# Mathematics for Machine Learning: Multivariate Calculus

- Offered byCoursera

## Mathematics for Machine Learning: Multivariate Calculus at Coursera Overview

Duration | 18 hours |

Start from | Start Now |

Total fee | Free |

Mode of learning | Online |

Difficulty level | Beginner |

Official Website | Explore Free Course |

Credential | Certificate |

## Mathematics for Machine Learning: Multivariate Calculus at Coursera Highlights

- 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

## Mathematics for Machine Learning: Multivariate Calculus at Coursera Course details

- 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.

## Mathematics for Machine Learning: Multivariate Calculus at Coursera Curriculum

**What is calculus?**

Welcome to Multivariate Calculus

Welcome to Module 1!

Functions

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

Examples

Linearisation

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

**Regression**

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 at Coursera Admission Process

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## Mathematics for Machine Learning: Multivariate Calculus at Coursera Students Ratings & Reviews

- 3-41

**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

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