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Mathematics for Machine Learning: Multivariate Calculus 

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Mathematics for Machine Learning: Multivariate Calculus


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Mathematics for Machine Learning: Multivariate Calculus

  • Shareable Certificate Earn a Certificate upon completion
  • 100% online Start instantly and learn at your own schedule.
  • Course 2 of 3 in the Mathematics for Machine Learning Specialization
  • Flexible deadlines Reset deadlines in accordance to your schedule.
  • Beginner Level
  • Approx. 18 hours to complete
  • English Subtitles: Arabic, French, Portuguese (European), Greek, Italian, Vietnamese, German, Russian, English, Spanish
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Mathematics for Machine Learning: Multivariate Calculus
Course details

Skills you will learn
More about this course
  • This course offers a brief introduction to the multivariate calculus required to build many common machine learning techniques. We start at the very beginning with a refresher on the ?rise over run? formulation of a slope, before converting this to the formal definition of the gradient of a function. We then start to build up a set of tools for making calculus easier and faster. Next, we learn how to calculate vectors that point up hill on multidimensional surfaces and even put this into action using an interactive game. We take a look at how we can use calculus to build approximations to functions, as well as helping us to quantify how accurate we should expect those approximations to be. We also spend some time talking about where calculus comes up in the training of neural networks, before finally showing you how it is applied in linear regression models. This course is intended to offer an intuitive understanding of calculus, as well as the language necessary to look concepts up yourselves when you get stuck. Hopefully, without going into too much detail, you?ll still come away with the confidence to dive into some more focused machine learning courses in future.
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Mathematics for Machine Learning: Multivariate Calculus

What is calculus?

Welcome to Multivariate Calculus

Welcome to Module 1!


Rise Over Run

Definition of a derivative

Differentiation examples & special cases

Product rule

Chain rule

Taming a beast

See you next module!

About Imperial College & the team

How to be successful in this course

Grading Policy

Additional Readings & Helpful References

Matching functions visually

Matching the graph of a function to the graph of its derivative

Let's differentiate some functions

Practicing the product rule

Practicing the chain rule

Unleashing the toolbox

Multivariate calculus

Welcome to Module 2!

Variables, constants & context

Differentiate with respect to anything

The Jacobian

Jacobian applied

The Sandpit

The Hessian

Reality is hard

See you next module!

Practicing partial differentiation

Calculating the Jacobian

Bigger Jacobians!

Calculating Hessians

Assessment: Jacobians and Hessians

Multivariate chain rule and its applications

Welcome to Module 3!

Multivariate chain rule

More multivariate chain rule

Simple neural networks

More simple neural networks

See you next module!

Multivariate chain rule exercise

Simple Artificial Neural Networks

Training Neural Networks

Taylor series and linearisation

Welcome to Module 4!

Building approximate functions

Power series

Power series derivation

Power series details



Multivariate Taylor

See you next module!

Matching functions and approximations

Applying the Taylor series

Taylor series - Special cases

2D Taylor series

Taylor Series Assessment

Intro to optimisation

Welcome to Module 5!

Gradient Descent

Constrained optimisation

See you next module!

Newton-Raphson in one dimension

Checking Newton-Raphson

Lagrange multipliers

Optimisation scenarios


Simple linear regression

General non linear least squares

Doing least squares regression analysis in practice

Wrap up of this course

Did you like the course? Let us know!

Linear regression

Fitting a non-linear function

Mathematics for Machine Learning: Multivariate Calculus
Admission Process

    Important Dates

    May 25, 2024
    Course Commencement Date

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    Mathematics for Machine Learning: Multivariate Calculus
    Students Ratings & Reviews

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    Shivanjali Pratap Phalke
    Mathematics for Machine Learning: Multivariate Calculus
    Learning Experience: Content was good. Video timings were great. Only necessary content was taught. Assignments were challenging. Quizzes were a good booster.
    Faculty: Faculty was well prepared, experienced and friendly. The timings of lectures were good Course was up to date. I learnt new concepts that I never heard about. Assignments were great and challenging
    Reviewed on 4 Feb 2023Read More
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    Mathematics for Machine Learning: Multivariate Calculus

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