Deriving Euler's formula four ways!
Michael Penn
•
July 14, 2023
Michael Penn
View ChannelAbout
Math videos covering a wide variety of topics from theory to application. Calculus, Differential Equations, Number Theory, Proofs, unique problems and much more. I have a second channel that has full course material for higher level math called MathMajor which is geared toward more structured videos that support real classes I teach. My goal is to spread math education, knowledge, and understanding to as many people as possible.
Latest Posts
Upgrade Your Phone's Camera Today!
AI-recommended products based on this video
Loading...
![VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung](https://m.media-amazon.com/images/I/71bHSP1cRkL._AC_UL960_FMwebp_QL65_.jpg)
VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung
(54,882)
$32.25
FREE delivery Mon, Aug 25 on your first order
1K+ bought in past month
Loading...
![iPhone Charger Fast Charging [Apple MFi Certified] USB C to Lightning Cable 6FT USBC to Lightning Cable Nylon Braided Type C Cord for iPhone 14 13 12 11 Pro Max XR XS X 8 7 6 Plus SE, iPad](https://m.media-amazon.com/images/I/517jTqwo1nL._AC_UL960_FMwebp_QL65_.jpg)
iPhone Charger Fast Charging [Apple MFi Certified] USB C to Lightning Cable 6FT USBC to Lightning Cable Nylon Braided Type C Cord for iPhone 14 13 12 11 Pro Max XR XS X 8 7 6 Plus SE, iPad
(4,036)
$8.99
FREE delivery Sun, Jun 29 on your first order
2K+ bought in past month
Loading...
![iPhone Charger [Apple MFi Certified] 3FT, 3Pack USB A to Lightning Cable Braided Fast Charging Apple Cord Compatible with iPhone 14 13 12 11 Pro Max XS XR X 8 7 6 5 Plus iPad/iPod/AirPods](https://m.media-amazon.com/images/I/71xZOlUELbL._AC_UL960_FMwebp_QL65_.jpg)
iPhone Charger [Apple MFi Certified] 3FT, 3Pack USB A to Lightning Cable Braided Fast Charging Apple Cord Compatible with iPhone 14 13 12 11 Pro Max XS XR X 8 7 6 5 Plus iPad/iPod/AirPods
(5,626)
$17.99
FREE delivery Sat, Jun 14 on your first order
50+ bought in past month
Loading...

2Pack 10ft iPhone Charger 90 Degree Lightning Cable Right Angle Long USB Charging Cord Compatible with Apple iPhone 14 13 12 11 Pro Max XS XR X 8 7 6 5 Plus iPad iPod
(2,193)
$14.24
FREE delivery Sat, Jun 14 on your first order
400+ bought in past month
Loading...

Wireless Charger for Samsung - NANAMI 3 in 1 Charging Station for Multiple Devices,Fast Charger Stand Dock for Galaxy S25 S24 S23 Ultra S22 S21 S20 Z Flip Fold,Galaxy Watch 5/5 Pro/4/3,Galaxy Buds Pro
(2,272)
$43.99
PrimeFREE delivery Sat, Jun 14
200+ bought in past month
Loading...

45W Super Fast Charger USBC Charger, 2Pack 10FT Samsung Charger Fast Charging Cord Cable& Samsung Type C Charger Block for Galaxy S25 S24 S23 S22 S21 Ultra/Plus, Tab S10 S9 S8 S7,iPad,Android Phone
(52)
$22.79
FREE delivery Fri, Oct 3 on your first order
1K+ bought in past month
Loading...

TAURI for iPhone 17 Pro Max Case 6.9" with 1-Pack Screen Protector, Camera Lens Full Protection, Military-Grade Protection, Shockproof Transparent Back Bumper Phone Cover - Clear Global Recycled Standard
(0)
$10.76
FREE delivery Thu, Oct 16 on your first order
2K+ bought in past month
Loading...
![Ailun 3 Pack Screen Protector for iPhone 17 [6.3 inch] + 3 Pack Camera Lens Protector with Installation Frame,Sensor Protection,Dynamic Island Compatible,Case Friendly Tempered Glass Film](https://m.media-amazon.com/images/I/71Ps91qFQ9L._AC_UL960_FMwebp_QL65_.jpg)
Ailun 3 Pack Screen Protector for iPhone 17 [6.3 inch] + 3 Pack Camera Lens Protector with Installation Frame,Sensor Protection,Dynamic Island Compatible,Case Friendly Tempered Glass Film
(216,515)
$9.67
Prime
2K+ bought in past month
Loading...

Best Seller
TAURI for iPhone 17 Pro Case 6.3" with 1-Pack Screen Protector, Camera Lens Full Protection, Military-Grade Protection, Shockproof Transparent Back Bumper Phone Cover - Clear Global Recycled Standard
(61,696)
$10.76
Prime
2K+ bought in past month
Loading...
![Ailun 3 Pack Screen Protector for iPhone 17 Pro [6.3 inch] + 3 Pack Camera Lens Protector with Installation Frame,Sensor Protection,Dynamic Island Compatible,Case Friendly Tempered Glass Film](https://m.media-amazon.com/images/I/71ZyAPjoBhL._AC_UL960_FMwebp_QL65_.jpg)
Ailun 3 Pack Screen Protector for iPhone 17 Pro [6.3 inch] + 3 Pack Camera Lens Protector with Installation Frame,Sensor Protection,Dynamic Island Compatible,Case Friendly Tempered Glass Film
(216,323)
$9.67
Prime
Loading...

Phone Case for iPhone 12 Pro Max Case Compatible with MagSafe, YUANDMI Case for iPhone 12 Pro Max Magnetic Slim Thin Translucent Matte Back Shockproof Anti-Yellow Protective Cover Case Black
(130)
$12.99
FREE delivery Sat, Jun 14 on your first order
Loading...
![iPhone Charger Fast Charging [Apple MFi Certified] USB C to Lightning Cable 6FT USBC to Lightning Cable Nylon Braided Type C Cord for iPhone 14 13 12 11 Pro Max XR XS X 8 7 6 Plus SE, iPad](https://m.media-amazon.com/images/I/517jTqwo1nL._AC_UL960_FMwebp_QL65_.jpg)
iPhone Charger Fast Charging [Apple MFi Certified] USB C to Lightning Cable 6FT USBC to Lightning Cable Nylon Braided Type C Cord for iPhone 14 13 12 11 Pro Max XR XS X 8 7 6 Plus SE, iPad
(4,036)
$8.99
FREE delivery Sun, Jun 29 on your first order
2K+ bought in past month
Loading...
![iPhone Charger [Apple MFi Certified] 3FT, 3Pack USB A to Lightning Cable Braided Fast Charging Apple Cord Compatible with iPhone 14 13 12 11 Pro Max XS XR X 8 7 6 5 Plus iPad/iPod/AirPods](https://m.media-amazon.com/images/I/71xZOlUELbL._AC_UL960_FMwebp_QL65_.jpg)
iPhone Charger [Apple MFi Certified] 3FT, 3Pack USB A to Lightning Cable Braided Fast Charging Apple Cord Compatible with iPhone 14 13 12 11 Pro Max XS XR X 8 7 6 5 Plus iPad/iPod/AirPods
(5,626)
$17.99
FREE delivery Sat, Jun 14 on your first order
50+ bought in past month
Loading...

2Pack 10ft iPhone Charger 90 Degree Lightning Cable Right Angle Long USB Charging Cord Compatible with Apple iPhone 14 13 12 11 Pro Max XS XR X 8 7 6 5 Plus iPad iPod
(2,193)
$14.24
FREE delivery Sat, Jun 14 on your first order
400+ bought in past month
Loading...

USB C Cable 6ft Type C Charger Cable 3.1A Fast Charging Nylon Braided USB A to USB C Charge Cord for Samsung Galaxy S25 S24 S23 S22 S21 S20 A12 A13 A14 A15 A16 A32 A53 5G Android Phone Tablet PS5 LG
(4,378)
$8.41
FREE delivery Sat, Jun 14 on your first order
400+ bought in past month
Loading...

Wireless Charger for Samsung - NANAMI 3 in 1 Charging Station for Multiple Devices,Fast Charger Stand Dock for Galaxy S25 S24 S23 Ultra S22 S21 S20 Z Flip Fold,Galaxy Watch 5/5 Pro/4/3,Galaxy Buds Pro
(2,272)
$43.99
PrimeFREE delivery Sat, Jun 14
200+ bought in past month
Loading...

koolehaoda L Shape Camera Bracket, Video Vertical Shooting Quick Release Plate L Stand Arca Swiss Compatible for Tripod Head Ballhead DSLR Camera
(87)
$23.98
FREE delivery Thu, Jun 19 on your first order
Loading...

ANXRE 71" Phone Tripod, NT79 Extendable Selfie Stick for Cell Phone&Camera Photo Video Kits, Travel Tripod Stand with Remote for Video Recording, Phone Holder Tripod Compatible with Phone Camera Gopro
(752)
$23.99
FREE delivery Tue, Aug 19 on your first order
2K+ bought in past month
Loading...

NEEWER Advanced 18 inch LED Ring Light for Phone, LCD Touch Screen, 2.4G Remote Lights Control, 3200-5600K, Tripod Light for iPhone Action Camera, for Studio Makeup TikTok YouTube Video Salon (Black)
(2,807)
$181.49
FREE delivery Sun, Aug 10
Loading...

SmallRig ZV-E1 Camera Baseplate for Sony ZV-E1, Built-in Cold Shoe Mount and QR Plate (for Arca) Quick Switch Between Tripod and Stabilizer for DJI RS 2 / RSC 2 / RS 3 / RS 3 Pro - 4314
(3)
$44.99
FREE delivery Thu, Jun 19
Loading...

Bayjebu Parts for Lenovo ThinkPad L14 LCD Cover and Bezel for Standard Camera (Not for IR)
(0)
$195.50
FREE delivery Jun 19 - 25Only 3 left in stock.
Loading...

Digital Camera,3in LCD Screen Portable Camera,18X Zoom HD SLR Long Focal Length Camera with Large Capacity Battery for Photography (Standard Type)
(3)
$56.76
FREE delivery Aug 27 - Sep 18
Loading...

ESR for iPhone 17 Pro Case with Stash Stand, Camera Control, Compatible with MagSafe, Shockproof Military-Grade Protection, Magnetic Phone Case for iPhone 17 Pro, Classic Hybrid Case (HaloLock), Clear
(2)
$24.99
FREE delivery Sat, Sep 20 on your first order
Loading...

ESR for iPhone 16 Pro Max Case, Silicone Case with Stand, Compatible with MagSafe, Built-in Camera Stash Stand, Magnetic Phone Case for iPhone 16 Pro Max, Cloud Series, Light Blue
(23,148)
$19.54
FREE delivery Sat, Jun 14 on your first order
Loading...

SmallRig FX3 / FX30 HawkLock Quick Release Camera Cage Kit for Sony with Cable Clamp, Bulit-in QR Cold Shoe NATO Rail/QR Plate for Arca, Modular Design Compatible with Original XLR Handle - 4770
(35)
$124.94
FREE delivery Thu, Jun 19
Loading...

SmallRig FX3 / FX30 HawkLock Quick Release Camera Cage Kit for Sony with XLR Handle Extension, Wrist Strap and Cable Clamp for HDMI, QR Cold Shoe, NATO Rail/QR Plate for Arca,Titanium Gray - 4771
(72)
$174.24$162.04
FREE delivery Thu, Jun 19
Loading...

eufy Security, eufyCam S220 (eufyCam 2C Pro) 2-Cam Kit, Wireless Home Security Camera, 2K Resolution, 180-Day Battery Life, HomeKit Compatibility, IP67, Night Vision, Motion Only Alert, No Monthly Fee
(2,743)
$219.99
FREE delivery Thu, Sep 4
100+ bought in past month
Loading...

OHLPRO Tablet Holder for Car, iPad Holder for Car Air Vent Mount, Universal Dashboard Windshield 2-in-1 Cradle TPU Suction Sticky Gel for iPad/iPad mini Samsung Galaxy Size 6"- 10.5" iPad Car Holder
(1,961)
$22.99$15.09
FREE delivery Tue, Jun 17 on your first order
50+ bought in past month
Loading...

OHLPRO Tablet Car Mount Universal Tablet Holder for Car Windshield Dash Dashboard, 360 Degree Rotation,TPU Suction Gel Stick, for iPad Mini 4/3/2/1Samsung Galaxy Size 7"- 10.5" Tablet Mount
(1,515)
$18.99
FREE delivery Tue, Jun 17 on your first order
Loading...
![Miracase Car Phone Mount, [2025 Upgraded Strong Military Grade Suction Cup] Long Arm Phone Holder for Car Dashboard Windshield Vent, Hands Free Cell Phone Holder Compatible with All Mobile Phones Global Recycled Standard](https://m.media-amazon.com/images/I/81oehGW5OLL._AC_UL960_FMwebp_QL65_.jpg)
Miracase Car Phone Mount, [2025 Upgraded Strong Military Grade Suction Cup] Long Arm Phone Holder for Car Dashboard Windshield Vent, Hands Free Cell Phone Holder Compatible with All Mobile Phones Global Recycled Standard
(39,711)
$22.49
FREE delivery Sat, Sep 20 on your first order
4K+ bought in past month
Loading...
![VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung](https://m.media-amazon.com/images/I/71bHSP1cRkL._AC_UL960_FMwebp_QL65_.jpg)
VANMASS [85+LBS Strongest Suction & Clip] 2025 Upgrade Car Phone Holder [Patent & Safety Certs] Cell Phone Mount Truck Stand for Dashboard Windshield Vent for iPhone 16 Pro Max 15 14 13 12 Samsung
(54,882)
$32.25
FREE delivery Mon, Aug 25 on your first order
1K+ bought in past month
Loading...

for Magsafe Car Mount【20 Strong Magnets 】Magnetic Phone Holder for Car Phone Holder Mount Dash【360°】Cell Phone Mount for Car Accessories,Car Mount for iPhone 16 Pro Max 15 14 13 12 Plus MagSafe Cases
(11,563)
$16.98
FREE delivery Tue, Jun 17 on your first order
3K+ bought in past month



