Master calculus 1 using Python derivatives and applications

Master calculus 1 using Python derivatives and applications

What you’ll learn

Differential calculus
Mathematical functions (rational, polynomial, transcendantal, trig)
Limits and tricks for solving limits problems
Differentiation rules
Tips and tricks for differentiation
Proofs
Python (numpy and sympy)
Numerical processing
Applied calculus
Visualizing math functions (matplotlib)

Requirements

Basic high-school math
No programming experience needed
No prior experience with calculus needed!

Description

The beauty and importance of calculusCalculus is a beautiful topic in mathematics. No, really!At its heart, calculus is about change. Life is full of change, and calculus is the language that humans developed (invented or discovered — that’s an ongoing debate!) to understand how physical, biological, and abstract systems change. Calculus is more than just some equations you have to memorize; it’s a way of looking at the world and trying to understand how the tiniest infinitesimal changes can lead to gigantic complexity bigger than the imagination.OK, but aside from all that fluff, calculus is also really important for basically every piece of engineering and digital technology that has touched humanity. Indeed, the history of calculus is the history of civilization.You want to learn data science? => You need calculus.You want to learn machine-learning? => You need calculus.You want to learn deep learning? => You need calculus.You want to learn computational science? => You need calculus.You want to learn… I think you see the pattern here ;)Why learn calculus?There are three reasons to learn calculus.It has applications for understanding data science and machine-learning algorithms, but it’s also a beautiful topic in its own right. Learning math will train your critical thinking and reasoning skills. Any branch of mathematics will train your brain, but calculus especially so, because doing calculus is a lot of like running scientific experiments — generate hypotheses, test them in experiments by holding variables constant, and measuring the output.It’s a better hobby than sitting around watching netflix. Seriously. Learning math will help protect you from age-related cognitive decline. Challenge your mind to keep it sharp!Learn calculus the traditional way or the modern way?So, how do you learn calculus? You can learn it the way most people do — by watching someone else scratch on a chalkboard while you furiously take notes and try to decipher their sloppy handwriting, all the while having a little voice in your head telling you that you don’t get it because you’re not smart enough.Or you can try a different approach.I follow the maxim “you can learn a lot of math with a bit of coding.” In this course, you will use Python (mostly the numpy and sympy libraries) as a novel tool to help you learn concepts, proofs, visualizations, and algorithms in calculus.So this is just about coding math?No, this course is not about coding math. And it’s not about using Python to cheat on your math homework. Python’s symbolic math and plotting engines are incredibly powerful — and yet underutilized — tools to help you learn math. By translating formulas into code, implementing algorithms, and solving challenging coding exercises, you will gain a deep knowledge of concepts in calculus.And the graphics engine in Python will let you see equations and functions in a way that helps you develop intuition for why functions behave the way they do.You will also learn the limits of computers for learning calculus, and why you still need to use your brain and freshly developed calculus skills.New to Python?Python is a popular multi-purpose programming language that is light-weight and free. If you are new to Python, then don’t worry! This course comes with a 7+ hour Python coding tutorial (potentially up to 12 hours if you complete all the exercises) that is designed for beginners and will teach you the coding skills you’ll need for this course. Are there exercises?Everyone knows that you need to solve math problems to learn math. This course has exercises for you to solve in nearly every video — and I explain the answers to every single exercise (not only the odd-numbered ones, lol).But wait, there’s more! I don’t just give you problems to work on; I will teach you how to create your own exercises (and solutions) so you can custom-tailor your own homework assignments to practice exactly the skills you most need to work on. Because you know, “give someone a fish” versus “teach someone to fish.” Is this the right course for you?One thing I’ve learned from 20+ years of teaching is that no two learners are the same, which means that no course will be right for everyone. I hope you find this course a valuable learning resource — and fun to work through! — but the reality is that this course won’t be ideal for everyone. Please watch the preview videos and check out the reviews before enrolling.And if you enroll but then decide that this course isn’t a good match for you, then that’s fine! Check out Udemy’s 30-day return guarantee.

Overview

Section 1: Introductions

Lecture 1 Prerequisites and how to rock this course

Lecture 2 Gradient fields forever (hands-on activity)

Lecture 3 Using the Udemy platform

Section 2: Download all course materials

Lecture 4 IMPORTANT: Downloading and using the code

Lecture 5 My policy on sharing code

Lecture 6 Should you watch the Python tutorial?

Section 3: Functions

Lecture 7 Section summary and goals

Lecture 8 Terminology in math vs. coding

Lecture 9 What is a “function”?

Lecture 10 Domain and range of a function

Lecture 11 Linear and nonlinear functions

Lecture 12 CodeChallenge: math in python, part 1

Lecture 13 CodeChallenge: math in python, part 2

Lecture 14 Polynomial functions

Lecture 15 CodeChallenge: polynomials, part 1

Lecture 16 CodeChallenge: polynomials, part 2

Lecture 17 Transcendental functions

Lecture 18 Exponential and log functions

Lecture 19 CodeChallenge: exp and log, part 1

Lecture 20 CodeChallenge: exp and log, part 2

Lecture 21 CodeChallenge: Power and log, part 1

Lecture 22 CodeChallenge: Power and log, part 2

Lecture 23 Trigonometric functions

Lecture 24 CodeChallenge: trigonometry

Lecture 25 Piecewise functions

Lecture 26 CodeChallenge: piecewise functions, part 1

Lecture 27 CodeChallenge: piecewise functions, part 2

Lecture 28 Continuous and discontinuous functions

Lecture 29 CodeChallenge: discontinuities, part 1

Lecture 30 CodeChallenge: discontinuities, part 2

Lecture 31 Intermediate value theorem

Lecture 32 Composite functions

Lecture 33 Inverse functions

Lecture 34 CodeChallenge: Composite and inverse, part 1

Lecture 35 CodeChallenge: Composite and inverse, part 2

Lecture 36 Function symmetry (even and odd)

Lecture 37 Sketching functions by hand

Lecture 38 CodeChallenge: Infinite functions to sketch, part 1

Lecture 39 CodeChallenge: Infinite functions to sketch, part 2

Section 4: Tangent: Levels of understanding

Lecture 40 What does it mean to “understand math”?

Lecture 41 Timescales of discovering vs. learning math

Section 5: Limits

Lecture 42 Section summary and goals

Lecture 43 Limits in geometry and algebra

Lecture 44 CodeChallenge: Limits via Zeno’s paradox

Lecture 45 “Easy” limits by plugging in or factoring

Lecture 46 One-sided limits and infinities

Lecture 47 CodeChallenge: limits in numpy & sympy, part 1

Lecture 48 CodeChallenge: limits in numpy & sympy, part 2

Lecture 49 CodeChallenge: properties of limits, part 1

Lecture 50 CodeChallenge: properties of limits, part 2

Lecture 51 Continuity and discontinuities, revisited

Lecture 52 CodeChallenge: Limits at discontinuities, part 1

Lecture 53 CodeChallenge: Limits at discontinuities, part 2

Lecture 54 Limits of trig functions, part 1

Lecture 55 CodeChallenge: Confirm the trig limits

Lecture 56 Squeeze theorem

Lecture 57 Limits of trig functions, part 2

Lecture 58 CodeChallenge: Trig limits in sympy, part 1

Lecture 59 CodeChallenge: Trig limits in sympy, part 2

Lecture 60 Limited limits possibilities

Lecture 61 What the ?$%# is an “infinitesimal”??

Lecture 62 Sketching functions by hand, redux

Lecture 63 CodeChallenge: Infinite limits exercises, part 1

Lecture 64 CodeChallenge: Infinite limits exercises, part 2

Section 6: Tangent: Accountability in online learning

Lecture 65 The pros and cons of self-directed learning

Lecture 66 Suggestions for learning accountability

Section 7: Differentiation fundamentals

Lecture 67 Section summary and goals

Lecture 68 Slope of a line

Lecture 69 CodeChallenge: Global and local slopes

Lecture 70 Formal definition of the derivative

Lecture 71 Derivative of a constant is 0 (proof)

Lecture 72 Various notations of the derivative

Lecture 73 CodeChallenge: derivatives in sympy

Lecture 74 Interpreting derivatives plots

Lecture 75 CodeChallenge: Linearity of differentiation

Lecture 76 Derivatives of polynomials

Lecture 77 Derivatives of cosine and sine

Lecture 78 CodeChallenge: trig derivatives

Lecture 79 Derivatives of absolute value and square root

Lecture 80 Derivatives of log and exp

Lecture 81 Critical points: Definition and applications

Lecture 82 Finding critical points

Lecture 83 CodeChallenge: Critical points in Python, part 1

Lecture 84 CodeChallenge: Critical points in Python, part 2

Lecture 85 CodeChallenge: Infinite derivatives exercises

Section 8: Tangent: Where does math come from?

Lecture 86 Is math discovered or invented?

Section 9: Differentiation rules and theorems

Lecture 87 Section summary and goals

Lecture 88 Linearity of differentiation (proof)

Lecture 89 Theorem: Differentiability implies continuity

Lecture 90 Product rule

Lecture 91 Chain rule

Lecture 92 Quotient rule

Lecture 93 CodeChallenge: product and quotient rules

Lecture 94 CodeChallenge: chain rule

Lecture 95 Implicit differentiation

Lecture 96 Implicit differentiation proofs (log, exp, power)

Lecture 97 CodeChallenge: implicit differentiation, part 1

Lecture 98 CodeChallenge: implicit differentiation, part 2

Lecture 99 CodeChallenge: derivative of c^x and x^x

Lecture 100 Higher-order derivatives

Lecture 101 CodeChallenge: Derivatives of derivatives… (part 1)

Lecture 102 CodeChallenge: Derivatives of derivatives… (part 2)

Lecture 103 L’Hospital’s Rule for indeterminant limits

Lecture 104 Rolle’s Theorem

Lecture 105 Mean value theorem

Lecture 106 CodeChallenge: Implement the MVT algorithm

Lecture 107 CodeChallenge: Use the MVT to explore functions

Lecture 108 CodeChallenge: numerical approximations to MVT

Lecture 109 CodeChallenge: More differentiation exercises, part 1

Lecture 110 CodeChallenge: More differentiation exercises, part 2

Section 10: Tangent: Learn from multiple sources

Lecture 111 Benefits of varied learning sources

Section 11: Applications

Lecture 112 Section summary and goals

Lecture 113 Racing functions to infinity and beyond!

Lecture 114 The second derivative test

Lecture 115 Code challenge: The second derivative test, part 1

Lecture 116 Code challenge: The second derivative test, part 2

Lecture 117 Linear approximations

Lecture 118 CodeChallenge: linear approximations, part 1

Lecture 119 CodeChallenge: linear approximations, part 2

Lecture 120 Newton’s method for finding roots

Lecture 121 CodeChallenge: Newt’s roots, part 1

Lecture 122 CodeChallenge: Newt’s roots, part 2

Lecture 123 Solving simple optimization problems

Lecture 124 Optimize for surface area

Lecture 125 Optimize for volume

Lecture 126 CodeChallenge: farmers and Qberts

Lecture 127 Gradient descent

Lecture 128 CodeChallenge: Gradient descent in numpy

Lecture 129 CodeChallenge: Gradient descent using sympy

Section 12: Tangent: The joys and challenges of learning

Lecture 130 Embrace difficulties

Section 13: Multivariate differentiation

Lecture 131 Section summary and goals

Lecture 132 2D functions

Lecture 133 CodeChallenge: Fun with 2D functions (numpy), part 1

Lecture 134 CodeChallenge: Fun with 2D functions (numpy), part 2

Lecture 135 CodeChallenge: 2D functions in sympy

Lecture 136 Partial derivatives

Lecture 137 CodeChallenge: Partial derivatives

Lecture 138 Higher-order partial derivatives

Lecture 139 CodeChallenge: Higher-order partial derivatives

Lecture 140 CodeChallenge: Complete partial exercises

Lecture 141 Gradients and gradient fields

Lecture 142 CodeChallenge: Gradient fields, part 1

Lecture 143 CodeChallenge: Gradient fields, part 2

Lecture 144 Gradient descent in 2D

Lecture 145 CodeChallenge: 2D gradient descent, part 1

Lecture 146 CodeChallenge: 2D gradient descent, part 2

Section 14: Python intro: Data types

Lecture 147 Read this before the Python tutorials

Lecture 148 Variables

Lecture 149 Math operators

Lecture 150 Lists

Lecture 151 Tuples

Lecture 152 Booleans

Lecture 153 Dictionaries

Section 15: Python intro: Indexing and slicing

Lecture 154 Indexing

Lecture 155 Slicing

Section 16: Python intro: Functions

Lecture 156 Inputs and outputs

Lecture 157 The numpy library

Lecture 158 Getting help on functions

Lecture 159 Creating functions

Lecture 160 Global and local variable scopes

Lecture 161 Generating random numbers

Section 17: Python intro: Flow control

Lecture 162 If-else statements, part 1

Lecture 163 If-else statements, part 2

Lecture 164 For loops

Lecture 165 While loops

Lecture 166 Initializing variables

Lecture 167 Enumerate and zip iterables

Lecture 168 Single-line loops (list comprehension)

Section 18: Python intro: Sympy and latex

Lecture 169 Intro to sympy, part 1

Lecture 170 Intro to LaTex

Lecture 171 Intro to sympy, part 2

Section 19: Python intro: Text and data visualization

Lecture 172 String interpolation and f-strings

Lecture 173 Plotting dots and lines

Lecture 174 Subplot geometry

Lecture 175 Making the graphs look nicer

Lecture 176 Images

Lecture 177 Export plots in low and high resolution

Section 20: Bonus section

Lecture 178 Bonus content

Calculus students looking for better educational material,Mathematicians who want to implement math in code,Coders who want to use Python to learn math,Data scientists (current or aspiring),Machine-learning and A.I. enthusiasts,Anyone curious about the amazing beauty of calculus on computers!,Anyone looking for an intellectually stimulating hobby

Course Information:

Udemy | English | 41h 24m | 12.04 GB
Created by: Mike X Cohen

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