### University of Toronto Mississauga

## MAT157Y5Y: Analysis 1, 2020-2021

**Course outline**

Here
is information about reporting missed term work without a doctors' note.

**Information on using Crowdmark**.

** Office hours, second term:**
David: Wednesdays, 4:00-5:00 pm EST.
Yael: Mondays, 9:30-10:00 am and 12:30-1:00 pm EST, or by appointment.

No office hours on Monday April 12th.

** Special office hours:**
David: Wednesday April 14th, from 3:30 pm to 5:30 pm EST.

Yael: Monday April 19th, from 9:00 to 11:00 am EST
and **(added:)** from 5:00 until 6:00 pm EST

**Zoom links:** the zoom links are posted on Quercus.

**For-Credit Assignments**, 1st term:
1,
2,
3,
4,
5,
6,
7,
8,
9

**For-Credit Assignments**, 2nd term:
10,
11,
12,
13,
14,
15,
16,
17,
18,
19

**Supplementary notes**, 1st term:

Postulates for the real numbers and some consequences

Approximations

Natural numbers

Square roots

Limits and continuity

"Hard theorems"

Differentiation

Uniform continuity

Applications of derivatives

Convex functions

**Supplementary notes**, 2nd term:

Length of a curve
21Jan2021: slightly revised ``Characterization of length''.
1Feb2021: fixed typo in hint for Exercise ``Invariance under rotations''.

The Riemann integral

Length of a
continuously differentiable curve

The logarithm and exponential
functions

Definitions of sine and cosine

Lim-sup and lim-inf

Criteria for convergence of series

Uniform convergence - Part 1

Uniform convergence - Part 2

Uniform convergence - Addendum

**Weightless Assignments**:
the weightless assignments are posted on the Quercus modules.

Copies of the weightless assignments, 1st term:
1,
2,
3,
4,
5,
6,
7,
8,
9,
10

Copies of the weightless assignments, 2nd term:
11,
12,
13,
14,
15,
16,
17,
18,
19,
20

**First term test:**
Guidelines.
Tests:
2017-2018,
2018-2019,
2020-2021

**Second term test:**
Guidelines.
Tests:
2017-2018 +comments,
2018-2019,
2020-2021

**Third term test:**
Guidelines.
Tests:
2017-2018 +comments,
2018-2019,
2020-2021

**Fourth term test:**
Guidelines.
Tests:
2017-2018,
2018-2019,
2020-2021

**Final exam:**
Guidelines.
Tests:
2017-2018,
2018-2019

Homework assignments from 2018-19: 1st term:
1,
2,
3,
4,
4½,
5,
6,
7,
8,
9
2nd term:
10,
11,
12,
12½,
14,
15,
16,
16½,
16¾.

** LaTeX**.

LaTeX is not required for this course, but I strongly recommend
that you eventually learn it.
Here is a three-page sample file and the resulting pdf:
latex-samplefile.tex,
latex-samplefile.pdf.

(Many people use specialized LaTeX interfaces.
I prepare my LaTeX source file on an ubuntu terminal window
with the "vi" editor, and from a second terminal window
I run "pdflatex" to create the pdf file and "evince" to view it.)