Department of Mathematics and statistics
Mathematics 62-141,
Section 05, Integral Calculus
Winter 2005
| Announcements |
Jan 10: Class begins. Welcome.
Jan 12: Homework 1 is assigned, please see "Homework" part below.
Jan 14: Tutorial 1 questions are psoted
Jan 17: Homework for today's lecture is assigned.
Jan 19: Homework for today's lecture is assigned.
Jan 21: Tutorial 2 questions are psoted
Jan 21: Homework for today's lecture is assigned.
Jan 24: Homework for today's lecture is assigned.
Test 1 will be held on this friday (Jan 28) during the class. This test will cover Lecture 1--Lecture 7. For review, please see: Lecture notes, Homework, Tutorial 1, 2 questions and solutions, text book: Section 4.10, 5.1, 5.2, 5.3, 5.4
Jan 26: Homework for today's lecture is assigned.
Feb 1: Homework for Monday's lecture is posted.
Feb 3: Homework for Wednesday's lecture is posted.
Feb 4: Homework for Friday's lecture is posted.
Feb 4: Tutorial 3 questions are psoted.
Feb 9: Homework for Wednesday's lecture is posted.
Feb 12: Tutorial 4 questions were psoted.
The following are some useful online resources that I demonstrated during the lecture:1. Section 6.2 notes
2. Solids of revolution
3. Method of Cylindrical Shells
Test 2 will be held on this friday (Feb 18) during the class. This test will cover Lecture 10--Lecture 17. For review, please see: Lecture notes, Homework, Tutorial 3, 4 questions and solutions, text book: Section 5.5, 6.1, 6.2, 6.3, 7.1
Feb 16: Homework for Wednesday's lecture was posted.
Feb 17: Tutorial 3 and 4 solutions are posted.
Feb 18: Homework for Friday's lecture was posted.
Feb 21: Homework for today's lecture is posted.Feb 23: Homework for today's lecture is posted.
Feb 26: Tutorial 5 questions are posted. The due date of Tutorial 5 is March 7th during the class.
Mar 8: Test 2 Solutions, Tutorial 5 Solutions, homework are posted.
Test 3 will be held on this friday (Mar 11) during the class. This test will cover Lecture 17--Lecture 23. For review, please see: Lecture notes, Homework, Tutorial 5 questions and solutions, text book: Section 7.1--7.5
Mar 9: Homework is posted.
Mar 14: Homework for today's lecture is posted.
Mar 18: Test 3 Solutions, Tutorial 6 Questions, homework are posted.
Mar 23: Homework is posted.
Test 4 will be held on this friday (April 1) during the class. This test will cover Lecture 26--Lecture 29. For review, please see: Lecture notes, Homework, Tutorial 6 questions and solutions, text book: Section 7.8, 8.1, 8.2
Parametric Curves
Mar 30: Homework is posted. Tut6 solutions are posted.
Apr 8: Homework is posted. Test 4 solutions and tutorial 7 are posted.
The due date of tutorial 7 is Apr 13 (WED).
Apr 13: Homework is posted.
You can find your tentative final marks here
If you have any questions about your marks or want to look at your final exam paper, come to see me in my office on next Monday or Tuesday 2:00pm-4:00pm.
| Course Information |
Please see course Syllabus.
| Handouts |
In the following, you will find the handouts of this course. I try to make the tutorial and test questions and solutions available as soon as possible. (Unfortunately, this is often not until shortly after each tutorial.)
|
Date |
Questions |
Solutions |
| Jan 14 | Tutorial 1 | Tutorial 1 solutions |
| Jan 21 | Tutorial 2 | Tutorial 2 solutions |
| Jan 28 | Test 1 | Test 1 Solutions |
| Feb 4 | Tutorial 3 | Tutorial 3 Solutions |
| Feb 11 | Tutorial 4 | Tutorial 4 Solutions |
| Feb 18 | Test 2 | Test 2 Solutions |
| Feb 25 | Tutorial 5 | Tutorial 5 Solutions |
| Mar 11 | Test 3 | Test 3 Solutions |
| Mar 18 | Tutorial 6 | Tutorial 6 Solutions |
| Apr 1 | Test 4 | Test 4 Solutions |
| Apr 8 | Tutorial 7 | Tutorial 7 Solutions |
| Apr 15 | Tutorial 8 | Tutorial 8 Solutions |
| Lectures |
See here a running list of topics covered in class.
|
Date |
Lecture and Tutorial |
Topic |
Reading |
| Jan 10 | Lecture 1 | Introduction. Antiderivatives | Section 4.10 |
| Jan 12 | Lecture 2 | Antiderivatives. Areas. | Section 4.10 |
| Jan 14 | Lecture 3 | Areas | Section 5.1 |
| Tutorial 1 | |||
| Jan 17 | Lecture 4 | The definite integral |
Section 5.2 |
| Jan 19 | Lecture 5 | The definite integral | Section 5.2 |
| Jan 21 | Lecture 6 | Fundamental Theorem of Calculus PartI | Section 5.3 |
| Tutorial 2 | |||
| Jan 24 | Lecture 7 | Fundamental Theorem of Calculus PartII. Indefinite Integral. | Section 5.3, 5.4 |
| Jan 26 | Lecture 8 | Indefinite Integral. | Section 5.4 |
| Jan 28 | Lecture 9 | Net Change Theorem. | Section 5.4 |
| Test 1 | |||
| Jan 31 | Lecture 10 | The Substitution Rule | Section 5.5 |
| Feb 2 | Lecture 11 | The Substitution Rule and the Area Problem. | Section 5.5 and 6.1 |
| Feb 4 | Lecture 12 | The Areas between Curves | Section 6.1 |
| Tutorial 3 | |||
| Feb 7 | Lecture 13 | Volumes | Section 6.2 |
| Feb 9 | Lecture 14 | Volumes | Section 6.2 |
| Feb 11 | Lecture 15 | Volumes | Section 6.2 |
| Tutorial 4 | |||
| Feb 14 | Lecture 16 | Volumes By Cylindrical Shell |
Section 6.3 |
| Feb 16 | Lecture 17 | Integration By Parts | Section 7.1 |
| Feb 18 | Lecture 18 | Tignometric Integrals | Section 7.2 |
| Test 2 | |||
| Feb 21 | Lecture 19 | Tignometric Integrals | Section 7.2 |
| Feb 23 | Lecture 20 | Tignometric Substitution | Section 7.3 |
| Feb 25 | Lecture 21 | Tignometric Substitution | Section 7.3 |
| Tutorial 5 | |||
| Mar 7 | Lecture 22 | Integration of Rational Functions by Partial Fractions | Section 7.4 |
| Mar 9 | Lecture 23 | Integration of Rational Functions by Partial Fractions | Section 7.4 |
| Mar 11 | Lecture 24 | Integration of Rational Functions by Partial Fractions | Section 7.4 |
| Test 3 | |||
| Mar 14 | Lecture 25 | Strategy for Integration | Section 7.5 |
| Mar 16 | Lecture 26 | Improper Integrals | Section 7.8 |
| Mar 18 | Lecture 27 | Improper Integrals | Section 7.8 |
| Tutorial 6 | |||
| Mar 21 | Lecture 28 | Arc Length | Section 8.1 |
| Mar 23 | Lecture 29 | Arc Length and Area of a surface of Revolution | Section 8.1, 8.2 |
| Mar 28 | Lecture 30 | Area of a surface of Revolution | Section 8.2 |
| Mar 30 | Lecture 31 | Curves Defined by Parametric Equations | Section 10.1 |
| Apr 1 | Lecture 32 | ||
| Test 4 | |||
| Apr 4 | Lecture 33 | Calculus with Parametric Curves | Section 10.2 |
| Apr 6 | Lecture 34 | Calculus with Parametric Curves. Polar Coordinates | Section 10.2, 10.3 |
| Apr 8 | Lecture 35 | Polar Coordinates | Section 10.3 |
| Tutorial 7 | |||
| Apr 11 | Lecture 36 | Areas and Lengths in Polar Coordinates. | Section 10.4 |
| Apr 13 | Lecture 37 | Areas and Lengths in Polar Coordinates. | Section 10.4 |
| Apr 15 | Lecture 38 | Review Lecture |
|
| Tutorial 8 | Review Lecture |
| Homework |
Selected
Exercises From The Text.
|
|
|
| Week 1(Jan 10-14) |
pp385 Q1, Q3, Q5, Q7, Q9, Q11, Q13, Q15, Q17,
Q19, Q21, Q23, Q25, Q27, Q29, Q31, Q33, Q35, Q37, Q39, Q41, Q44. |
| Week 2(Jan 17-21) |
pp378 Q3,Q5,Q22 pp390 Q3, Q17, Q19, Q21 |
| pp391 Q23, Q25,
Q27, Q29, Q33, Q35, Q37, Q39, Q41, Q43, Q45, Q47, Q49, Q51, Q53, Q55,
Q59, Q61, Q64 pp402 Q5, Q7, Q9, Q11, Q13, Q15, Q17 |
|
| Week 3(Jan 24-28) | pp402 Q19, Q21, Q23, Q25, Q27, Q29, Q31, Q33,
Q35, Q37, q39, Q41, q47, Q49, Q53, q56 pp411 Q2, Q3, Q5, Q7, Q9, Q11, Q13, Q17, Q19, Q21, Q23, Q25, Q27, Q29, Q31, Q33, q35, Q37, Q39 |
| pp411 Q47, Q53, Q55 pp420 Q1, Q3, Q5, Q7, Q9,
Q11, Q13, Q15, Q17, Q21, Q23, Q27 |
|
| Week 4(Jan 31-Feb4) |
pp420 Q33, Q37, Q41, Q43, Q49, Q51, Q53, Q57,
Q61, Q65, Q68,Q73, Q74, Q75, Q79, Q81 |
| pp429 Q1, Q3, Q5, pp431 Q4, Q5,
Q8(a)(c), Q9, Q11, Q13, Q15, Q17, Q19, Q21, Q23, Q27, Q29, Q31, Q35,
Q37, Q49, Q51, Q60 |
|
| pp442 Q1, Q3, Q5, Q7, Q9, Q11, Q13, Q17, Q19, Q21, Q23, Q25, Q27, Q29, Q32. | |
| Week 5(Feb7-Feb11) | pp452 Q1, Q3, Q5, Q7, Q9, Q11, Q13, Q15, Q17, Q19, Q21, Q23, Q25, Q27, Q29, Q31, Q33, Q35 |
| Week 6(Feb14-Feb18) | pp458 Q1, Q3, Q5,
Q7, Q9, Q11, Q13, Q15, Q17, Q19, Q21, Q23, Q25, Q27, Q29, Q31, Q37,
Q39, Q41, Q43, Q45 |
| pp480 Q1, Q3, Q5,
Q7, Q9, Q11, Q13, Q15, Q17, Q19, Q21, Q23, Q25, Q27, Q29, Q33, Q41,
Q42, Q43, Q45, Q46, Q47, Q48, Q51, Q55, Q57 |
|
| Week 7(Feb21-Feb25) | pp488 Q1, Q3, Q5, Q7, Q9, Q11, Q13, Q15, Q17, Q19, Q21, Q23, Q25, Q27, Q29, Q31, Q33, Q35, Q37, Q39, Q41, Q43, Q45, Q47 |
| pp494 Q1, Q3, Q5, Q7, Q9, Q11, Q13, Q15, Q17, Q19, Q21, Q23, Q25, Q27 | |
| Week 8(Mar 7-Mar11) | pp505 Q1, Q3, Q5 |
| pp505 Q7, Q9, Q11, Q13, Q15, Q17, Q19, Q21, Q23, Q25, Q27, Q29, Q31, Q33, Q39, Q41, Q43, Q45, Q49 | |
| Week 9(Mar 14-Mar18) | pp510 Q1, Q3, Q5, Q7, Q9, Q11, Q13, Q15, Q17, Q19, Q21, Q23, Q25, Q27, Q29, Q31, Q33, Q35, Q37, Q39, Q41, Q43, Q45, Q47, Q49, Q51, Q53, Q55, Q57, Q59, Q61, Q63, Q65, Q67, Q69, Q71, Q73, Q75, Q77, Q79 |
| pp537 Q1, Q5,
Q7, Q9, Q11, Q13, Q15, Q17, Q19, Q21, Q23, Q25, Q27, Q29, Q31, Q33,
Q37, Q39 |
|
| Week 10(Mar 21-Mar25) | pp552 Q1, Q5, Q7, Q9, Q11, Q13, Q15, Q17, Q19, Q31 |
| pp559 Q1, Q3, Q5, Q7, Q9, Q11, Q13, Q15, Q25 | |
| Week 11(Mar 28-Apr1) | pp656 Q1, Q3, Q5, Q7, Q9, Q11, Q13, Q15, Q17, Q19, Q21, Q24, Q25 |
| Week 12(Apr4-Apr8) | pp666 Q1, Q3, Q5, Q7, Q9, Q11, Q13, Q15, Q17, Q19, Q25, Q27, Q29, Q31,Q33, Q37, Q39, Q41, Q43, Q51, Q52, Q57,Q59, Q61, Q65 |
| pp677 Q1, Q3, Q5, Q7, Q9, Q11, Q13, Q15, Q17, Q19, Q21, Q25, Q29, Q33, Q37, Q39, Q55, Q57, Q61, Q65 | |
| Week 13(Apr10-Apr15) | pp683 Q1, Q3, Q5, Q7, Q9, Q11, Q17, Q19, Q21, Q23, Q25, Q27, Q29, Q31, Q33, Q35, Q37, Q39, Q45, Q47 |