Course title: Calculus 1
Course code: SIM1002
Telegram group
Please join the group at: https://t.me/+ers01-43AiZjNmEy
Any announcement on lecture/tutorial reschedule, cancellation, etc. will be communicated via this group.
Microsoft Teams group
Please join the group at:
The Team code is: 0y73rr8
Lecture schedules
Lectures are on:
Tuesdays, 2-4 in DKM2
Thursdays, 2-4 in DKM2
Course textbook
The textbook used is Thomas' Calculus, 12th Edition, Global Edition, by George B. Thomas, Maurice D. Weir, Joel R. Hass, published by Pearson Education, Inc.
I use the 12th edition because I do not have the solutions to the 14th edition.
Lecture jottings
Week 1:
Tuesday, 14 March 2023: introduction to the number systems, intervals
Thursday, 16 March 2023: examples on solving rational inequalities
Week 2:
Tuesday, 21 March 2023: absolute values and intervals
Thursday, 23 March 2023: the triangle inequality, exercises on absolute value inequality
Week 3:
Tuesday, 28 March 2023: introduction to functions, domain, co-domain, range
Thursday, 30 March 2023: even and odd function, composition of functions
Week 4:
Tuesday, 4 April 2023: an example on composition of functions, shifting and scaling of functions
Thursday, 6 April 2023: questions on shifting and scaling of functions
Week 5:
Tuesday, 11 April 2023: introduction to limits
Thursday, 13 April 2023: the limit laws, precise definition of limits
Week 6
Tuesday, 18 April 2023: lecture is postponed to Thursday, 20 April 2023
Thursday, 20 April 2023: lecture is postponed to Tuesday, 2 May 2023
Mid semester break: 24 - 30 April 2023
Week 7:
Tuesday, 2 May 2023: epsilon-delta definition of limit, linear function example
Thursday, 4 May 2023: public holiday, no lecture
Week 8:
Tuesday, 9 May 2023: continuity
Thursday, 11 May 2023: the Intermediate Value Theorem
Week 9:
Tuesday, 16 May 2023: introduction to derivative, derivative as a function
Thursday, 18 May 2023: derivative rules, the chain rule
Week 10:
Tuesday, 23 May 2023: local and absolute extrema, critical points
Thursday, 25 May 2023: Rolle's theorem, the mean value theorem
Week 11:
Tuesday, 30 May 2023: monotonic functions, the first derivative test
Thursday, 1 June 2023: worked example, concavity
Week 12:
Tuesday, 6 June 2023: second derivative test, concavity, curve sketching
Thursday, 8 June 2023: implicit differentiation
Week 13:
Tuesday, 13 June 2023: definite and indefinite integrals
Thursday, 15 June 2023: the fundamental theorem of calculus, part 1 and part 2
Tutorial questions from Thomas' Calculus
Tutorial 1 - Exercises A.1 - Appendices p1042
Questions 7, 8, 9, 10, 11, 12, 16, 17, 22, 23, 27, 28
Tutorial 2 – Functions
1. Exercises 1.1: Questions 1-6, 14, 17-222. Exercises 1.2: Questions 13, 14, 17-20, 25-34, 57-66
3. Exercises 1.3: Questions 1, 2, 51-54, 55, 61, 62
3. Exercises 1.3: Questions 1, 2, 51-54, 55, 61, 62
Tutorial 3 – Limits and Continuity
1. Exercises 2.2: Questions 1, 3, 11, 12, 20-22, 23-42 37-42, 75, 76Tutorial 4 – Limits and Continuity
1. Exercises 2.4: Questions 21-42,2. Exercises 2.5: Questions 44-46,
3. Exercises 2.6: Questions 23-36, 99-104
3. Exercises 2.6: Questions 23-36, 99-104
Tutorial 5 – Derivatives
1. Exercises 3.2: 1, 3, 4, 6, 23-262. Exercises 3.3: 8, 12, 13, 15, 17, 18, 23, 41, 44, 45, 49, 50
Tutorial 6 – Trigonometric functions, the chain rule, implicit differentiation
1. Exercises 3.5: Questions 1–182. Exercises 3.6: Questions 19, 20, 33, 34, 57, 58
3. Exercises 3.7: Questions 1–18, 31-35, 41, 50
3. Exercises 3.7: Questions 1–18, 31-35, 41, 50
Tutorial 7 – Applications of derivatives
1. Exercises 4.1: 23-25, 29, 42, 46, 47, 48, 49, 53, 57, 852. Exercises 4.2: 1-6, 15-22,
3. Exercises 4.3: 41, 45, 47, 50, 52, 63-66, 94
4. Exercises 4.4: 12, 16, 31, 32, 49, 50, 91-94
5. Exercises 4.7: 1, 5, 7, 10, 23, 32, 34, 49-54
3. Exercises 4.3: 41, 45, 47, 50, 52, 63-66, 94
4. Exercises 4.4: 12, 16, 31, 32, 49, 50, 91-94
5. Exercises 4.7: 1, 5, 7, 10, 23, 32, 34, 49-54
Tutorial 8 – Integrals
1. Exercises 5.3: 15-22, 71, 72, 732. Exercises 5.4: 33-46,
3. Exercises 5.5: 1-16, 17-50
4. Exercises 5.6: 51-58, 59-66, 71-74, 78-82
3. Exercises 5.5: 1-16, 17-50
4. Exercises 5.6: 51-58, 59-66, 71-74, 78-82
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