(old) SIM 1002, SJEM 1111, Calculus 1

(old) SIM 1002, SJEM 1111, Calculus 1

Test 2 may be held on Tuesday, 24 May 2016, 1430-1530 hrs in DKM2


Test 1 results

You may view your result here



Tutorial class

Tutorial starts in Week 3 (7-11 March 2016). You may choose one of classes

     (i) Tuesday, 9-10 am in BTM 4, ISM

     (ii) Tuesday, 11-12 am in BTM 4, ISM

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.

The print book can be purchased at University Bookshop and at any good bookshops, MPH, Kinokuniya among others. The ebook may also be used. However there are minor differences in the table of contents in the print book and the ebook.

The course contents are based on the print book. Where the table of contents differ from that of the ebook version, they are highlighted.


Section 1.1 Functions and their graphs


Course contents

Week 1
Preliminaries
1.1 Functions and their graphs

Week 2
1.2 Combining functions; shifting and scaling
1.3 Trigonometric functions

Week 3
2.1 Rates of change and tangents to curves
2.2 Limit of a function and limit laws

Week 4
2.4 One-sided limits
2.6 Limits Involving Infinity; Asymptotes of Graphs

Week 5
7.5 Indeterminate Forms and L'Hopital's Rule (or section 4.5 of the ebook)
2.3 The precise definition of a limit

Week 6
2.5 Continuity

Week 7: Revision, Test 1

Week 8
3.2 The derivative as a function
3.3 Differentiation rules
3.5 Derivatives of trigonometric functions

Week 9
3.6 The chain rule
3.7 Implicit differentiation
4.1 Extreme values of functions

Week 10
4.2 The Mean Value theorem
4.3 Monotonic Functions and the First Derivative Test

Week 11
4.4 Concavity and Curve Sketching
5.3 The Definite Integral

Test 2

Week 12
5.4 The fundamental theorem of Calculus
5.5 Indefinite integrals and the substitution method
5.6 Substitution and Area Between Curves

Week 13
7.2 Natural Logarithms (or section 7.1 of the ebook)
7.3 Exponential Functions

Week 14: Revision

Tutorials questions

Tutorial 1

     Exercise 1.1

          (a) All even-numbered questions from questions 2-26, 30-58

          (b) Questions 64, 70

Tutorial 2
     Exercise 1.2: All even-numbered questions from Question 2-20, 26-86

Tutorial 3
     Exercise 1.3:
          (a) All even-numbered questions from Questions 8-22, 30-54
          (b) Questions 58(a), 60, 61, 62

Tutorial 4
     Exercise 2.1: All even numbered questions from questions 4-12
     Exercise 2.2 All even numbered questions from question 2-66

Tutorial 5

     Exercise 2.4: All even numbered questions from questions 2-46

     Exercise 2.6: All even numbered questions from questions 2-36, 42-68, 74-86, 100-102

     Exercise 7.5: All even numbered questions from questions 2-18 and 75, 76, 79

Tutorial 6

     Exercise 2.3: All even-numbered questions from Questions 2-6, 12-52
     Exercise 2.5: 2, 4, 6, 7 8, 9, 10, 

                           all even-numbered questions from questions 14-46, 52, 53, 54, 55, 57, 58,

                           60, 61, 62, 63

Tutorial 7

     Exercise 3.2: Questions 2, 4, 6, 21, 22, 24, 25, 26
     Exercise 3.3: Even numbered questions from 8-44
     Exercise 3.5: Even numbered questions from 4-24 and questions 47, 48, 53, 54, 57, 58

Tutorial 8

     Exercise 3.6: Even numbered questions from 12-76

     Exercise 3.3: Even numbered questions from 2-38

Tutorial 9

     Exercise 4.1: Even numbered questions from 22-68 and questions 69-70

     Exercise 4.2: Even numbered questions from 2-30

     Exercise 4.3: Even numbered questions from 2-8, 20-48, 54-58

Tutorial 10

     Exercise 4.4: Even numbered questions from 14-24, 30-38, 44-48, 50-56, 102-104
     Exercise 5.3: Even numbered questions from 2-62 and questions 71, 72

Tutorial 11

     Exercise 5.4: Even numbered questions from 2-54
     Exercise 5.5: Even numbered questions from 2-58
     Exercise 5.6: Even numbered question from 2-14 part (b), 16-62

Tutorial 12

     Exercise 7.2: Even numbered questions from 2-68
     Exercise 7.3: Even numbered questions from 2-118