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Study of infinite sequences and series, vector functions, and derivatives and integrals for multivariable functions
Updated on Sep, 2026
Teaching and Academics , Math, Calculus
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HOW THIS COURSE WORK:
This course, Ace Calculus 3 in 16 Hours (The Complete Course), is intended to introduce students to the study of infinite sequences and series, vector functions, and derivatives and integrals for multivariable functions. The course includes videos, notes from the whiteboard during lectures, and practice problem sets (with solutions!). I also show every single step in examples and proofs. The course is organized into the following topics:
Section 2: Infinite Sequences
Convergence of a sequence
Properties of a sequence: monotonic and bounded
Section 3: Infinite Series
Special series: geometric series, telescoping series, harmonic series
Six convergence/divergence tests: test for divergence, integral test, comparison test, limit comparison test, alternating test, ratio test, and root test
Section 4: Power Series
Taylor series and Maclaurin series
Three methods: direct computation, term-by-term differentiation/integration, and summation, multiplication, and division of power series
Section 5: Vectors and the Geometry of Space
Operations of vectors: the dot product, projection, and cross product
Equations of lines and planes in 3D
Section 6: Vector Functions
Derivative and integrals of vector functions
The arc length and curvature
Frenet-Serret Equations
Motion in Space: Velocity and Acceleration
Section 7: Partial Derivatives
Multivariable functions
Interpretations of partial derivatives
Linear approximations
The gradient vector and directional derivatives
Finding extreme values of a multivariable function
Lagrange multipliers
Section 8: Multiple Integrals
Estimating the volume under a surface
Iterated/double integrals
The double integral over general regions
Double integrals in polar coordinates
CONTENT YOU WILL GET INSIDE EACH SECTION:
Videos: I start each topic by introducing and explaining the concept. I share all my solving-problem techniques using examples. I show a variety of math issues you may encounter in class and make sure you can solve any problem by yourself.
Notes: In each section, you will find my notes as downloadable resources that I wrote during lectures. So you can review the notes even when you don't have internet access (but I encourage you to take your notes while taking the course!).
Assignments: After you watch me doing some examples, now it's your turn to solve the problems! Be honest and do the practice problems before you check the solutions! If you pass, great! If not, you can review the videos and notes again before moving on to the next section.
THINGS THAT ARE INCLUDED IN THE COURSE:
An instructor who truly cares about your success
Lifetime access to Ace Calculus 3 in 16 Hours (The Complete Course)
Downloadable lectures so you can watch the videos whenever and wherever you are.
Downloadable lecture notes so you can review the lectures without having a device to watch/listen.
Seven problem sets at the end of each section (with solutions!) for you to do more practice.
Step-by-step guide to help you solve problems.
See you on the course!
Check out the detailed breakdown of what’s inside the course
During my undergraduate years, I always looked forward to exams because I was well-prepared and found them rewarding. I know this isn’t the case for everyone, so I'm here to share my knowledge and help make your university journey a bit easier!
I earned my BSc in Atmospheric Science and Physics, with a minor in Mathematics, from McGill University in 2018. I then completed my MSc in 2019 and my PhD in 2024, both in Physics at the University of Toronto. My research focuses on the impact of wind observations on global predictability, Arctic climate, and weather processes.
Since my second year of undergrad, I’ve gained extensive tutoring experience, working with students at Liberty Tutoring, supporting high school and university students through SUS Peer Tutoring and Saturday Programs, and working with private students both in person and online. I also served as a teaching assistant for math and physics courses at both the undergraduate and graduate levels from 2017 to 2024.
I look forward to seeing you in class!
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