Professor Leonard

Why does e = 2.71828...? (Differential Equations 43)

26K views · 8d ago · 32:28

Why does e = 2.71828...? (Differential Equations 43) An exploration of the value of 'e', Euler's Number, using Euler's Method of numerical approximation.

Using Euler's Method (Differential Equations 42)

31K views · 19d ago · 59:37

Using Euler's Method (Differential Equations 42) Exploring and understanding the use of Euler's Method to numerically approximate first order differential equations.

Introduction to Euler's Method (Differential Equations 41)

48K views · 29d ago · 56:31

Introduction to Euler's Method (Differential Equations 41) An introduction to numerical methods of approximation for Differential Equations that cannot be solved explicitly or with traditional methods. Important foundation for further methods that are built around Euler's Method.

Acceleration and Velocity with Resistance, Part 2 (Differential Equations 40)

42K views · 1mo ago · 1:27:04

Acceleration and Velocity with Resistance, Part 2 (Differential Equations 40) When Acceleration is proportional to the square of velocity. Also discussed is Hyperbolic Tangent inverse and how in the world we can use it here!

Acceleration and Velocity with Resistance (Differential Equations 39)

40K views · 1mo ago · 1:29:39

Acceleration and Velocity with Resistance (Differential Equations 39) When Acceleration is proportional to velocity and inversely proportional to velocity.

Bernoulli Equations Made Easy (Differential Equations 24.5)

73K views · 2mo ago · 1:05:35

This is a technique that will make solving Bernoulli Equations MUCH easier by forcing them to be in the form of an Embedded Derivative. Enjoy!

Peterson Statistics Lesson 1

89K views · 2mo ago · 1:20

This is the first lesson in the Statistics Series I filmed for the Peterson Academy. I hope you like it! More content coming soon on my channel, for free as always.

The News -- An Update from Professor Leonard

437K views · 2mo ago · 4:57

An Update from Professor Leonard about the future and exciting times ahead!

What in the World Happened to Professor Leonard?!

387K views · 4y ago · 4:17

I thought I'd give you all an update about what's been going on!! Hope everyone of you is doing well :)

How to Graph Advanced Polar Equations with Symmetry (Precalculus - Trigonometry 42)

155K views · 4y ago · 46:38

How to graph Polar Equations WITHOUT converting into Rectangular Equations by using symmetry of Polar Functions and plotting a limited number or points.

How to Graph Basic Polar Equations (Precalculus - Trigonometry 41)

57K views · 4y ago · 24:48

An introduction to graphing Polar Equations by converting them into Rectangular Equations and graphing them as conic sections or basic functions in the rectangular coordinate system.

How to Convert From Polar Equations to Rectangular Equations (Precalculus - Trigonometry 40)

35K views · 4y ago · 26:24

How to convert equations from Polar form to Rectangular form using trigonometric identities.

How to Convert From Rectangular Equations to Polar Equations (Precalculus - Trigonometry 39)

29K views · 4y ago · 28:27

How to convert equations from Rectangular form to Polar form using trigonometric identities.

How to Convert From Rectangular Coordinates to Polar Coordinates (Precalculus - Trigonometry 38)

38K views · 4y ago · 48:53

How to use trigonometric relationships to change Rectangular Coordinate represented points into Polar Coordinate represented points including how to determine the correct quadrant for Tangent Inverse.

How to Convert From Polar Coordinates to Rectangular Coordinates (Precalculus - Trigonometry 37)

43K views · 4y ago · 34:24

How to use trigonometric relationships to change Polar Coordinate represented points into Rectangular Coordinate represented points

Introduction to Polar Coordinates (Precalculus - Trigonometry 36)

76K views · 4y ago · 38:06

What Polar Coordinates are, how to plot them, and why they are used in math.

Simple Harmonic Motion in Trig (Precalculus - Trigonometry 35)

45K views · 4y ago · 33:23

A brief discussion of Simple Harmonic Motion, how it is related to Sine and Cosine, and the functional models it creates.

How to Find the Area of a Triangle with Trigonometry (Precalculus - Trigonometry 34)

45K views · 4y ago · 16:19

How to find the area of a triangle without explicitly knowing the height. The area formulas will find the area of a triangle if Side-Angle-Side or Side-Side-Side is known.

How to Use the Law of Cosines in Trigonometry (Precalculus - Trigonometry 33)

34K views · 4y ago · 56:36

An Introduction into the Law of Cosines, how it is related to Pythagorean Theorem, and how to find missing sides and angles if Side-Angle-Side or Side-Side-Side is known in a triangle.

How to Use the Law of Sines in Trigonometry (Precalculus - Trigonometry 32)

41K views · 5y ago · 1:27:46

What the Law of Sines is, When it works, and how to use it to find missing sides and angles in oblique triangles.

How to Use Product to Sum and Sum to Product Formulas in Trig (Precalculus - Trigonometry 29)

36K views · 5y ago · 45:47

Several examples of the Product to Sum and Sum to Product Formulas for Sine and Cosine that are used in Trigonometry. Proofs of the formulas are also demonstrated.

How to Use the Double and Half Angle Formulas for Trigonometry (Precalculus - Trigonometry 28)

53K views · 5y ago · 1:20:34

LOTS of examples of using the Double Angle and Half Angle formulas in Trigonometry.

Proving the Double and Half Angle Formulas for Trigonometry (Precalculus - Trigonometry 27)

64K views · 5y ago · 27:17

The proofs of Double Angle Formulas and Half Angle Formulas for Sine, Cosine, and Tangent. These proofs help understand where these formulas come from, and will also help in developing future identities.

Using Sum and Difference Formulas in Trigonometry (Precalculus - Trigonometry 26)

35K views · 5y ago · 58:07

How to use the Sum and Difference Formulas to find angles in Trigonometry including Inverse Trig functions, Unit Circle applications, and proofs of phase shift identities for Sine and Cosine.

Introduction to Sum and Difference Formulas in Trigonometry (Precalculus - Trigonometry 25)

62K views · 5y ago · 51:27

What the Sum and Difference formulas are for the three basic trig functions, where they come from, and how to use them to find exact solutions to angles that are not on the Unit Circle.

Finding Sides and Angles with Right Triangle Trigonometry (Precalculus - Trigonometry 31)

31K views · 5y ago · 42:46

Guest: Right Triangle Trigonometry

How to find missing sides and angles of Right triangles using Right Triangle Trigonometry. Focus is on using the basic trig functions Sine (sin), Cosine (cos) and Tangent (tan).

Introduction to Right Triangle Trigonometry (Precalculus - Trigonometry 30)

33K views · 5y ago · 1:01:47

What Sine, Cosine, Tangent and the reciprocal functions refer to in a Right Triangle and how to use them. Also discussed is the Co-Function relationships and the identities that come from them.

How to Prove Trigonometric Identities (Precalculus - Trigonometry 24)

85K views · 5y ago · 55:39

A very in-depth look at proving trigonometric identities. Several techniques are explored in many different examples of solving trig functions.

Introduction to Using Trigonometric Identities (Precalculus - Trigonometry 23)

89K views · 5y ago · 23:44

A quick look at Trig Identities and how to use them. Basic identities such as the Pythagorean Identity, Reciprocal Identities, and Even/Odd Identities are explored.

How to Solve Trigonometric Equations (Precalculus - Trigonometry 22)

101K views · 5y ago · 1:34:36

A very In-Depth look into solving equations that involve trig functions. We will focus on solving equations without having to use inverse trigonometric functions and relating solutions to the unit circle.

An Indepth Look at Using Inverse Trig Functions (Precalculus - Trigonometry 21)

41K views · 5y ago · 1:18:27

A very detailed explanation of Inverse Trigonometric Functions and how to use them in conjunction with Basic Trig Functions. Pretty much all you need to know about using inverse trig functions.

How to Solve Basic Inverse Trigonometric Functions (Precalculus - Trigonometry 20)

32K views · 5y ago · 7:14

A very brief introduction to solving equations that involve inverse trigonometric functions.

How to Find Inverse Trigonometric Functions (Precalculus - Trigonometry 19)

35K views · 5y ago · 32:14

A step by step approach to find inverse trig functions along with their domain and range.

How to Use Inverse Trigonometric Functions (Precalculus - Trigonometry 18)

56K views · 5y ago · 53:55

An in-depth look at how to use inverse trig functions and how they relate to basic trig functions. The domain and range of these functions is also thoroughly discussed.

Introduction to Inverse Trigonometric Functions (Precalculus - Trigonometry 17)

98K views · 5y ago · 30:58

What Inverse Trigonometric Functions are, where they come from, and why we need to restrict domain to be able to use them. Special focus will be on the nature of one-to-one functions and how they relate to the common trigonometric functions.

How to Graph Phase Shifts of Trigonometric Functions (Precalculus - Trigonometry 16)

45K views · 5y ago · 37:52

How to perform Horizontal shifts, called a Phase shift or Horizontal Translation, on trigonometric functions. While only Sine and Cosine are demonstrated, these techniques can be with all trig functions.

How to Graph Cosecant and Secant (Precalculus - Trigonometry 15)

31K views · 5y ago · 29:55

An introduction to the graphs of Secant and Cosecant by using their relationships with Cosine and Sine. Transformations are also explored and explained.

Graphing Transformations with Tangent and Cotangent (Precalculus - Trigonometry 14)

34K views · 5y ago · 40:39

How to graph the Tangent function and the Cotangent function with transformations. Focus is on Vertical translation, amplitude, reflection, and manipulating the period.

How to Graph Tangent and Cotangent (Precalculus - Trigonometry 13)

49K views · 5y ago · 26:14

The basics of graphing the Tangent and Cotangent functions, why the graphs look like they do, along with discussion of vertical asymptotes, intercepts, and key points.

Graphing Transformations with Sine and Cosine (Precalculus - Trigonometry 12)

62K views · 5y ago · 1:06:48

How to Graph Sine and Cosine (sin and cos) along with all their transformations as easily as possible (Phase shifting, or horizontal translation, is a separate video).

The Graphs of Sine and Cosine (Precalculus - Trigonometry 11)

69K views · 5y ago · 34:34

The graphs of Sine and Cosine (sin and cos) and where they come from. Much of this video is focused on WHY the graphs look the way they do.

Pythagorean Identities for Trigonometric Functions (Precalculus - Trigonometry 10)

49K views · 5y ago · 37:54

How to use Even, Odd, and Pythagorean Identities in trigonometry and where they come from. Special focus will be paid to the Unit Circle and corollaries of the typical Pythagorean Identities.

Reciprocal Identities in Trigonometry (Precalculus - Trigonometry 9)

47K views · 5y ago · 46:54

How the reciprocal identities in trigonometry work and how to use them. The major focus will be on connecting the ideas of a Unit circle with Right Triangle Trigonometry.

Basic Properties of Trigonometric Functions (Precalculus - Trigonometry 8)

81K views · 5y ago · 1:10:54

A discovery of the basic properties of Trigonometric Functions and why they work. Also, a technique for using the period of Trig Functions to simplify angles more than 2pi.

How to Use the Unit Circle in Trigonometry (Precalculus - Trigonometry 7)

90K views · 5y ago · 42:57

How to use the Unit Circle to evaluate Trigonometric Functions; Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Trigonometric Functions and the Unit Circle (Precalculus - Trigonometry 6)

143K views · 5y ago · 39:59

The creation of the Unit Circle and how it relates to Right Triangle Trigonometry and the creation of Trigonometric Functions.

Area of a Sector, Angular Velocity, Applications (Precalculus - Trigonometry 5)

56K views · 5y ago · 36:57

How to find the Area of a Sector, Arc Length on a great circle of a sphere, Angular Velocity, Rotational Velocity, and other applications.

Converting Radians and Degrees (Precalculus - Trigonometry 4)

62K views · 5y ago · 38:45

How to convert from Radians to Degrees and Degrees to Radians. Focus will be on the development of the formulas and practicing the conversions.