Math 0-1: Calculus For Data Science & Machine Learning

A Casual Guide for Artificial Intelligence, Deep Learning, and Python Programmers

What you'll learn

Limits, limit definition of derivative, derivatives from first principles

Derivative rules (chain rule, product rule, quotient rule, implicit differentiation)

Integration, area under curve, fundamental theorem of calculus

Vector calculus, partial derivatives, gradient, Jacobian, Hessian, steepest ascent

Optimize (maximize or minimize) a function

l'Hopital's Rule

Newton's Method

Requirements

Firm understanding of high school math

Description

Common scenario: You try to get into machine learning and data science, but there's SO MUCH MATH.Either you never studied this math, or you studied it so long ago you've forgotten it all.What do you do?Well my friends, that is why I created this course.Calculus is one of the most important math prerequisites for machine learning. It's required to understand probability and statistics, which form the foundation of data science. Backpropagation, the learning algorithm behind deep learning and neural networks, is really just calculus with a fancy name.If you want to do machine learning beyond just copying library code from blogs and tutorials, you must know calculus.Normally, calculus is split into 3 courses, which takes about 1.5 years to complete.Luckily, I've refined these teachings into just the essentials, so that you can learn everything you need to know on the scale of hours instead of years.This course will cover Calculus 1 (limits, derivatives, and the most important derivative rules), Calculus 2 (integration), and Calculus 3 (vector calculus). It will even include machine learning-focused material you wouldn't normally see in a regular college course. We will even demonstrate many of the concepts in this course using the Python programming language (don't worry, you don't need to know Python for this course). In other words, instead of the dry old college version of calculus, this course takes just the most practical and impactful topics, and provides you with skills directly applicable to machine learning and data science, so you can start applying them today.Are you ready?Let's go!Suggested prerequisites:Firm understanding of high school math (functions, algebra, trigonometry)

Overview

Section 1: Introduction and Outline

Lecture 1 Introduction

Lecture 2 Outline

Lecture 3 How to Succeed in this Course

Lecture 4 Where to Get the Code

Section 2: Review

Lecture 5 Functions Review

Lecture 6 Functions Review in Python

Section 3: Limits

Lecture 7 What Are Limits?

Lecture 8 Precise Definition of Limit (Optional)

Lecture 9 Limit Laws

Lecture 10 Infinities and Asymptotes

Lecture 11 Indeterminate Forms

Lecture 12 Limits in Python

Lecture 13 Limits with Plotting in Python

Section 4: Derivatives From First Principles

Lecture 14 Slopes, Tangent Lines, and Derivatives

Lecture 15 More On Tangent Lines, Derivative Checking

Lecture 16 Exercise: Quadratic

Lecture 17 Exercise: Cubic

Lecture 18 Exercise: Reciprocal

Lecture 19 Exercise: Root

Lecture 20 Alternate Notations & Higher Order Derivatives

Lecture 21 Derivative Checking in Python

Section 5: Derivative Rules

Lecture 22 Power Rule

Lecture 23 Constant Multiple, Addition, Subtraction Rules

Lecture 24 Exponent Rule

Lecture 25 Exponent Rule (continued)

Lecture 26 Chain Rule

Lecture 27 Exercises: Chain Rule

Lecture 28 Product and Quotient Rules

Lecture 29 Exercises: Product and Quotient Rules

Lecture 30 Implicit Differentiation

Lecture 31 Logarithm Rule

Lecture 32 Implicit Differentiation Applications

Lecture 33 Logarithmic Differentiation

Lecture 34 Exercise: Derivatives of Hyperbolic Functions

Lecture 35 Exercise: Sum of Polynomials

Lecture 36 Exercise: Gaussian Variance

Lecture 37 Exercise: Entropy

Lecture 38 Trigonometric Functions (Optional)

Lecture 39 Inverse Trigonometric Functions (Optional)

Section 6: Applications of Differentiation

Lecture 40 Finding the Minimum / Maximum

Lecture 41 Minimum / Maximum Clarifications and Examples

Lecture 42 Second Derivative Test

Lecture 43 Exercise: Minimums and Maximums

Lecture 44 Exercise: Entropy

Lecture 45 Exercise: Gaussian 1

Lecture 46 Exercise: Gaussian 2

Lecture 47 l'Hopital's Rule

Lecture 48 Newton's Method

Lecture 49 Newton's Method in Python

Section 7: Integration (Calculus 2)

Lecture 50 Integrals: Section Introduction

Lecture 51 Area Under Curve

Lecture 52 Fundamental Theorem of Calculus (pt 1)

Lecture 53 Fundamental Theorem of Calculus (pt 2)

Lecture 54 Definite and Indefinite Integrals

Lecture 55 Exercises: Definite Integrals

Lecture 56 Exercises: Indefinite Integrals

Lecture 57 Exercises: Improper Integrals

Lecture 58 Numerical Integration in Python

Section 8: Vector Calculus in Multiple Dimensions (Calculus 3)

Lecture 59 Functions of Multiple Variables

Lecture 60 Partial Differentiation

Lecture 61 The Gradient

Lecture 62 The Jacobian and Hessian

Lecture 63 Differentials and Chain Rule in Multiple Dimensions

Lecture 64 Why is the Gradient the Direction of Steepest Ascent?

Lecture 65 Steepest Ascent in Python

Lecture 66 Optimization and Lagrange Multipliers (pt 1)

Lecture 67 Optimization and Lagrange Multipliers (pt 2)

Anyone who wants to learn calculus quickly,Students and professionals interested in machine learning and data science but who've gotten stuck on the math