Theory, numerical approximations, intuition, and visualization in integral calculus. Enhance your math-coding skills.
40 learners
Level Beginner
Course period Unlimited
Understand integral calculus
How to integrate — with techniques like u-substitution, integration by parts, partial fractions
why integration works, from multiple conceptual perspectives: geometric, analytic, and numerical
Python (NumPy and SymPy)
Practice applied integration
If Calculus 1 was about understanding change, then Calculus 2 is about accumulation: how small changes stack up to build area, volume, probability, and complexity. Integration is where mathematics meets imagination — it's where the abstract and the physical merge.
From Riemann sums to probability distributions, from arc lengths to solids of revolution, integral calculus provides the tools to describe, quantify, and visualize everything from the motion of particles to the structure of data. It’s a gateway to multivariable calculus, mathematical modeling, and data science.
And it's not just a theoretical subject. Integration is foundational to fields including physics, engineering, machine learning, quantitative finance, and statistics. If you want to understand the algorithms behind data science or build the mathematical foundation needed for AI, you need to understand integrals.
So whether you're here to strengthen your math background, prep for a university course, or just challenge your brain — welcome.
There are three reasons to study integrals:
📌 Real-world relevance: Integral calculus is used in nearly every STEM discipline — especially in areas like physics, economics, biology, and computer science. You’ll learn how to compute volumes, model systems, and understand distributions — even extend into multivariable integration.
📌 Cognitive training: Integration requires both precision and creativity. You’ll develop deep reasoning skills as you learn to connect concepts, derive formulas, and implement algorithms. It’s like mental weightlifting.
📌 Math as a lifelong hobby: Instead of scrolling through another social-media feed, why not learn how to calculate the surface area of a rotating shape or simulate a probability distribution from scratch?? This course is a good way to keep your mind sharp and intellectually active.
You could learn integration by watching a lecture filled with blackboard equations and hoping it sinks in. Or you could take a more interactive, hands-on approach.
This course follows the principle that
“you can learn a lot of math with a bit of coding.”
You'll use Python — especially NumPy, SymPy, and Matplotlib — to visualize integrals, implement numerical approximations, explore convergence, and gain intuition for the fundamental ideas of calculus.
Deeper insight: Code helps make abstract concepts concrete. You’ll build simulations and generate visuals that bring integrals to life.
Practical skills: Numerical integration and symbolic computation are essential tools in applied mathematics and data science.
Active learning: Coding forces you to think precisely and analytically, which leads to better retention and understanding.
Not at all. This isn’t a programming course, and it's not about using Python to sidestep the math. The goal is to use code as a thinking tool — to help you understand what's going on mathematically, not to replace understanding with computation.
In this course, you'll learn both how to integrate — with techniques like u-substitution, integration by parts, partial fractions — and why integration works, from multiple conceptual perspectives: geometric, analytic, and numerical.
You’ll also explore integration in surprising contexts: creating art from math, modeling randomness with probability distributions, and measuring volumes and surface areas of 3D objects.
1️⃣
Calculus students looking for better educational material
2️⃣
Mathematicians who want to implement math in code
3️⃣
Coders who want to use Python to learn math
Yes — lots of them! Almost every theoretical concept includes one or more exercises for you to solve, and I walk through all of the solutions step-by-step.
Even better: You’ll learn how to create your own calculus exercises, complete with solutions, so you can tailor your practice to exactly what you need. Think of it as building your own personal study plan — powered by Python and guided by your intuition.
This course is designed for learners who already have some experience with derivatives (e.g., from my Calculus 1 course or a university-level intro class). If you're ready to go deeper — into integration, area, volume, probability, and multivariable calculus — then this course is for you.
It's particularly well-suited for:
University students or autodidacts learning integral calculus
Data scientists, engineers, or coders wanting to strengthen their math foundations
Lifelong learners who want a challenging and engaging intellectual pursuit
Basic high-school math
NO programming experience needed
NO prior experience with calculus needed!
This course provides a certification of completion in a format suitable for resumes and portfolios.
By completing the course, you can receive this, which can serve as official proof of your learning accomplishments.
You can switch both audio and subtitles according to your learning style. Select your preferred language.
Who is this course right for?
Mathematicians who want to implement math in code
Anyone who wants to understand calculus intuitively and through real applications
Coders who want to use Python to learn math
Those looking for a modern, practical approach rather than traditional chalkboard-style lectures
Students who want to review or rebuild their understanding of college-level calculus
Anyone seeking a brain-stimulating hobby
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Independent educator, ex-neuroscience professor. I make courses and write self-paced textbooks on applied math, coding (Python and MATLAB), data science, machine-learning, deep learning, and LLM mechanisms.
My motto is "you can learn a lot of math with a bit of coding."
저는 독립 교육자로 일하고 있으며, 이전에는 신경과학 교수로 활동했습니다.
응용수학, 코딩 (Python 및 MATLAB), 데이터 사이언스, 머신러닝, 딥러닝, 그리고 LLM 메커니즘에 관한 강의와 자기주도 학습용 교재를 제작하고 있습니다.
저의 모토는 간단합니다. "코딩을 조금만 할 줄 알면, 수학을 훨씬 쉽고 많이 배울 수 있다."
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