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Calc 1: Limits & Derivatives

Calc 1: Limits & Derivatives

Calc 1: Limits & Derivatives
Published 5/2023
MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHz
Language: English | Size: 1.76 GB | Duration: 4h 21m


We'll create whole new ways of interacting with functions, then use them to launch into a whole new realm of math!

What you'll learn
Understanding what happens as a function approaches a point
Extedning the idea of "slope" from straight lines to all curves
Applying these slopes to explore the behavior of graphs
Using these tools in real-world applications

Requirements
Experience with algebra and trigonometry — take a look at our other courses if you need a refresher!

Description
A typical calculus 1 course covers two main topics: limits and derivatives.Limits describe what happens to a function near a specific point (but not necessarily at that point). The intimately-related topic of continuity is perhaps that most important underpinning the theorems of the mathematics of functions. You'll learn how to think about questions like:What does it mean to be "close" to a point?What can we learn about a function on an interval given that the curve is connected? Smooth?How do we know what happens in the neighborhood of dividing by zero?How can we combine limits and the algebra equation for slope to think about the slope of a curve?Derivatives are functions which describe the slope of a corresponding function. Once we can think about the behavior of the derivative, a whole range of applications present themselves! You'll learn how to think about questions like:How do we evaluate the slope of a line that isn't straight?What simplifications can we use in evaluating derivatives based on the different types of basic operations?What does it mean for the slope to be zero?How do derivatives of multiple related functions interrelate?What happens if you take the derivative of the derivative?Can't wait to get started! Calculus 1 is a gateway into a whole new realm of math and way of thinking. Let's go!

Overview
Section 1: Introduction

Lecture 1 Welcome to Calc 1: Limits & Deriviatives!

Lecture 2 Prerequisites in More Detail

Lecture 3 Big Picture Idea: Limits

Lecture 4 Big Picture Idea: Derivatives

Lecture 5 Getting Ready

Section 2: Limit Concepts

Lecture 6 Does it Exist?

Lecture 7 Piecewise Functions

Lecture 8 Absolute Value

Lecture 9 What is Continuity?

Lecture 10 The Intermediate Value Theorem

Section 3: Limit Solutions

Lecture 11 Conjugates

Lecture 12 The Squeeze Theorem

Lecture 13 End Behavior

Lecture 14 Slant Asymptotes

Lecture 15 The Difference Quotient

Section 4: Core Function Derivatives

Lecture 16 Quadratics

Lecture 17 Linearity of Difference Quotient

Lecture 18 The Power Rule

Lecture 19 The "Derivative" Formally

Lecture 20 Exponentials & Logarithms

Lecture 21 Trig & Inverse Trig

Section 5: Derivative Tools

Lecture 22 The Product & Quotient Rules

Lecture 23 The Chain Rule

Lecture 24 Putting These Together

Lecture 25 Implicit Differentiation

Section 6: Derivative Applications

Lecture 26 Extrema, Average Rate, & Mean Value

Lecture 27 The Second Derivative

Lecture 28 Exploring Rational Functions

Lecture 29 Related Rates

Lecture 30 Optimization

Lecture 31 Content Conclusion

Section 7: Practice Set A

Lecture 32 Set A Introduction

Lecture 33 Problem 1

Lecture 34 Problem 2

Lecture 35 Problem 3

Lecture 36 Problem 4

Lecture 37 Problem 5

Lecture 38 Problem 6

Lecture 39 Problem 7

Lecture 40 Problem 8

Lecture 41 Problem 9

Lecture 42 Problem 10

Lecture 43 Problem 11

Lecture 44 Problem 12

Lecture 45 Problem 13

Lecture 46 Problem 14

Lecture 47 Problem 15

Lecture 48 Problem 16

Lecture 49 Problem 17

Lecture 50 Problem 18

Section 8: Bonus Lecture

Lecture 51 Bonus Lecture: UpGrade University

Lovers and future lovers of math who are ready to learn by exploring concepts,Calc 1 serves as a gateway to lots of technical fields, and is a common early college course for these kinds of majors


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