How Calculus Helps Us Really Understand Trigonometry

Understand Calculus in 2hrs! Learn Taylor series, Fourier analysis, limit, differentiation, and integration all at once!

What you'll learn

Thorough understanding of Taylor series expansion

Hands on experience with Fourier analysis

Thorough understanding of differentiation

Thorough understanding of integration

Understand the significance of fundamental theorem of Calculus

Requirements

You would need Excel to practice some of the math methods.

Description

This course will teach you Calculus in a brand new way! Traditional way to learn Calculus follows a sequential model: algebra-geometry-limit-differentiation-integration. Each piece was taught on an isolated basis. Hence it’s very difficult for students to make connections. Without being able to connecting the dots, it’s impossible to obtain a deep understanding about Calculus. Therefore most students walk away with random bits of memory about Calculus, they don’t really have a coherent and systematic understanding of Calculus.This course will do something totally different. It starts with the ultimate use of Calculus, and approach the core of Calculus step by step in a logical sequence. We wouldn’t throw you a concept out of blue, instead you will be prompted with a real problem, a problem that would encourage you to think proactively what to do next. You won’t be prompted with limit tool day 1, because there was no need at that time. Instead you will face a real problem: what should we do in order to understand sine? From there, you will see gradually the need to differentiate, then integrate. You will see why the limit tool would pop up. You would gain a thorough understanding of one of Calculus’ greatest tool: Taylor series expansion. You would also have hands-on experience with Fourier analysis.We believe the worst way to learn math is to follow the assembly line model where things are thrown at you without you seeing the actual need. This will prevent you from engaging with the mechanics, and learning becomes a boring course of memorizing and blind practicing. We believe the best way to learn math is to think from the end use, from the real problems, then think backwards you will understand how each piece of math snap into the right place effortlessly. And this will make your math learning experience smooth and enriched.Please join in this course if you want to have a systematic understanding of Calculus!

Overview

Section 1: Content overview

Lecture 1 What you will learn

Lecture 2 Content overview

Section 2: Introduction: An overview of Taylor series method

Lecture 3 Trigonometry: Middle ages Vs. Calculus

Lecture 4 An overview of Taylor series expansion

Lecture 5 How to get first level velocity

Lecture 6 How to get layers of velocities

Section 3: How to accumulate impacts from velocities: Integration

Lecture 7 A taste of integration

Lecture 8 How to integrate over lower level velocities

Section 4: How to get velocities: Differentiation

Lecture 9 A taste of differentiation

Lecture 10 How to differentiate a general polynomial

Lecture 11 How to differentiate sine

Lecture 12 How to differentiate cosine

Section 5: Put things together: Taylor series expansion

Lecture 13 Taylor series expansion of sine and cosine

Lecture 14 Implement Taylor series in Excel

Section 6: How sine is used in analyzing sound

Lecture 15 What is Fourier analysis

Lecture 16 How to create sound waves - Limitations of Taylor series

Lecture 17 Creating sound waves in Excel

Lecture 18 Why Fourier analysis works

Lecture 19 How to run Fourier analysis

Section 7: Resources

Lecture 20 Binomial coefficients

Lecture 21 Trig combination formula

Excel is used to implement some of the math methods discussed. While it’s preferred to follow the Excel exercise to enforce the understanding, it’s not required since you can just watch the video and still get a reasonable understanding.