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 

Solution to question 48, section 8.3 of Thomas' Calculus (12 Ed.) which was discussed during tutorial on Tuesday, 8 Nov 2022 

Solution to question 26, section 10.1 of Thomas' Calculus (12 Ed), which was discussed during tutorial on Tuesday, 29 Nov 2022

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:

Chapter 8.1 - Integration by parts
Chapter 8.2 - Trigonometric integrals


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

Revision week, 30-5 February




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