Ace Calculus Part 1: A Fundamentals Course
learn the basic concepts, methods, and applications of differential calculus
Updated on Jun, 2025
Language - English
Teaching and Academics ,Math,Calculus
Lectures -92
Resources -34
Duration -9 hours
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Course Description
How this course works:
This course, Ace Calculus 1, has everything you need to know for Calculus 1, including video and notes from the whiteboard during lectures, and practice problems (with solutions!). I also show every single step in examples and derivations of rules and theorems.
The course is organized into the following sections:
- Review: Precalculus.
- Limits and Continuity.
- Differentiation.
- Derivatives of Transcendental Functions.
- Limits - Indeterminate Forms.
- Applications of Differentiation.
The 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 this section, you will find the notes that I wrote during the lecture. So you can review the notes even when you don't have internet access (but I encourage you to take your own notes while taking the course!).
- Extra notes: I provide some extra notes, including formula sheets and some other useful study guidance.
- 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 or ask for help in the Q&A section.
Things that are included in the course:
- Lifetime access to Ace Calculus- Complete Course.
- Friendly support in the Q&A section.
- Certificate of Completion available for download.
- BONUS #1: Downloadable lectures so you can watch whenever and wherever you are.
- BONUS #2: Downloadable lecture notes and some extra notes (i.e. formula sheet) so you can review the lectures without having a device to watch/listen.
- BONUS #3: A review section on precalculus, including algebra, graphing, asymptotes, composition functions, and inverse functions.
- BONUS #4: Nine assignments with solutions for Calculus 1 in total that make you productive while taking the course.
- BONUS #5: Step-by-step guide to help you solve problems.
Goals
- Find limits of functions (graphically, numerically and algebraically).
- Analyze and apply the notions of continuity and differentiability to algebraic and transcendental functions.
- Determine derivatives by a variety of techniques including explicit differentiation, implicit differentiation, and logarithmic differentiation.
- Identify limits of indeterminate type and solve them using L'Hôpital's rule or other techniques.
- Understand the relationship between derivatives and rates of change.
- Verify a general or particular solution to a differential equation.
- Estimate using linear approximation.
- Use derivatives to study the characteristics of curves and construct detailed graphs of nontrivial functions using derivatives and limits.
- Solve optimization problems.
Prerequisites
- Precalculus (algebra, trigonometry, and functions).
Curriculum
Check out the detailed breakdown of what’s inside the course
Introduction
3 Lectures
-
Overview
02:46
02:46
-
Welcome and How It Works
02:10
02:10
-
Tips to Maximize Your Learning
Review on Precalculus
8 Lectures
Limits and Continuity
18 Lectures
Differentiation
17 Lectures
Derivatives of Transcendental Functions
11 Lectures
Limits - Indeterminate Forms
4 Lectures
Applications: Rates of Change
4 Lectures
Applications: Differential Equations
4 Lectures
Applications: Mean Value Theorem
3 Lectures
Applications: Linear Approximation
4 Lectures
Applications: Curve Sketching
12 Lectures
Applications: Optimization Problems
4 Lectures
Conclusion
2 Lectures
Instructor Details
Gina Chou
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!
A bit about me:
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!
Gina C.
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