due Date |
---|---|---|---|---|---|

1 | Jan 26 | Vector operations | §1.1: §1.2: §1.3: §1.4: | — 12, 16. 16, 25. 4, 17, 18, 20. | |

2 | 28 | Matrix multiplication | §1.5: §1.6: | 2, 20, 34, 39. 10, 18, 30–32. | Feb 2 |

3 | Feb 2 | Spherical & Cylindrical coordinates | §1.7: §2.1: | 24, 32. 4, 18, 42, 44. | |

4 | 4 | Limits, Derivative | §2.2: | 6, 18, 46, 53. | Feb 9 |

5 | 9 | Derivatives, cont’d | §2.3: §2.4: | 10, 16, 24, 30, 36, 59. 2, 6, 22. | |

6 | 11 | Chain rule | §2.5: | 2, 8, 22, 24, 28. | Feb 16 |

7 | 16 | Implicit 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. | |

8 | 18 | Curvature, div, curl | §3.4: | 5, 8, 12, 14, 31. | Feb 23 |

9 | 23 | Taylor’s formula in several variables | §4.1: | 8, 12, 16, 32. | |

10 | 25 | Review | Mar 9 | ||

† | Mar 2 | FIRST MIDTERM (lectures 1–8) | |||

11 | 4 | Extreme values | §4.2: | 12, 18, 20, 28, 36. | Mar 9 |

12 | 9 | Lagrange multipliers | §4.3: | 4, 8, 12, 22, 38. | |

13 | 11 | Double integrals Changing the order of integration | §5.1: §5.2: | 2, 4, 8. 6, 12, 20, 28. | Mar 23 |

— | 16–22 | Spring Break | |||

14 | 23 | Order of integration Triple integrals | §5.3: §5.4: | 4, 14, 16, 18. 8, 14, 20. | |

15 | 25 | Change of variables | §5.5: | 2, 4, 8, 16, 26, 34. | Apr 6 |

16 | 30 | Path & line integrals Conservative vector fields | §6.1: §6.3: | 4, 14, 24, 34. 2, 6, 18, 22. | Apr 6 |

17 | Apr 3 | Green’s theorem | §6.2: | 8, 10, 14, 16. | |

18 | 6 | Parametrized surfaces | §7.1: | 2, 10, 12, 24, 26, 28. | |

19 | 8 | Surface integrals | §7.2: | 4, 6, 8, 10, 16, 22, 28. | Apr 20 |

† | 13 | SECOND MIDTERM (lectures 9–16) | |||

20 | 15 | Stokes’s and Gauss’s theorems | §7.3: | 4, 6, 10, 12, 16, 18, 22, 27, 31, 34. | |

21 | 20 | Introduction to differential forms | §8.1: | 4, 10, 14, 18. | |

22 | 22 | Manifolds, integration of k-forms | §8.2: | 2, 6, 10, 12. | Apr 27 |

23 | 27 | Generalized Stokes’s theorem | §8.3: | 2, 4, 6, 8, 10, 12. | |

24 | 29 | Loose ends | |||

‡ | May 12 | FINAL EXAM (lectures 1–24) |

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