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This course is intended to prepare students for the physical sciences. Topics to be covered include: techniques of integration, Newton's method, approximation of functions by Taylor polynomials, numerical methods of integration, complex numbers, sequences, series, Taylor series, differential equations.

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Lech 04h ) dx JFFz - -12 -1 Try u=xt2 . x - u X y = zh - dx When du n > o , no positive integer f 2 the same solution Instead - Fermat last theorem mutiplyrx - J Tfa - sub here try Complete the square x -2X = Cx - DH - S...

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Spring 2019

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MATA36

MATA36 SYLLABUS 2019 WINTER

UNIVERSITY OF TORONTO SCARBOROUGH

Welcome to MATA36!

Course Description:

This is the second half of a ﬁrst-year Introduction to Calculus course, con-

taining some applications to the Sciences. The depth of mathematics will be

taught at the standard level accessibly to all ﬁrst-year undergraduate stu-

dents, with signiﬁcant emphasis on computation. In general, theorems will

be stated without proofs, but with an indication of the mathematical ideas

involved. No emphasis will be put on rigorous mathematic proofs.

Prerequisite:

Any ﬁrst half of a ﬁrst-year Introduction to Calculus course is acceptable,

preferably with depth taught at the standard level for ﬁrst-year undergrad-

uate students.

Some examples of the course include, but is not limited to:

MATA30, MAT135; MATA31;

MATA32, MAT133; MATA29;

Note that one can only complete the second half of a ﬁrst-year Introduc-

tion to Calculus course once, regardless of the depth of the courses or the

order of the courses taken.

In the event that one needs a speciﬁc course (such as MATA36) for a program

requirement as a repeat of the second half of ﬁrst-year Calculus course, no

credit nor GPA will be counted for the second repeated course.

Lecture Time and Location, Contact Information:

Room: IC 130

Monday 8 - 10 AM

Thursday 8 - 9 AM

Instructor: Xiao Jie

Email: xiao.jie@mail.utoronto.ca

You should use your UofT email if you contact your instructor.

Author: Xiao Page 1

MATA36

Topics Covered:

The topics to be covered in this course include:

1. Integration Techniques:

Substitution, Integration by Parts;

Trignometric Integrals, Trignometric Substitutions;

Partial Fractions, Reduction Formulas;

2. Improper Integral

3. Arc Length, Surface Area (from revolution)

4. Introduction to Diﬀerential Equations

5. Sequences and Series

6. Taylor Series

And if time permits:

7. Complex Numbers i=√−1

8. Solution Approximation:

Newton’s Method (for approximating roots)

Numerical Integration (for approximating area)

Course Materials:

Lecture Notes, including all material covered, will be posted on Quercus.

Lecture Slides, hand-written from each lecture, will be posted on Quercus.

Most questions in the Lecture Notes will be solved in lecture, with solu-

tions on the posted Lecture Slides.

Textbook:

Single Variable Calculus: Early Transcendentals, Stewart (8th Edition)

The textbook is optional, and is not necessary to the course.

Grade Distribution:

Weekly Quizzes 20%

Midterm 35%

Final Exam 45%

Author: Xiao Page 2

MATA36

Test and Exam Question Distribution:

There will be 3 types of questions on the test/exam:

1. Easy level questions - makes up 50% of all questions on test/exam

They test for knowledge of concepts presented in the course.

The solutions would be short, with minimal ingenuity needed.

2. Medium level questions - makes up 35% of all questions on test/exam

They test for problem solving techniques presented in the course.

The solutions would be longer, and may need some ingenuity.

3. Very hard questions - makes up 15% of all questions on test/exam

They test for the ability to use the tools presented in the course, and

solve a problem that may have not been presented in the course.

Firm knowledge of the concepts presented in the course, and some

ingenuity is needed to solve the problem, which may span multiple parts.

Example: Suppose the concept tested is limits using L’hopital’s Rule:

1. Easy level question: lim

x→0

sin 3x

2x

2. Medium level question: lim

x→0(cos(x))1/x2

3. Very hard question: Given k≥0, compute L= lim

x→∞

(1 + kx)1/x

(Answer depends on k:L= 1 for k≤1, L=kfor k > 1)

Tutorials and Weekly Quizzes:

Tutorials begin the 2nd week of class (week of Jan 14).

Tutorials are mandatory, and there will be weekly quizzes starting the

3rd week of class, held during the last 15 minutes of tutorial. You must

know your tutorial number and attend your registered tutorial on ACORN.

Going to the incorrect tutorial section will most likely result in a mark of 0.

There are a total of 10 quizzes in the semester.

2 of the 10 quiz marks will be dropped at the end of the semester.

8 of your highest quiz marks will be averaged into 20% for ﬁnal mark.

Any missed quiz, due to any reason, justiﬁable or not, will be graded as

0 (and will be one of the two grades that will get dropped).

Author: Xiao Page 3

MATA36

Homework:

There will be weekly homework. The questions will be posted on Quercus

every Monday, starting with the 2nd Monday (Jan 14). You would have one

week to ﬁnish the homework. Then during the week that follows, the quiz

will be one question exactly from the homework given in the previous

week, or a slight variation.

It is not necessary to do all homework questions. You should do

enough to make sure you would be comfortable if a similar problem is pre-

sented to you.

Oﬃce Hours and Math Aid Center:

The instructor and TAs will have oﬃce hours in Math Aid Center.

Location: IC 404.

(Take elevator to the 4th ﬂoor, room is on the right.)

Oﬃce hours will start during the 2nd week of class. The oﬃce hour schedule

will be announced during the 1st week of class.

Missed Test/Exam:

There is no make up midterm test. If you miss the midterm due to a legiti-

mate reason, your midterm grades will be shifted to the ﬁnal. If you miss the

midterm, you must notify your intructor and submit acceptable documen-

tation within a week of the test. If the reason is medical, an oﬃcial UTSC

medical form should be downloaded from:

https://www.utsc.utoronto.ca/registrar/veriﬁcation-illness-or-injury

If no notiﬁcation is received, you will most likely receive a mark of 0.

All exam deferrals are handled by the registrar. You must submit your

petition to your registrar, and they’ll determine whether your reasons are

acceptable. The registrar will arrange for a make up exam for you in the

following term. Your deferred exam will not be written by me, but by the

instructor at the time your deferred is exam is arranged, and will be the

same exam written by everyone else who is taking MATA36 at that time. It

is your responsibility to learn the material taught in MATA36 during that

term, as the materials taught may be diﬀerent than this term.

Author: Xiao Page 4

MATA36

Academic Integrity:

In the event that you are caught cheating on quiz/test/exam, you may be

subject to one or more of the following:

1. Get a warning from the TA/instructor.

(Typical for mild oﬀence, with no past history of academic oﬀence.)

2. Get a mark deduction or a mark of 0 for the quiz/test/exam.

(Typical for severe oﬀence, or with a history of academic oﬀence.)

3. Get reported to the Oﬃce of Academic Integrity.

(Typical for severe oﬀence on test/exam.)

Once reported to the Oﬃce of Academic Integrity, a formal proce-

dure will be followed, and the instructor is no longer in control. In the

event that the academic oﬀence is conﬁrmed by the Oﬃce of Academic

Integrity, a ﬂag will be put on your transcript, lasting 1 to 5 years.

Once an investigation starts at the Oﬃce of Academic Integrity, you

are no longer able to drop the course. When the investigation ﬁnishes,

and the academic oﬀence is conﬁrmed, you would still not be able to

drop the course. All course work is still required from the student, and

will be graded as usual, while the investigation is in progress.

In all scenario, you have the right to dispute your situation with the

Oﬃce of Academic Integrity.

Author: Xiao Page 5

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