Master calculus 1 using Python: derivatives and applications
What you'll learn
- Differential calculus
- Mathematical functions (rational, polynomial, transcendantal, trig)
- Limits and tricks for solving limits problems
- Differentiation rules
- Tips and tricks for differentiation
- Python (numpy and sympy)
- Numerical processing
- Applied calculus
- Visualizing math functions (matplotlib)
- Basic high-school math
- No programming experience needed
- No prior experience with calculus needed!
The beauty and importance of calculus
Calculus is a beautiful topic in mathematics. No, really!
At its heart, calculus is about change. Life is full of change, and calculus is the language that humans developed (invented or discovered -- that's an ongoing debate!) to understand how physical, biological, and abstract systems change. Calculus is more than just some equations you have to memorize; it's a way of looking at the world and trying to understand how the tiniest infinitesimal changes can lead to gigantic complexity bigger than the imagination.
OK, but aside from all that fluff, calculus is also really important for basically every piece of engineering and digital technology that has touched humanity. Indeed, the history of calculus is the history of civilization.
You want to learn data science? => You need calculus.
You want to learn machine-learning? => You need calculus.
You want to learn deep learning? => You need calculus.
You want to learn computational science? => You need calculus.
You want to learn... I think you see the pattern here ;)
Why learn calculus?
There are three reasons to learn calculus.
It has applications for understanding data science and machine-learning algorithms, but it's also a beautiful topic in its own right.
Learning math will train your critical thinking and reasoning skills. Any branch of mathematics will train your brain, but calculus especially so, because doing calculus is a lot of like running scientific experiments -- generate hypotheses, test them in experiments by holding variables constant, and measuring the output.
It's a better hobby than sitting around watching netflix. Seriously. Learning math will help protect you from age-related cognitive decline. Challenge your mind to keep it sharp!
Learn calculus the traditional way or the modern way?
So, how do you learn calculus? You can learn it the way most people do -- by watching someone else scratch on a chalkboard while you furiously take notes and try to decipher their sloppy handwriting, all the while having a little voice in your head telling you that you don't get it because you're not smart enough.
Or you can try a different approach.
I follow the maxim "you can learn a lot of math with a bit of coding." In this course, you will use Python (mostly the numpy and sympy libraries) as a novel tool to help you learn concepts, proofs, visualizations, and algorithms in calculus.
There are three reasons to use Python to learn calculus:
Practical applications: Calculus is essential for understanding data science, machine learning, deep learning, computational science, and many other fields.
Mental exercise: Learning calculus, particularly in combination with Python, will train your critical thinking and reasoning skills.
Lifelong benefits: Engaging your mind with calculus can help protect against age-related cognitive decline and offer a fulfilling alternative to passive leisure activities.
So this is just about coding math?
No, this course is not about coding math. And it's not about using Python to cheat on your math homework. Python's symbolic math and plotting engines are incredibly powerful -- and yet underutilized -- tools to help you learn math. By translating formulas into code, implementing algorithms, and solving challenging coding exercises, you will gain a deep knowledge of concepts in calculus.
And the graphics engine in Python will let you see equations and functions in a way that helps you develop intuition for why functions behave the way they do.
You will also learn the limits of computers for learning calculus, and why you still need to use your brain and freshly developed calculus skills.
New to Python?
Python is a versatile and user-friendly programming language that complements calculus, especially when using libraries like NumPy and SymPy. By incorporating Python into your calculus studies, you can gain a deeper understanding of mathematical concepts, proofs, visualizations, and algorithms.
If you are new to Python, then don't worry! This course comes with a 7+ hour Python coding tutorial (potentially up to 12 hours if you complete all the exercises) that is designed for beginners and will teach you the coding skills you'll need for this course.
Are there exercises?
Everyone knows that you need to solve math problems to learn math. This course has exercises for you to solve in nearly every video -- and I explain the answers to every single exercise (not only the odd-numbered ones, lol).
But wait, there's more! I don't just give you problems to work on; I will teach you how to create your own exercises (and solutions) so you can custom-tailor your own homework assignments to practice exactly the skills you most need to work on. Because you know, "give someone a fish" versus "teach someone to fish."
Is this the right course for you?
One thing I've learned from 20+ years of teaching is that no two learners are the same, which means that no course will be right for everyone. I hope you find this course a valuable learning resource -- and fun to work through! -- but the reality is that this course won't be ideal for everyone. Please watch the preview videos and check out the reviews before enrolling.
And if you enroll but then decide that this course isn't a good match for you, then that's fine! Check out Udemy's 30-day return guarantee.
Who this course is for:
- Calculus students looking for better educational material
- Mathematicians who want to implement math in code
- Coders who want to use Python to learn math
- Data scientists (current or aspiring)
- Machine-learning and A.I. enthusiasts
- Anyone curious about the amazing beauty of calculus on computers!
- Anyone looking for an intellectually stimulating hobby
I am a full-time educator and writer, and former professor of neuroscience. I "retired" from that position so I could focus my time and energy creating high-quality educational material just for you.
I have 20 years of experience teaching programming, data analysis, signal processing, statistics, linear algebra, and experiment design. I've taught undergraduate students, PhD candidates, postdoctoral researchers, and full professors. I have taught in "traditional" university courses, special week-long intensive courses, and Nobel prize-winning research labs. I have >100 hours of online lectures on neuroscience data analysis that you can find on my website and youtube channel. And I've written several technical books about these topics with a few more on the way.
I'm not trying to show off -- I'm trying to convince you that you've come to the right place to maximize your learning from an instructor who has spent two decades refining and perfecting his teaching style.
Over 200,000 students have watched over 15,000,000 minutes of my courses. Come find out why!
I have several free courses that you can enroll in. Try them out! You got nothing to lose ;)
By popular request, here are suggested course progressions for various educational goals:
MATLAB programming: MATLAB onramp; Master MATLAB; Image Processing
Python programming: Master Python programming by solving scientific projects; Master Math by Coding in Python
Applied linear algebra: Complete Linear Algebra; Dimension Reduction
Signal processing: Understand the Fourier Transform; Generate and visualize data; Signal Processing; Neural signal processing