UNIVERSITY OF WAIKATO
Department of Mathematics MATH101-08A
Introduction to Calculus MATH101-08A
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Tutorial 11 has been posted - do the exercises set for each class. Nothing to be handed in.
The marked Test 2 answer booklets are available from the receptionist, School of Computing
and Mathematical Sciences, ground floor block G. Worked solutions are on the web, linked below. Grades are on the 3rd floor block G notice board.
This week will be revision/final exam preparation. On Thursday I will continue with the 2007
Semester B math101 exam paper, describe the structure of the final examination and indicate where and when extra help will be available. To access final exam papers go to
iWaikato/Quick Links/Library/Exam Paper Collection.
During study week and the days leading up to the final examination MathHelp will be available each day in G3.33 from noon-2pm. I will have office hours in G3.22 from 2-5pm on Wednesday
18th June and Thursday 19th June.
Links:
Lecturer for teaching weeks 1-13:
Associate Professor Kevin Broughan, Office G3.22, Tel 838-4423, email kab@waikato.ac.nz
Office Hours: Normally Thursday 4-5.30 pm in G3.22 during the teaching weeks (but week 1
28th Feb is from 5-6pm).
Text book: Thomas' Calculus
This book will be referred to often for reading and exercises. You will
need to have access to the 11th edition, available from Bennett's Bookstore.
Math Help:
This is available at 1-2pm Monday through Friday inclusive during teaching weeks 2-13 and then at specified times during the study beak, on Mondays and Wednesdays in I.G.02, in Tuesdays and Thursdays in G.B.19 and on Fridays in KB.07.
Exercises and readings set set in class 2008 to attempt before the tutorial the following week (don't hand these in, check your own answers at the back of TC):
- Functions and graphs: Read Thomas' Calculus (TC) section 1.3, Do p26 # 1,3,7,13,23,29,37.
- Limits of functions: Read TC p77-81, Do p81 # 1,3,21,27. Read TC Section 2.2, Do p89 # 7,15, 19, 23, 29, 37, 39.
- One sided and infinite limits: Read TC Sections 2.4, Do p111, #1,3,11,15,21,25,41,47,49.
- Continuous functions: Read TC Section 2.6, Do p132 # 5,7,29,37,39.
- Derivative: Read TC Section 2.7, Do p140 # 3,5,9,13,33.
- Derivative rules: Read TC Sections 3.1, 3.2, Do p155 #1,3,37,41, p169 #1,7,13,17,27,31.
- chain rule, rates: Read TC Sect 3.3, Do p179 #1,15. Sect 3.5 p190-195 Do p201#1,9,11,19,49.
- derivatives of trig functions: Read TC Sect 3.4 Do p188#1,5,9,17,27,39,47.
- Implicit differentiation: Read TC Sect 3.6, Do p211 #19, 23, 39, 47,59.
- Related Rates: Read TC Sect 3.7, Do p218 #1,3,7,13,15,25.
- Optimization and the Mean Value Theorem: Read Thomas' Calculus (TC) section
4.1 p244 Do p253 # 19, 25, 35, 51.
- Higher Derivatives and the 2nd derivative test:
Read TC sect 4.4, Do p274 # 1,3,5,9,41.
- Revision preparation for Test 1.
- Curve sketching, linear approximation, Taylor's Theorem, differentials:
Read TC sect 3.8, 11.8, Do p231 # 1,3,5,13,21,35,43,51.
- Newton's method for finding roots: Read TC sect 4.7 p299, Do p305 #1,3,7,9,11.
- Summation: Read TC sect 5.1,5.2, Do p342 #1,5,7,9,11,17,23,29.
- Riemann sums: Read TC sect 5.3 Do p352 # 1,3,15,17,51.
- Riemann Sums application: volumes using washers and shells:
Read TC sect 6.1,6.2 p396-405, 409-414, Do p406 # 3,13,17,45. p414 # 1,3,23,35.
- Inverse functions, Inverse trig functions: Read TC Sect 7.1 p466-472, Do p473 # 3,7,11,29,31,33.
- Natural logarithm function ln and logarithmic differentiation, exponential function:
Read TC Sect 7.2, p476-482, Do p482 # 1,3,9,23,25,31.
- Riemann Sums application: arc length of plane curves:
Read TC sect 6.3 p416-422, Do p423 # 1,7,9,27,29.
- Riemann Sums application: surface area for surfaces of revolution:
Read TC sect 6.5 p436-442, Do p444 # 9,11,15,17,27.
- Substitution and other techniques of integration I:
Read TC p553-558, Do p558 # 1,3,7,23,25,37,43,47,53,63.
- Techniques of integration II, integration by parts:
Read TC Sect 8.1 p553-558 (again!), Do p560 # 71, 77, 79, 83, 87.
- Integration by parts II, by partial fractions I:
Read TC Sect 8.2 p561-568, Do p568 # 5,9,23,25,33,43.
- Integration by partial fractions II, trig integrals:
Read TC Sect 8.3 p570-579 Do p579 # 1,5,13,17,25,35,45.
Read TC Section 8.4 p 581. Do p585 # 3,7,15,19,23,33.
- Trigonometric substitution:
Read TC Section 8.5 p586, Do p591 # 1,19,31,43,47.
- Application of volumes and surface areas: light bulb problem. HW:Preparation for
Test 2.
- Hyperbolic functions:
Read TC Section 7.8 p535-p542, Do p542# 1,5,9,12,13,25,41,53,67.
Continue with
your revision by going back over the lectures and problems, sumarizing important results,
and looking at last year's test paper and solutions linked below.
- Preparation for Test 2 - Test 2 Semester B 2007.
- Numerical integration/trapezoidal rule: Read TC Section 8.7 p603 Do p614 #11,15.
- Partial derivatives, l'Hopital's rule, irrational numbers: Read TC Section 4.6 Do p298 #3,5,9,17,23,25.
- Revision: The 2007 Semester B examination paper.
- Revision continued: The 2007 Semester B examination paper. Potential theory questions.
- Revision completed. (Theory revision)
Tutorial assignments:
Your worked answers to these set problems, given below, should be handed in through the slot marked with
the name of your tutor, by the given date. Please take care to select the correct slot.They will be marked and handed back during the tutorial of the following week. Late assignments cannot be accepted. Please ensure all work handed in to be marked is your own work. There are
serious penalties for copying.
- Tutorial 1 (week of Monday 3rd March for lectures 1,2) hand in by 9am Monday 10th March.
TC p26 # 3,7,29a, p89 #3,21.
- Tutorial 2 (week of Monday 10th March for lectures 3,4,5) hand in by 9am Monday 17th March.
TC p111 #1,11,25, p132 #5, p155#5 (make certain you use the limit definition).
- Tutorial 3 (week of Monday 17th March relating to Lectures 6,7,8) hand in by 9am Wednesday 26th March. Exercises p169 # 7,17,27, p179 # 1,15.
- Tutorial 4 (week of Monday 31st March, relating to Lectures 9,10,11)
Hand in by 9am Monday 7th April. Exercises p211 # 19, 47(a), p219 #17,35, p255 # 49.
- Tutorial 5 (week of Monday 7th April, relating to Lectures 12,14,15)
Hand in by 9am Monday 28th April. Exercises p274 # 1,41, p231 #3,35, p305 #3.
- Tutorial 6 (week of Monday 7th April, relating to Lectures 16, 17, 18.)
Hand in by 9am Monday 5th May. Exercises p342#9,25, p352#3, p406# 19, 3.
- Tutorial 7 (week of Monday 5th May, relating to Lectures 19,20
Hand in by 9am Monday 12th May. Exercises p473#13,31, p484#25, p493#37, p531#70.
- Tutorial 8 (week of Monday 12th May, relating to Lectures 21, 22, 23.
Hand in by 9am Monday 19th May. Exercises p423 #7, p444#15, p558#1,53,87.
- Tutorial 9 (week of Monday 19th May, relating to Lectures 24,25,26.
Hand in by 9am Monday 26th May. Exercises p568#31(a),41 p579 #15, 17, 25,45.
- Tutorial 10 (week of Monday 26th May, relating to Lectures 27,28,29.
Hand in by 9am Tuesday 3rd June. Exercises p585#7,33, p591#1,19,43.
- Tutorial 11 (week of Monday 8th October, relating to Lectures 30,32.
There are no exercises to be handed in. Attempt the problems set for each of the lectures.
Test solutions 2008:
- Test 1, 2008:
questions and MC answers,,
solutions for Part B.
- Test 2, 2008:
questions and MC answers,,
solutions for Part B.
Lecture notes:
(Please note the page numbers of the links don't necessarily correspond with the page numbers on the
printed lecture note pages.)
- Functions and graphs:
page 1,
2,
3,
4,
5,
6.
- Limits of functions:
page 6b,
7,
8,
9,
10,
11,
12.
- One sided and infinite limits:
page 13c,
14,
15,
16,
17,
18.
- Continuous functions:
page 19,
20,
21.
- Derivative:
page 22,
23,
24,
25,
26,
27,
28.
- Derivative Rules:
page 29,
30,
31,
32,
33,
34.
- Chain rule, rates:
page 35,
36c,
37,
38c,
39,
40.
- Derivatives of trig functions:
page 41,
42,
43,
44,
45.
- Implicit differentiation:
page 46,
47,
48.
- Related Rates:
page 49,
50,
51,
52,
53,
54.
- Optimization and the Mean value theorem:
page 1,
2,
3,
4,
5.
- Higher Derivatives and the second derivative test:
page 1,
2,
3,
4.
- Revision preparation for test 1: see the questions and solutions for 2007 below.
- Curve sketching, linear approx,Taylors Theorem, differentials:
page 1,
2,
3,
4,
5.
page 1,
2,
3,
3b,
4.
- Newton's method for finding roots:
page 1,
2,
3,
4,
5,
6.
- Summation (new series of page numbers):
page 26,
27,
28,
29,
30,
31,
32.
- Riemann sums:
page 33,
34,
35,
36,
37,
38,
39.
- Volumes using washers and shells:
page 40,
41,
42,
43,
44,
45.
- Inverse functions:
page 62,
63,
64,
65,
66,
67,
68,
69.
- Natural logarithm function ln, logarithmic differentiation, exponential function:
page 1,
2,
3,
4,
5,
6,
7.
- Arc length of plane curves:
page 46,
47,
48,
49,
50,
51,
52.
- Surface area:
page 54,
55,
56,
57,
58,
59,
60,
61.
- Substitution and other techniques of integration I:
page 85-1,
85-2,
85-3,
85-4,
85-5,
86,
87,
88,
89.
- Techniques of integration II, integration by parts:
page 90,
91,
92,
93,
94,
95,
96,
97.
- Integration by parts, by partial fractions I:
page 98,
99,
100,
101,
102,
103,
104,
105.
- Integration by partial fractions II, trig integrals:
page 106,
107,
108,
109.
page 110,
111,
112.
- Trigonometric substitution:
114,
115,
116,
117,
118.
119.
- Application of volumes and surface areas - light bulb problem:
127,
128,
129,
130,
131,
132,
133.
- Hyperbolic functions:
70,
71,
72,
73,
74,
75,
76.
- Preparation for Test 2.
- Numerical integration/trapezoidal rule:
120,
121,
122,
123,
124,
125,
126.
- Partial derivatives,l'Ho^pital's rule, irrational numbers:
page 1,
2,
3.
133b,
134,
135,
136,
137,
138,
139.
- Examination preparation.
- Examination preparation.
- Examination preparation. (Theory revision).
Example tests and solutions from 2007:
- Test 1, 2007:
questions,,
solutions.
- Test 2, 2007:
questions,,
solutions.
Kevin Broughan
6th June 2008
