MAT 187H1S CALCULUS II: COURSE OUTLINE

Spring semester, 2002

Course Description:

MAT187H1S is the direct continuation of MAT186H1F, and uses the same book. We will do most of Chapters 8, 9, 10 and 11, plus selected sections of Chapters 12, 13 and 16. (Chapters 14 and 15 represent the core material of Calculus III, should you ever have to take such a course.) Note: the material on vectors in Sections 12.3 to 12.6 is the same as material covered in MAT188H1F, and will not be repeated in MAT187H1S.

Section Instructors:

By now you should be scheduled into one of the following Sections:

LEC0101 Burbulla
LEC0102 Pugh
LEC0103 Wagneur
LEC0104 Lun

Tutorials:

In addition to lectures you will attend a tutorial each week, during which you will have the opportunity to go over problems, and to receive help from your tutor. Tutorials start on Tuesday Jan 15/Wednesday Jan 16, and end on Apr 10.

Tuesday 11 am, Tut0107, SF 1013, Lynch, gdlynch@math.toronto.edu
Tuesday 11 am, Tut0108, GB 304, Lawi, slawi@math.toronto.edu
Tuesday 11 am, Tut0109, GB 405, Bouchette, bouchette@control.toronto.edu
Tuesday 11 am, Tut0110, HA 403, Ghomeshi, shahin@mie.toronto.edu
Tuesday 11 am, Tut0111, HA 401, Yang, zyang@mie.toronto.edu
Tuesday 11 am, Tut0112, WB 130, Zhou, gangzhou@math.toronto.edu
Wednesday 5 pm, Tut0101, HA 401, Yang, zyang@mie.toronto.edu
Wednesday 5 pm, Tut0102, GB 304, Lawi, slawi@math.toronto.edu
Wednesday 5 pm, Tut0103, WB 242, Lynch, gdlynch@math.toronto.edu
Wednesday 5 pm, Tut0104, HA 410, Ghomeshi, shahin@mie.toronto.edu
Wednesday 5 pm, Tut0105, GB 244, Bouchette, bouchette@control.toronto.edu
Wednesday 5 pm, Tut0106, WB 119, Zhou, gangzhou@math.toronto.edu

Textbook:

The textbook for this course is CALCULUS for Engineers, 2nd edition , by Donald Trim, published by Prentice Hall.

Marking Scheme:

Tutorial quizzes will count for 20% of your final grade; the term test will also count for 20%. The final exam counts as the remaining 60% of your final grade.

Mid-Term Test:

There will be a term test during the week of March 4th The test will be written during tutorial time in a location ( probably your tutorial room) to be announced in class by your instructor.

Quizzes:

Three 30-min quizzes will be written in tutorial during the weeks of Jan 21st, Feb 4th, and Mar 25th Only the best 2 of 3 quizzes will be counted.

A Word About Written Tests:

All quizzes, tests and exams in this course require you to show your work and explain what you are doing. The final answer, even if it is correct, will never be worth full marks unless you have explained your solution. It is not our responsibility to figure out what you have done; you are supposed to make it clear what you are doing.

Homework:

Some of the suggested homework exercises have been highlighted in boldface; these are for tutorial discussion.

Final Exam:

There will be a common final exam, 2 and 1/2 hours long, to be scheduled by the Faculty office during the exam period, Apr 17 to Apr 30.

Course Coordinator:

is D. Burbulla. Office: SF B670, ph: 946-3165, email: burbull@ecf; office hours: M 1:30-3; W 11:30-4; R 2-4; F 11:30-1

Notes:

(1) In Trim's book, for polar coordinates, r > 0 or r = 0 always . (2) You should look at the graphs in Sec. 12.2, when we start Chapter 12.

Lecture Schedule:

The sequence of 39 lectures, listed on the reverse, is only an approximate schedule. Your instructor could spend more or less time than indicated on each topic.

Lecture 1 -- Inverse Trigonometric Functions (Sec 8.1) Problems 9, 10 , 20, 26, 28 , 30, 34 , 36, 49, 50
Lecture 2 -- and their Derivatives (Sec 8.2) Problems 12, 20 , 28, 30, 31 , 32, 36
Lecture 3 -- Hyperbolic Functions (skim) (Sec 8.3) Problems 12, 14, 16, 20
Lecture 4 -- Substitutions/Change of Variables (Sec 9.1) Problems 4, 6 , 14, 18, 22 , 24, 26, 28
Lecture 5 -- Exponential Growth and Decay (Sec 9.2) Problems 2, 4 , 8, 10 , 12, 16 , 17, 18, 24
Lecture 6 -- Integration by Parts (Sec 9.3) Problems 10, 12 , 14 , 15 , 16, 18 , 26, 28
Lecture 7 -- Trigonometric Integrals (Sec 9.4) Problems 6, 8 , 17, 18 , 22, 25 , 26
Lecture 8 -- Trigonometric Substitutions (Sec 9.5) Problems 4 , 14 , 18 , 22, 32, 34, 36

-- and Completing the Square (Sec 9.6) Problems 2, 4, 6 , 8, 10 , 14

Lectures 9 and 10 -- Partial Fractions (Sec 9.7) Problems 6 , 8 , 14 , 16, 18, 21, 22, 28 , 30

Lecture 11 -- Reduction Formulas (Sec 9.8) Problems 22, 28 (see Problems 31), 30

Lecture 12 -- Numerical Integration (skim) (Sec 9.9) Problems 4, 8, 12, 14, 20

Lectures 13 and 14 -- Parametric Equations (Sec 10.1) Problems 8 , 18 , 21 , 22 , 26 , 28, 32, 40 , 41

Lecture 15 -- Polar Coordinates (Sec 10.2) Problems 4, 6, 10

-- and Polar Curves (Sec 10.3) Problems 6, 14 , 16 , 22, 24 , 30, 34, 36, 47 , 48

Lecture 16 -- Areas of Polar Curves (Sec 10.4) Problems 4 , 6 , 10, 12, 13 , 14 , 18, 20

Lecture 17 -- Derivatives and Integrals of Vectors (Sec 12.9 ) Problems 10 , 14, 18 , 20 , 25

Lecture 18 -- Parametric Curves and Vectors (Sec 12.10) Problems 4, 10, 12 , 14

Lecture 19 -- Tangent Vectors; Length (Sec 12.11) Problems 2, 6 , 12, 14

Lecture 20 -- Displacement, Velocity, Acceleration (Sec 12.13) Problems 4, 6 , 12, 14 , 22, 28, 30, 32

Lecture 21 -- Infinite Sequences of Numbers (Sec 11.1) Problems 6, 8, 10 , 18 , 26, 28 , 40, 42

-- and Functions (skim both) (Sec 11.2) Problems 2, 10 , 14

Lectures 22 to 25 -- Taylor Polynomials, (Sec 4.12) Problems 2 , 8 , 10

-- Taylor's Theorem, (Sec 11.3) Problems 2 , 7 , 8, 14

-- Taylor Series, (Sec 11.4) Problems 10, 14 , 20, 22 , 23 , 26, 30

-- and Power Series (Sec 11.5) Problems 2 , 12, 16 , 24, 26, 32 , 33, 36

-- (NB: Trim covers Taylor Series (Sec 11.6) Problems 2 , 4 , 6 , 8, 10 (hard)

-- before series of constants.) (Sec 11.7) Problems 2, 6 , 12, 14 , 16 , 18, 20, 22, 32

Lecture 26 -- Infinite Sequences (skim) (Sec 11.8) Problems 26, 28

Lecture 27 -- Infinite Series (Sec 11.9) Problems 2 , 4 , 8, 10 , 18, 20 , 22

Lectures 28 and 29 -- Integral and Comparison Tests (Sec 11.10) Problems 10, 12 , 16 , 19 , 24 , 26, 28

Lecture 30 -- Ratio and Root Tests (Sec 11.11) Problems 6 , 8 (easy!), 12 , 16 , 18, 20

Lecture 31 -- Absolute, Conditional Convergence (Sec 11.12) Problems 2, 4 , 10 , 12, 14 , 18, 22

Lecture 32 -- Computations with Series (Sec 11.13) Problems 8 , $ 12 $ (note!!! numerator should be x^2) , 14 , 16, 18, 30 , 32, 33

Lecture 33 -- Functions of Two Variables (Sec 13.1) Problems 10, 18, 20, 24, 25, 28

-- and Partial Derivatives (Sec 13.3) Problems 4 , 14, 16 , 28, 32 , 34

Lecture 34 -- Higher-order Partial Derivatives (Sec 13.5) Problems 2, 4, 12 , 14 , 22, 24 , 26

Lecture 35 -- Relative Extrema (Sec 13.10) Problems 2 , 3, 4 , 8, 10 , 12, 14, 22

Lecture 36 -- Separable Differential Equations (Sec 16.2) Problems 2, 8 , 12, 18 , 20, 22 , 42, 43

Lecture 37 -- Linear First Order DE's (Sec 16.3) Problems 2, 4 , 10 , 14, 16, 24 , 26

Lecture 38 -- Homogeneous Second Order Linear DE's (Sec 16.8) Problems 1, 2 , 4 , 5, 14

Lecture 39 -- Vibrating Mass-Spring Systems (Sec 16.10) Problems 1 , 10

Lecture schedule by weeks:

1 week on Chapter 8; 3 weeks on Chapter 9; 4 weeks on Chapter 11; 1 week on Chapter 13; 4 weeks on selected topics from Chapters 10, 12 and 16. Reading Week is Feb 18-22.