Department of Mathematics and statistics
Mathematics 62-140,
Section 01, Differential 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 posted.
Jan 17: Homework for today's lecture is assigned.
Jan 19: Homework for today's lecture is assigned.
Jan 21: Tutorial 2 questions are posted.
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 6. For review, please see: Lecture notes, Homework, Tutorial 1, 2 questions and solutions, text book: Appendix A,B,C, D and section 1.1
Jan 26: Homework for today's lecture is assigned.
Feb 1: Homework for Monday's lecture was posted.
Feb 3: Homework for Wednesday's lecture was posted.
Feb 4: Tutorial 3 questions are posted.
Feb 8: Homework for Monday's lecture was posted.
Feb 10: Homework for Wednesday's lecture was posted.
Feb 12: Tutorial 4 questions were posted.
Test 2 will be held on this friday (Feb 18) during the class. This test will cover Lecture 7--Lecture 12. For review, please see: Lecture notes, Homework, Tutorial 3, 4 questions and solutions, text book: Section 1.3, 1.5, 1.6, 2.1, 2.2, 2.3
Feb 16: Homework for Wednesday's lecture was posted.
Feb 17: Tutorial 3 and 4 solutions are psoted.
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.
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 11--Lecture 16. For review, please see: Lecture notes, Homework, Tutorial 5 questions and solutions, text book: Section 2.2--2.9
Mar 9: Homework is posted.
Mar 14: Homework is posted.
Mar 18: Test 3 Solutions, Tutorial 6 questions, homework are posted.
Mar 23: Homework for this week's lecture is posted.
Test 4 will be held on friday (April 1) during the class. This test will cover Lecture 17--Lecture 22. For review, please see: Lecture notes, Homework, Tutorial 6 questions and solutions, text book: Section 3.1, 3.2, 3.4, 3.5, 3.6, 3.7, 3.8.
In order to better prepare for Test 4, I assign tutorial 7 now, you can find from the below "Handout" part. The due date is March 30 in class.
Mar 30: Homework for this week's lecture is posted. Tut6, Tut7 solutions are posted.
Apr 8: Homework for this week's lecture is posted. Test 4 solutions and tutorial 8 are posted.
The Due Date of Tutorial 8 is April 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 |
| Mar 30 |
Tutorial 7 | Tutorial 7 Solutions |
| Apr 1 | Test 4 | Test 4 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 to
course. Numbers,
inequalities. |
Appendix A |
| Jan 12 | Lecture 2 | Inequalities, absolute values. Coordinate Geometry and Lines | Appendix A,B |
| Jan 14 | Tutorial 1 | ||
| Jan 17 | Lecture 3 | Grahps of second-degree equations. Radians measure of angles | Appendix C, D |
| Jan 19 | Lecture 4 | Trigonometric functions. Trigonometric Identities | Appendix D |
| Jan 21 | Tutorial 2 | ||
| Jan 24 | Lecture 5 | Graphs of Trigonometric Functions. Introduction to Functions | Appendix D ,Section 1.1 |
| Jan 26 | Lecture 6 | Some special functions. Essential Functions. Algebra of functions. | Section
1.1 and 1.2 |
| Jan 28 | Test 1 | ||
| Jan 31 | Lecture 7 | New functions from old functions. | Section 1.2 and 1.3 |
| Feb 2 | Lecture 8 | Transformation of functions. Exponential Functions. | Section 1.3, 1.5 |
| Feb 4 | Tutorial 3 | ||
| Feb 7 | Lecture 9 | Exponential functions. Inverse Functions.Logarithmic Functions. | Section 1.5, 1.6 |
| Feb 9 | Lecture 10 | Inverse trigonometric functions. Tangent problems. | Section 1.6, 2.1 |
| Feb 11 | Tutorial 4 | ||
| Feb 14 | Lecture 11 | The limit of a function | Section 2.2 |
| Feb 16 | Lecture 12 | Limit Laws | Section 2.3 |
| Feb 18 | Test 2 | ||
| Feb 21 | Lecture 13 | Continuity. | Section 2.5 |
| Feb 23 | Lecture 14 | Limits at Infinity. | Section 2.6 |
| Feb 25 | Tutorial 5 | ||
| Mar 7 | Lecture 15 | Tangent, Velocity, Rate of change. Derivatives. | Section 2.7, 2.8 |
| Mar 9 | Lecture 16 | The Derivative as a Function. | Section 2.9 |
| Mar 11 | Test 3 | ||
| Mar 14 | Lecture 17 | Differentiation Rules | Section 3.1 |
| Mar 16 | Lecture 18 | The product and quotient rule. Derivatives of Trigonometric Functions. | Section 3.2, 3.4 |
| Mar 18 | Tutorial 6 | ||
| Mar 21 | Lecture 19 | The Chain Rule. | Section 3.5 |
| Mar 23 | Lecture 20 | Implicit Differentiation.Derivatives of Inverse Trigonometric Functions | Section 3.6 |
| Mar 28 | Lecture 21 | Higher Derivatives. Derivatives of Logarithmic Functions. | Section 3.7, 3.8 |
| Mar 30 | Lecture 22 | Maximum and Minimum Values | Section 4.1 |
| Apr 1 | Test 4 | ||
| Apr 4 | Lecture 23 | The Mean Value
Theorem.Curve Sketching I |
Section 4.2, 4.3 |
| Apr 6 | Lecture 24 | Indeterminate Forms and L'Hospital's Rule. | Section 4.4 |
| Apr 8 | Lecture 25 | Concavity and Second Derivative Test | Section 4.3 |
| Apr 11 | Lecture 26 | Curve Sketching II | Section 4.5 |
| Apr 13 | Lecture 27 | Optimization Problems | Section 4.7 |
| Apr 15 | Tutorial 8 | Review |
| Homework |
Selected
Exercises From The Text.
|
|
|
| Week 1(Jan 10-14) |
ppA9 Q10, Q11,Q20,Q22,Q25,Q34 Q46 Q56 ppA 10 Q60 ppA15 Q4 Q7 Q14 |
| ppA15 Q17, Q30, Q36 ppA16 Q47,Q50,Q52 | |
| Week 2(Jan 17-21) |
ppA23 Q8, Q11, Q16, Q30,Q34 ppA32 Q1, Q4, Q7, Q8, Q12, Q17, Q20, Q22 |
| ppA32 Q23, Q24, Q26, Q30, Q32, Q34, Q36, Q38, Q39, Q42, Q44, Q48,Q50, Q54, | |
| Week 3(Jan 24-28) | ppA32
Q60, Q62, Q65, Q69, Q74, Q76, Q78 pp22 Q1,Q5,Q9,Q19, |
| pp22 Q21,Q23,Q25,Q27,Q31,Q33,Q39,Q43 pp35 Q1 (b)(d)(f) Q2 (b)(d)(f), Q3, Q5, Q11, Q11, Q15, Q16 | |
| Week 4(Jan 31-Feb4) | pp47 Q31, Q33,
Q35, Q37, Q39, Q42. |
| pp62 Q1, Q5, Q9, Q11, Q13, Q19 pp74 Q1,Q3,Q9, Q17, | |
| Week 5(Feb7-Feb11) | pp74 Q1,Q3,Q9, Q17, Q19, Q20, Q23, Q24, Q25, Q27, Q31, Q33, Q35, Q36, Q37, Q38, Q40, Q42 (a), |
| pp74 Q49, Q51, Q63, Q65, Q67, Q69, Q71 pp91 Q3, Q4,Q5 | |
| Week 6(Feb14-Feb18) | pp102 Q2, Q4, Q5, Q12, Q13, Q15, Q19, Q23, Q25, Q33 |
| pp111 Q1, Q3, Q5, Q8, Q10, Q13, Q15, Q18, Q20, Q23, Q25, Q28, Q30, Q35, Q36, Q37, Q39, Q45, Q46, Q49 | |
| Week 7(Feb21-Feb25) | pp133 Q3, Q7, Q9, Q11, Q13, Q15, Q17, Q19, Q22, Q25, Q31, Q32, Q35, Q37, Q39, Q41 |
| pp146 Q2, Q4, Q5, Q7, Q11,Q13, Q15, Q17, Q21, Q23, Q37, Q39 | |
| Week 8(Mar7-Mar11) | pp155 Q1, Q3, Q5, Q7, Q9, Q11, Q15, Q17, Q24, Q27 pp163 Q1, Q3, Q4, Q9, |
| pp163 Q13, Q15,
Q17, Q19, Q21, Q23, Q25, Q27 pp173 Q4, Q13, Q20, Q21, Q23, Q25, Q27, Q29, Q32, Q46 pp177 Q3, Q5, Q7, Q9, Q11, Q13, Q15, Q17, Q19, Q24, Q26, Q31, Q34, Q37 |
|
| Week 9(Mar14-Mar18) | pp191
Q3, Q5, Q7, Q9, Q11, Q13,
Q15, Q17, Q21, Q23, Q27, Q29, Q31, Q39, Q45, Q49 |
| pp197 Q2, Q3, Q5, Q7, Q9, Q11, Q13, Q15, Q17,
Q19, Q21, Q23, Q25, Q31,
Q32, Q33, Q38, Q43 pp216 Q1, Q3, Q5, Q7, Q9, Q11, Q13, Q15, Q17, Q20, Q21, Q22, Q24, Q30, Q35, Q37, Q39, Q43 |
|
| Week 10(Mar21-Mar25) | pp216 Q35, Q37, Q39, Q43 |
| pp224 Q1, Q3, Q5, Q7, Q9, Q11, Q13, Q15, Q17,
Q19, Q21, Q23, Q25, Q27, Q29, Q33, Q35, Q37, Q41, Q43, Q45, Q51, Q53, Q61, Q63 pp233 Q1, Q3, Q5, Q7, Q9, Q11, Q13, Q15, Q17, Q19, Q21, Q23, Q25 Q27, Q41, Q43, Q45. |
|
| Week 11(Mar28-Apr 1) | pp240 Q5, Q7, Q9,
Q11, Q13, Q15,
Q23, Q25, Q27, Q29, Q31,
Q33, Q35. pp249 Q2, Q3, Q5, Q7, Q9, Q11, Q13, Q15, Q17, Q19, Q21, Q23, Q25, Q27, Q29, Q31, Q35, Q37, Q39, Q41, Q43, Q45, Q48, Q49 pp286 Q15, Q17, Q19, Q21, Q29, Q31, Q33, Q35, Q37, Q41, Q43, Q47, Q49, Q51, Q53, Q55, Q57 |
| Week 12(Apr 4-Apr 8) | pp304 Q8, Q11, Q13, Q14, Q15, Q17, Q21, Q23, Q27, Q33, Q35, Q37, Q39, Q41, Q45, Q47, Q49 |
| pp313 Q3, Q7, Q9, Q11, Q15, Q17, Q19, Q27, Q29, Q31, Q33, Q35, Q37, Q39, Q41, Q43, Q45, Q47, Q49, Q51, Q53, Q55, Q57, Q59, Q67 | |
| Week 13(Apr 11-Apr15) | pp323 Q1, Q3, Q5,
Q7, Q9, Q11,
Q13, Q15, Q17, Q19, Q21, Q23,
Q25, Q27, Q33, Q41, Q45 pp336 Q3, Q5, Q7, Q9, Q11, Q14, Q15, Q20, Q21, Q23, Q25, Q28, Q31, Q43, Q44 |