# Weekly exercises and tests in TMA4115 - Calculus 3, spring 2013

### Announcements

March 18th | There were some minor errors in the solutions for test 7. These have now been corrected . |
---|---|

February 14th | There has been a change in the exercise problems for test 5 (Feb 18-22) 1.6.7 is replaced with 1.6.9 |

### Exercises and tests

Each week there will be a test at the exercise sessions. **You must pass at least 8 of these 13 tests in order to take the exam**. Students who previously have had compulsory assignments approved in TMA4110/TMA4115 do not need to pass 8 tests in order to take the exam.

The questions on the tests will be very similar to the exercises listed below. It is recommended that you try to solve all the exercises before going to the exercise sessions. You can then ask the student assistant at the exercise session to explain the exercises you had problems with and/or discuss the exercises with the other students. The test will take place during the last 20 minutes of the exercise session. Permitted support material at the tests are the same as for the exam: A Citizen SR-270X or Hewlett Packard HP30S calculator, and Rottman's “Matematisk formelsamling”.

Students who, due to a chronic illness, a disability, an injury, or other valid causes, are not able to take the weekly tests can contact Louise Meier Carlsen louise [dot] carlsen [at] math [dot] ntnu [dot] no and make other arrangements. Since you only need to pass 8 of the 13 tests, it is not a problem if you are unable to take a couple of the tests, but if you have a valid excuse which you can back up with documentation (like a note from your doctor), then you can request to take a make-up test by sending an email to *Geir.Bogfjellmo (at) math.ntnu.no*. You must send your request within 3 days from the date you were suppose to the test. **There will not be any extra tests in addition to the 13 scheduled tests, so you must pass at least 8 of these 13 tests in order to take the exam.**

### Exercise groups

Information about the exercise groups and information about which exercise group you belong to can be found in the spreadsheet Exercise groups.

You can also see which exercise group you belong to on ovsys.

There has been a small change in the group assignment compared to the original assignment. This only affects MTNANO and MTTK. For all other programs the group assignment is unchanged. For MTNANO group 25 and group 26 have been merged into one group (25) with supervision in room S21. For MTTK, a new group (group 32) has been created.

There has been another change, which affects MTFYMA. Group 5 has been moved from room B23 to Room 524 in Høgskoleringen 3.

Finally, we have added a group to the MTDT, so there are now five groups for MTDT-students.

Note for MTIØT students: Unfortunately there was a mix-up which resulted in a schedule conflict. We have therefore had to change the group allocation for MTIØT students. MTIØT-EMIL students should attend either group 14 or 15 Tuesdays 14:15-16:00 (please consult the spreadsheet to see which group you are assigned to), and MTIØT-DATA students should attend group 20 Thursdays 10:15-12:00.

Some students do not belong to any of the groups described in the spreadsheet. For those students:
either contact the student assistant(s) of a group whose exercise sessions are scheduled at a time you may attend and ask to join his/her group, or send an email to the head student assistant (*juliedb (at) stud.ntnu.no*) and ask to be assigned to a group.

### Exercise Status

You can check how many tests you have passed by navigating to this page and entering your NTNU-username in the field.

### Exercise problems

Test | Dates | Sections in the book | Exercises | Test and solution |
---|---|---|---|---|

1 | Jan 21-25 | "Complex Numbers" (pages ix-xviii) | Exercises 1, 13, 17, 21, 25, 31, 33, 43, 45, 47, 53 and 55 on page xvii in the textbook. A copy of the exercises can be found here. Answers to these exercises (with the exception of exercise 45) can be found here. | Test 1 Solution |

2 | Jan 28 - Feb 1 | "Complex Functions" (pages xix-xxvii), and 4.1 and 4.3 in "Second-Order Equations" (pages xxxv-xlv and xlix-lv) | Exercises 3, 11, 31, and 35 on page xxvii in the textbook, Exercises 4.1.3, 4.1.7, 4.1.8, 4.1.18, and 4.1.21 on page xliv in the textbook, and Exercises 4.3.8, 4.3.15, 4.3.20 and 4.3.36 on page lv in the textbook. A copy of the exercises can be found here. Answers to the first 4 exercises can be found here, and answers to the last 9 exercises can be found here. | Test 2 Solution |

3 | Feb 4-8 | 4.4-4.7 in "Second-Order Equations" (pages lv-lxxxvi) | Exercises 4.4.13, 4.4.14 and 4.4.21 on pages lxii-lxiii in the textbook, Exercises 4.5.2, 4.5.7, 4.5.10, 4.5.20, 4.5.25 and 4.5.38 on pages lxxi-lxxii, Exercises 4.6.10 and 4.6.13 on page lxxvi in the textbook, and this exercise. Copy of the other exercises. Answers to the exercises (with the exception of exercise 4.4.14 and 4.4.21). | Test 3 Solution |

4 | Feb 11-15 | 1.1-1.3 in "Linear Algebras and Its Applications" (pages 1-34) | Exercises 1.1.1, 1.1.3, 1.1.7, 1.1.15 and 1.1.17 on page 10 in the textbook, Exercises 1.2.1, 1.2.3, 1.2.7, 1.2.17, 1.2.19 and 1.2.29 on pages 21-23 in the textbook, and Exercises 1.3.1, 1.3.5, 1.3.9, 1.3.13, 1.3.15, 1.3.21, 1.3.27(a-b), and 1.3.31 on pages 32-34 in the textbook. Answers to the exercises can be found at the end of the textbook. | Test 4 Solution |

5 | Feb 18-22 | 1.4-1.6 in "Linear Algebras and Its Applications" (pages 34-55) | Updated: Exercises 1.4.1, 1.4.7, 1.4.11, 1.4.15, 1.4.17, and 1.4.21 on pages 40-41, Exercises 1.5.5, 1.5.7, 1.5.13, 1.5.17 and 1.5.21 on page 47, and Exercises 1.6.1, 1.6.9 and 1.6.13 on pages 54-55. Answers to the exercises can be found at the end of the textbook. | Test 5 Solution |

6 | Feb 25 - March 1 | 1.7-1.10 in "Linear Algebras and Its Applications" (pages 55-90) | Exercises 1.7.1, 1.7.11, 1.7.15, and 1.7.31 on pages 60-61, Exercises 1.8.7, 1.8.9, 1.8.11, 1.8.15, 1.8.19, 1.8.23, and 1.8.31 on pages 68-70, Exercises 1.9.1, 1.9.7, 1.9.19, 1.9.27 and 1.9.29 on pages 78-79, and Exercises 1.10.1, and 1.10.9 on pages 86-87. | Test 6 Solution |

7 | March 4-8 | 2.1-2.3 in "Linear Algebras and Its Applications" (pages 91-116) | Exercises 2.1.1, 2.1.7, 2.1.9, 2.1.19 and 2.1.25 on pages 100-101, Exercises 2.2.1, 2.2.5, 2.2.19, 2.2.21 and 2.2.31 on pages 109-110, and Exercises 2.3.5, 2.3.7, 2.3.13, 2.3.23, 2.3.33 and 2.3.37 on pages 115-116. | Test 7 Solution (corrected) |

8 | March 11-15 | 3.1-3.3 in "Linear Algebras and Its Applications" (pages 163-187) | Exercises 3.1.1, 3.1.9, 3.1.17, and 3.1.37 on pages 167-168, Exercises 3.2.1, 3.2.3, 3.2.7, 3.2.11, 3.2.15, 3.2.21, 3.2.25, 3.2.29, 3.2.31, 3.2.39, and 3.2.41 on pages 175-176, and Exercises 3.3.5, 3.3.7, 3.3.15, and 3.3.29 on pages 184-185 in the textbook. | Test 8 Solution |

9 | March 18-22 | 4.1-4.4 in "Linear Algebras and Its Applications" (pages 189-225) | Exercises 4.1.1, 4.1.3, 4.1.5, 4.1.11, 4.1.15, and 4.1.21 on pages 195-196, Exercises 4.2.1, 4.2.5, 4.2.15, 4.2.17, and 4.2.31 on pages 205-207, Exercises 4.3.1, 4.3.5, 4.3.13, 4.3.15, 4.3.23, 4.3.31, and 4.3.33 on pages 213-215, and Exercises 4.4.3, 4.4.7, 4.4.13, and 4.4.31 on pages 222-223 in the textbook. | Test 9 Solution |

10 | April 3-9 | 4.5-4.6, 4.9 and 5.1-5.2 in "Linear Algebras and Its Applications" (pages 225-238, 253-264, and 265-281) | Exercises 4.5.9, 4.5.11, 4.5.15, 4.5.21, and 4.5.23 on pages 229, Exercises 4.6.1, 4.6.5, 4.6.13, and 4.6.19 on pages 236-237, Exercises 4.9.3 and 4.9.13 on pages 260-261, Exercises 5.1.5, 5.1.9, 5.1.15, 5.1.17, and 5.1.31 on page 271-272, and Exercises 5.2.7, 5.2.13, 5.2.17, 5.2.23, and 5.2.25 on pages 279-280 in the textbook. | Test 10 Solution |

11 | April 10-16 | 5.3, 5.5, 5.7 in "Linear Algebras and Its Applications" (pages 281-288, 295-301, and 311-319) and 4.2 in "Second-Order Equations" (pages xlv-xlix) | Exercises 5.3.3, 5.3.5, 5.3.15, and 5.3.23 on pages 286-287, Exercises 5.5.5 and 5.5.15 on page 300, Exercise 4.2.1 on page xlviii, and Exercises 5.7.1, 5.7.5, 5.7.7, and 5.7.13 on pages 317-318 in the textbook. | Test 11 Solution |

12 | April 17-23 | 6.1-6.4 in "Linear Algebras and Its Applications" (pages 329-360) | Exercises 6.1.1, 6.1.3, 6.1.7, 6.1.11, 6.1.13, 6.1.17 and 6.1.29 on pages 336-337, Exercises 6.2.3, 6.2.9, 6.2.11, 6.2.15, 6.2.17 and 6.2.27 on pages 344-345, 6.3.1, 6.3.7, 6.3.15, and 6.3.23 on pages 352-353, and Exercises 6.4.3, 6.4.7, 6.4.11, and 6.4.15 on pages 358-359 in the textbook. | Test 12 Solution |

13 | April 24-30 | 6.5-6.6 and 7.1-7.2 in "Linear Algebras and Its Applications" (pages 360-375 and 393-408) | Exercises 6.5.3, 6.5.7, 6.5.15, and 6.5.25 on pages 366-367, Exercises 6.6.3, 6.6.5, and 6.6.9 on page 374, Exercises 7.1.7, 7.1.13, 7.1.17, 7.1.25, 7.1.31, and 7.1.33 on pages 399-400, and Exercises 7.2.3, 7.2.5, 7.2.7, 7.2.9, and 7.2.11 on pages 406-407 in the textbook. | Test 13 Solution |

Note that this list is not final and might be changed during the semester.