General query: Multivariate calculus

Course Q&A Math for Machine Learning Calculus for Machine Learning and Data Science
1

Hi, I’m a beginner. For this course Calculus for Machine Learning & Data Science, does it cover “Multivariate Calculus” ? Thank you

Multivariate calculus
2

Hello @Matt5129
Welcome to the discourse community. Thanks a lot for bringing this question up.

It appears that the only topic that is covered in the field of Multivariate calculus is “Multivariate Newton’s method”.

Here is a list of the topics of the “Calculus for Machine Learning & Data Science” :

Calculus for Machine Learning and Data Science:

Week 1: Functions of one variable: Derivative and optimization

Lesson 1: Derivatives

  • Example to motivate derivatives: Speedometer
  • Derivative of common functions (c, x, x^2, 1/x)
  • Meaning of e and the derivative of e^x
  • Derivative of log x
  • Existence of derivatives
  • Properties of derivative

Lesson 2: Optimization with derivatives

Video 1: Intro to optimization: Temperature example

Video 2: Optimizing cost functions in ML: Squared loss

Video 3: Optimizing cost functions in ML: Log loss

Week 2: Functions of two or more variables: Gradients and gradient descent

Lesson 1: Gradients and optimization

  • Intro to gradients
  • Example to motivate gradients: Temperature
  • Gradient notation
  • Optimization using slope method: Linear regression

Lesson 2: Gradient Descent

  • Optimization using gradient descent: 1 variable
  • Optimization using gradient descent: 2 variable
  • Gradient descent for linear regression

Week 3: Optimization in Neural Networks and Newton’s method

Lesson 1: Optimization in Neural Networks

  • Perceptron with no activation and squared loss (linear regression)
  • Perceptron with sigmoid activation and log loss (classification)
  • Two-layer neural network with sigmoid activation and log loss
  • Mathematics of Backpropagation

Lesson 2: Beyond Gradient Descent: Newton’s Method

  • Root finding with Newton’s method
  • Adapting Newton’s method for optimization
  • Second derivatives and Hessians
  • Multivariate Newton’s method

A list of all courses under Mathematics for Machine Learning and Data Science Specialization
is on this link .

3

Thanks for the prompt response! Can i just clarify, for week 2: Functions of two or more variables, is not really considered “multivariate calculus” ?

Thanks once again