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1

## What is calculus?

10 個視頻 （總計 46 分鐘）, 4 個閱讀材料, 6 個測驗
10 個視頻
Welcome to Module 1!1分鐘
Functions4分鐘
Rise Over Run4分鐘
Definition of a derivative10分鐘
Differentiation examples & special cases7分鐘
Product rule4分鐘
Chain rule5分鐘
Taming a beast5分鐘
See you next module!39
4 個閱讀材料
About Imperial College & the team5分鐘
How to be successful in this course5分鐘
6 個練習
Matching functions visually20分鐘
Matching the graph of a function to the graph of its derivative20分鐘
Let's differentiate some functions20分鐘
Practicing the product rule20分鐘
Practicing the chain rule20分鐘
Unleashing the toolbox20分鐘
2

## Multivariate calculus

9 個視頻 （總計 41 分鐘）
9 個視頻
Variables, constants & context7分鐘
Differentiate with respect to anything4分鐘
The Jacobian5分鐘
Jacobian applied6分鐘
The Sandpit4分鐘
The Hessian5分鐘
Reality is hard4分鐘
See you next module!23
5 個練習
Practicing partial differentiation20分鐘
Calculating the Jacobian20分鐘
Bigger Jacobians!20分鐘
Calculating Hessians20分鐘
Assessment: Jacobians and Hessians20分鐘
3

## Multivariate chain rule and its applications

6 個視頻 （總計 19 分鐘）
6 個視頻
Multivariate chain rule2分鐘
More multivariate chain rule5分鐘
Simple neural networks5分鐘
More simple neural networks4分鐘
See you next module!34
3 個練習
Multivariate chain rule exercise20分鐘
Simple Artificial Neural Networks20分鐘
Training Neural Networks25分鐘
4

## Taylor series and linearisation

9 個視頻 （總計 41 分鐘）
9 個視頻
Building approximate functions3分鐘
Power series3分鐘
Power series derivation9分鐘
Power series details6分鐘
Examples5分鐘
Linearisation5分鐘
Multivariate Taylor6分鐘
See you next module!28
5 個練習
Matching functions and approximations20分鐘
Applying the Taylor series15分鐘
Taylor series - Special cases30分鐘
2D Taylor series15分鐘
Taylor Series Assessment20分鐘

## 關於 数学在机器学习领域的应用 專項課程

For a lot of higher level courses in Machine Learning and Data Science, you find you need to freshen up on the basics in mathematics - stuff you may have studied before in school or university, but which was taught in another context, or not very intuitively, such that you struggle to relate it to how it’s used in Computer Science. This specialization aims to bridge that gap, getting you up to speed in the underlying mathematics, building an intuitive understanding, and relating it to Machine Learning and Data Science. In the first course on Linear Algebra we look at what linear algebra is and how it relates to data. Then we look through what vectors and matrices are and how to work with them. The second course, Multivariate Calculus, builds on this to look at how to optimize fitting functions to get good fits to data. It starts from introductory calculus and then uses the matrices and vectors from the first course to look at data fitting. The third course, Dimensionality Reduction with Principal Component Analysis, uses the mathematics from the first two courses to compress high-dimensional data. This course is of intermediate difficulty and will require Python and numpy knowledge. At the end of this specialization you will have gained the prerequisite mathematical knowledge to continue your journey and take more advanced courses in machine learning....

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