• views: 242
• date: 28 February 2023
• posted by: voska89

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

Homepage

https://www.udemy.com/course/calculus-data-science/

   
   
   

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