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Calculus • Series

AoPS Calculus

Jose Roberto Cossich G

Series Details

Sessions

Public Discussion

This series was cancelled by the tutor on August 26, 2024. We're very sorry–you can explore more Calculus series here. All 1:1 and group chats related to this series are disabled 7 days after the last session.

Series Details

About

This is a full course covering the AoPS curriculum for Calculus, that prepares thoroughly for the AP Calculus Exam (Calculus 1 and 2) as well as serves as an introduction to Real Analysis (a full-course on proof-based Calculus).

Sessions are 1h30m three times a week + 1h on Thursdays

Prerequisites:
-Algebra 2 with trig (with previous proof-writing or AoPS course experience preferred but not required)

This course will cover significantly more content than the standard AP Calculus class, placing greater emphasis on mathematical rigour through proofs and very challenging problems than on rote repetition and memorization.

You will still benefit if you already have experience with Calculus because of its radically different emphasis from most Calculus courses.

Syllabus:
Unit 0 - Sets and Functions (Review)
Unit I - Limits and Continuity
Unit II - The Derivative
Unit III - Applications of the Derivative
Unit IV - Integration
Unit V - Infinity
Unit VI - Series
Unit VII - Plane Curves
Unit VIII - Differential Equations
We will use the AoPS Calculus textbook, which I will provide for those unable to get it themselves. We will also supplement from various other sources.

Note: Required reading of 10 pages of reading before each session + homework due for each unit (with feedback).

✋ ATTENDANCE POLICY

I try to make the session times as accommodating as possible, however make-up sessions are always available. Please feel free to ask for one if you can't attend a session!

Dates

August 13 - August 24

Learners

15 / 15

Total Sessions

6

About the Tutor

A little about me: I'm about the biggest Indie fan there is, I almost exclusively watch (John Hughes>>) 80s movies or the upcoming Star Wars series, and I read sci-fi in my spare time. I tutor for the sake of those aha moments, and have taken Multivariable Calc, Linear Algebra, Real Analysis, and Complex Analysis. Who knows what I'll tutor next, hope to see you soon.

View Jose Roberto Cossich G's Profile

Upcoming Sessions

0

Past Sessions

6
13
Aug

Session 1

Other Topics

Review - Sets and Functions
-Sets
-Numbers and intervals
-Functions
-Graphs of functions
-Trigonometric functions
-Basic trigonometric identities
-Exponentials and logarithms
-Review and challenge problems
15
Aug

Session 2

Other Topics

We'll continue last session's topics.
Review - Sets and Functions
-Sets
-Numbers and intervals
-Functions
-Graphs of functions
-Trigonometric functions
-Basic trigonometric identities
-Exponentials and logarithms
-Review and challenge problems
16
Aug

Session 3

Limits and continuity

Unit I - Limits and Continuity
-Epsilon-delta defintion of a limit
-Proving basic limit laws
-Squeeze theorem
-One-sided limits
19
Aug

Session 4

Limits and continuity

-Definition of continuity
-Intermediate Value Theorem
-Boundedness and Extreme Value Theorems
21
Aug

Session 5

Office Hours

Unit I - Limits and Continuity
-Epsilon-delta defintion of a limit
-Proving basic limit laws
-Squeeze theorem
-One-sided limits
24
Aug

Session 6

Office Hours

-Definition of continuity
-Intermediate Value Theorem
-Boundedness and Extreme Value Theorems

Public Discussion

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