What you'll learn
Precalculus, including functions, their graphs, and how to modify functions
Limits & Continuity, including how to solve every kind of limit problem, and how to find discontinuities in a function
Derivatives, including all of the derivative rules, the infamous chain rule, and how to do implicit differentiation
Applications of Derivatives, including two of the hardest topics from Calc 1: optimization and related rates

https://www.youtube.com/channel/UCkyLJh6hQS1TlhUZxOMjTFw

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0:00:00 Graphs and Limits

0:07:31 When Limits Fail to Exist

0:13:08 Limit Laws

0:18:47 The Squeez Theorem

0:24:35 Limits Using Algebraic Tricks

0:37:45 When the Limit of the Denominator is 0

0:50:20 Limits at Infinity And Graph

0:57:16 Limits at infinity and Algebraic Tricks

1:05:19 Continuity At a Point

1:13:06 Recitation 2 Recording for Math 231, fall 2020

1:24:31 Continuity Example With a piecewise Defined Function

1:31:53 Continuity on Intervals

1:38:14 Continuity and Domains

1:41:55 Intermediate Value Theorem

1:45:50 Derivatives and Tangnet lines

2:00:31 Computing Derivatives from the Definition

2:11:38 Interpreting Derivatives

2:20:09 Derivatives as Functions Graphs of Derivatives

2:34:01 Proof that differentiable and Graphs of Derivatives

2:38:46 Power Rule and Other rules for derivatives

2:45:19 Higher Order derivatives and notation

2:48:40 Derivativess of E^x

2:56:10 Proof of the power rule and other derivative rules

3:05:48 Product rule and quotient rule

3:11:26 Proof of product rule and quotient rule

3:19:58 special trigonometric Limits

3:26:49 Derivatives of Trig Functions

3:33:10 proof of trigonometric limits and derivatives

3:41:25 derivatives and rates of change (Rectilinear Motion)

3:58:28 Marginal Cost

4:03:38 the Chain rule

4:12:55 More chain rule Examples and Justification

4:21:54 Justification of the chain rule

4:24:12 Implicit Differentiation

4:34:39 Derivatives of Exponential Functions

4:39:49 Derivatives of log Funcition

4:43:49 Logarithmic Differentiation

4:51:19 Inverse Trig Functions
5:00:53 derivatives of inverse trigonometric functions

5:12:07 related rates - distance

5:17:52 related rates - volume and flow

5:22:18 related rates - angle and rotation

5:28:17 Maximums and minimums

5:39:41 Mean Value theorem

5:47:17 Proof of mean value theorem

5:54:52 Derivatives and the shape of the Graph

6:03:0 First derivative test and second Derivatives test

6:08:23 Extreme value Example

6:18:19 Linear approximation

6:33:16 The differential

6:43:59 L Hospital's Rule

6:51:15 L Hospital's Rule on other indeterminate forms

7:01:01 Newtons Method

7:09:56 Antiderivatives

7:18:13 Finding antiderivatives using initial conditions

7:26:47 Any two antiderivatives differ by a constant

7:30:07 summation notation

7:34:01 Approximation ARea

7:49:11 The fundamental theorem of Calculus, part 1

7:59:50 The fundamental theorem of Calculus, part 2

8:07:05 Proof of the fundamental theorem of calculus

8:14:06 The substitution Method

8:22:55 Why U-Substitution works

8:25:11 Average Value of a Function

8:32:46 Proof of the mean Value theorem for intergrals

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