SIM1003 - Calculus 2, semester 1, session 2022/2023
Lecturer: Mr Mohamad Bakri bin Zubir
Lecture room: DKM2, Institut Sains Matematik
Lecture times: Monday, 11-1 and Wednesday, 11-1
Course materials
Textbook: We will use Thomas' Calculus, the 12th edition.
You may download the textbook and the complete solution to exercises.
Lecture schedules and weekly exercise problems
Weekly lecture topics and exercises. These are tentative guides, they may change and may not be strictly adhered to.
Lecture jottings
Monday, 17 October 2022 - First lecture, jotting was lost as pc was being set up
Wednesday, 19 October 2022 - Second lecture, jottings were inexplicably lost
Monday, 24 October 2022 - Deepavali holiday, no lecture
Wednesday, 26 October 2022 - discussion on items 21 and 22 of the integral table
Monday, 31 October 2022 - integral powers of sin and cos, tan and sec, and trigonometric substitutions
Wednesday, 2 November 2022 - partial fractions
Monday, 7 November 2022 - Type 1 and Type 2 improper integrals
Wednesday, 9 November 2022 - direct comparison test and limit comparison test for integrals
Monday, 14 November 2022 - introduction to sequences, series, geometric series
Wednesday, 16 November 2022 - partial sums of an infinite series, the Integral Test
Wednesday, 21 November 2022 - no lecture, general election exemption for students
Wednesday, 23 November 2022 - comparison test and limit comparison test for series
Monday, 28 November 2022 - public holiday declared by the new prime minister
Wednesday, 30 November 2022 - the ratio and root test, and the alternating series test
Monday, 5 December 2022 - mid semester break, no lecture
Wednesday, 7 December 2022 - mid semester break, no lecture
Monday, 12 December 2022 - the alternating series test, absolute and conditional convergence
Tuesday, 14 December 2022 - Test 1, so no lecture
Monday, 19 December 2022 - 11.1 Parametrizations of plane curves, and 11.2 Calculus with parametric curves
Wednesday, 21 December 2022 - 11.2 Calculus with parametric curves, length of curves, questions 21 and 22 of section 11.2
Monday, 26 December 2022 - no lecture as the day before was a public holiday
Wednesday, 28 December 2022 - There dimensional coordinate system
Monday, 2 January 2023 - no lecture as the day before was a public holiday
Wednesday, 4 January 2023 - Introduction to Vectors, the dot product of vectors
Friday, 6 January 2023 - Vector projections
Monday, 9 January 2023 - The cross product
Wednesday, 11 January 2023 - The box product, lines and planes in space
Monday, 16 January 2023 - Parametric and cartesian equations of lines and planes, distance from a point to a line/plane
Wednesday, 18 January 2023 - Chapter 13, curves in space
Friday, 20 January 2023 - 13.3 Arc length in space, 13.4 curvature
Monday, 23 January 2023 - public holiday so no lecture
Wednesday, 25 January 2023 - T, N, B vectors, normal plane, osculating plane, curvature, torsion
Tutorial
Tuesday, 13 December 2022 - online tutorial class, summary on convergence tests
Thursday, 12 January 2023 - online tutorial class, discussed questions 47 and 29 of section 12.4
Thursday, 19 December 2023 - questions 23 and 31, section 12.5
Thursday, 26 December 2023 - question 10, section 13.4 and 13.5
Week 1, 17-21 October:
Exercises 8.1: questions 4, 5, 6, 12, 26, 29, 30, 39, 44, 46, 50, 67, 68, 69, 70
Exercises 8.2: questions 4, 9, 11, 20, 22, 27, 28, 31, 32, 33, 36, 38, 44, 63, 66, 68
Week 2, 24-28 October:
Chapter 8.3 - Trigonometric integrals
Chapter 8.4 - Integration of rational functions by partial fractions
Exercise 8.3: questions 1, 5, 10, 14, 16, 28, 31, 32, 43, 44, 47, 48
Exercise 8.4: questions 4, 5, 7, 8, 14, 15, 19, 20, 28, 29, 37, 38, 47-50
Week 3, 31-4 November:
Chapter 8.7 - Improper integrals
Exercise 8.7: questions 1, 2, 4, 10, 31, 32, 33, 34, 65,
Week 4, 7-11 November:
Chapter 10.1 - Sequences
Chapter 10.2 - Infinite series
Exercise 10.1: questions 13, 14, 19, 20, 25, 26, 27, 28, 49, 50, 59, 60
Exercise 10.2: questions 1, 2, 5, 6, 17, 18, 28, 30, 33, 36, 40
Week 5, 14-18 November:
Chapter 10.3 The integral test
Chapter 10.4 Comparison tests
Exercise 10.3: questions 1, 4, 9, 10, 11, 26, 35, 36, 57
Exercise 10.4: questions 1, 2, 8, 9, 10, 15, 16, 28, 33, 36
Week 6, 21-25 November:
Chapter 10.5 - The ratio and root tests
Chapter 10.6 - Alternating series, absolute and conditional convergence
Exercise 10.5: questions 1, 2, 6, 7, 27, 28, 31, 32, 55, 58, 60
Exercise 10.6: questions 1, 2, 7, 8, 13, 14, 31, 37, 38, 59
Week 7, 28-2 December:
Test 1 - Integrals and series
Mid semester break, 5-11 December
Week 8, 12-16 December
Chapter 11.1 - Parametrizations of plane curves
Chapter 11.2 - Calculus with parametric curves
Exercise 11.1: questions 1, 2, 12, 14, 19
Exercise 11.2: questions 1, 2, 13, 14, 25, 26, 27
Chapter 12.1 - Three-dimensional coordinate systems
Chapter 12.2 - Vectors
Chapter 12.3 - The dot product
Exercise 12.1: questions 1, 2, 13, 14, 15, 16, 17, 22
Exercise 12.2: questions 1, 2, 5, 6, 11, 12, 17, 19, 22, 25, 28
Exercise 12.3: questions 1, 3, 6, 7, 11, 13, 18, 27, 28, 49, 50
Week 9, 19-23 December
Chapter 12.4 - The cross product
Chapter 12.5 - Lines and planes in space
Exercise 12.4: questions 1, 4, 6, 7, 15, 16, 21, 22, 33, 34, 46, 47, 48
Exercise 12.5: questions 1, 3, 7, 8, 10, 24, 25, 26, 30, 37, 38, 44, 45, 53, 55
Week 10, 26-30 December
Chapter 13.1 - Curves in space and their tangents
Exercise 13.1: questions 9, 10, 17, 18, 20, 21
Week 11, 2-6 January
Chapter 13.2 - Integrals of vector functions
Exercise 13.2: questions 1, 2, 5, 6, 9, 10
Week 12, 9-13 January
Chapter 13.3 - Arc length in space
Chapter 13.4 - Curvature and normal vectors of a curve
Exercise 13.3: questions 1, 2, 7, 8, 13, 14, 15
Exercise 13.4: questions 1, 2, 3, 4, 5, 6, 9, 10, 15, 16
Week 13, 16-20 January
Chapter 13.5 - Tangential and normal components of acceleration
Exercise 13.5: questions 1, 2, 5, 6, 7, 8, 9, 10, 15, 16
Test 2 - Vectors
Week 14, 23-27 January
Revision
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