![]() ![]() This course is a part of “Mathematics for Machine Learning Specialization” hosted at Coursera. Mathematics for Machine Learning: Multivariate Calculus– Imperial College London Jon has also created a similar course on linear algebra as part of foundational concepts to understand contemporary machine learning and data science techniques.ģ. It covers the foundations of calculus with topics like partial derivatives, delta method, power rule, etc. It is a playlist of 56 videos by Jon Krohn. ![]() Calculus for Machine Learning by Jon Krohn The calculus course covers concepts like limits, continuity, integrals, derivatives - basics and advanced topics like chain rule, second derivatives, etc.Ģ. Khan Academy videos and explanations make learning any new mathematics concept very easy, even for a newbie, and are highly recommended in general. List of Five Free Courses to Learn Calculus ![]() Further, I would highly recommend reading this excellent article by Khan Academy that emphasizes the key skills before starting a course in calculus. You should have a reasonable understanding of algebra, geometry, and trigonometry to grasp calculus. Now that we understand why calculus is an important prerequisite to understanding how machine learning algorithms work, let's learn what skills you need to learn calculus. Source: Image by storyset on Freepik Pre-requisites to Learn Calculus This study of multiple attributes is called multivariate calculus and is used in calculating the minimum and maximum values of a function, derivatives, cost functions, etc. Essentially, you need calculus to comprehend the association between a set of inputs and output variables. You need to know calculus to calculate derivatives, for example, to adjust the neuron weights in the backpropagation of a neural network. The post lists down the courses to learn calculus, but let's first understand the need to learn calculus. Linear algebra, statistics, probability, and calculus are the four key sub-fields that are pre-requisite to learning the internals of the algorithms. So hopefully this makes the product rule a little bit more tangible.You can not escape mathematics if you wish to understand how machine learning algorithms work. This is the same thing as e to the x times cosine Or, if you want, you could factor out an e to the x. To the x times cosine of x, times cosine of x minus e to the x. To the x without taking it's derivative - they are That's what's excitingĪbout that expression, or that function. This right over here, you can view this as this was the derivative as e to the x which happens to be e to the x. And it might be a little bit confusing, because e to the x is its own derivative. So, times the derivative of cosine of x which is negative sine. Plus the first expression, not taking its derivative, so e to the x, times the derivative of To the x which is just, e to the x, times the second expression, not taking it's derivative, Negative sine of x, and so, what's this going to be equal to? This is going to be equal to the derivative of the first expression. And v prime of x, we know as negative sine of x. So u prime of x is stillĮqual to e to the x. One of the things that makes e so special. And if u of x is equal to e to the x, we know that the derivative of that with respect to x is still e to the x. When you just look at it like that, it seems a little bit abstract and that might even be a little bit confusing, but that's why we haveĪ tangible example here and I color-coded intentionally. ![]() Times v is u prime times v, plus u times v prime. You'll take the derivative of the other one, but not the first one. Them, but not the other one, and then the other one In each of them, you're going to take the derivative of one of So the way you remember it is, you have these two things here, you're going to end up So times v of x and then we have plus the first expression, not its derivative, just the first expression. Not the derivative of it, just the second expression. So I could write that as u prime of x times just the second expression This is going to beĮqual to the derivative of the first expression. This is going to be equal to, and I'm color-coding it so we can really keep track of things. So if we take theĭerivative with respect to x of the first expression in terms of x, so this is, we couldĬall this u of x times another expression that involves x. And let me just write down the product rule generally first. But, how do we find theĭerivative of their product? Well as you can imagine, Respect to x of cosine of x is equal to negative sine of x. We know how to find theĭerivative cosine of x. So when you look at this you might say, "well, I know how to find "the derivative with e to the x," that's infact just e to the x. And like always, pause this video and give it a go on your own before we work through it. So let's see if we can find the derivative with respect to x, with either x times the cosine of x. ![]()
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