# Calculus 1 – Full College Course

July 7, 2024 2024-07-07 20:07## Calculus 1 – Full College Course

Learn Calculus 1 in this full college course.

This course was created by Dr. Linda Green, a lecturer at the University of North Carolina at Chapel Hill. Check out her YouTube channel: https://www.youtube.com/channel/UCkyLJh6hQS1TlhUZxOMjTFw

This course combines two courses taught by Dr. Green. She teaches both Calculus 1 and a Calculus 1 Corequisite course, designed to be taken at the same time. In this video, the lectures from the Corquisite course, which review important Algebra and Trigonometry concepts, have been interspersed with the Calculus 1 lectures at the places suggested by Dr. Green.

⭐️ Prerequisites ⭐️

🎥 Algebra: https://www.youtube.com/watch?v=LwCRRUa8yTU

🎥 Precalculus: https://www.youtube.com/watch?v=eI4an8aSsgw

⭐️ Lecture Notes ⭐️

🔗 Calculus 1 Corequisite Notes: http://lindagreen.web.unc.edu/files/2020/08/courseNotes_math231L_2020Fall.pdf

🔗 Calculus 1 Notes: http://lindagreen.web.unc.edu/files/2019/12/courseNotes_m231_2018_S.pdf

🔗 Viewer created notes (Thanks to Abdelrahman Ramzy): https://drive.google.com/file/d/1Py5hyiOz61i4lh2PEsjvBTH8AEuQzXK_/view?usp=sharing

⭐️ Course Contents ⭐️

(0:00:00) [Corequisite] Rational Expressions

(0:09:40) [Corequisite] Difference Quotient

(0:18:20) Graphs and Limits

(0:25:51) When Limits Fail to Exist

(0:31:28) Limit Laws

(0:37:07) The Squeeze Theorem

(0:42:55) Limits using Algebraic Tricks

(0:56:04) When the Limit of the Denominator is 0

(1:08:40) [Corequisite] Lines: Graphs and Equations

(1:17:09) [Corequisite] Rational Functions and Graphs

(1:30:35) Limits at Infinity and Graphs

(1:37:31) Limits at Infinity and Algebraic Tricks

(1:45:34) Continuity at a Point

(1:53:21) Continuity on Intervals

(1:59:43) Intermediate Value Theorem

(2:03:37) [Corequisite] Right Angle Trigonometry

(2:11:13) [Corequisite] Sine and Cosine of Special Angles

(2:19:16) [Corequisite] Unit Circle Definition of Sine and Cosine

(2:24:46) [Corequisite] Properties of Trig Functions

(2:35:25) [Corequisite] Graphs of Sine and Cosine

(2:41:57) [Corequisite] Graphs of Sinusoidal Functions

(2:52:10) [Corequisite] Graphs of Tan, Sec, Cot, Csc

(3:01:03) [Corequisite] Solving Basic Trig Equations

(3:08:14) Derivatives and Tangent Lines

(3:22:55) Computing Derivatives from the Definition

(3:34:02) Interpreting Derivatives

(3:42:33) Derivatives as Functions and Graphs of Derivatives

(3:56:25) Proof that Differentiable Functions are Continuous

(4:01:09) Power Rule and Other Rules for Derivatives

(4:07:42) [Corequisite] Trig Identities

(4:15:14) [Corequisite] Pythagorean Identities

(4:20:35) [Corequisite] Angle Sum and Difference Formulas

(4:28:31) [Corequisite] Double Angle Formulas

(4:36:01) Higher Order Derivatives and Notation

(4:39:22) Derivative of e^x

(4:46:52) Proof of the Power Rule and Other Derivative Rules

(4:56:31) Product Rule and Quotient Rule

(5:02:09) Proof of Product Rule and Quotient Rule

(5:10:40) Special Trigonometric Limits

(5:17:31) [Corequisite] Composition of Functions

(5:29:54) [Corequisite] Solving Rational Equations

(5:40:02) Derivatives of Trig Functions

(5:46:23) Proof of Trigonometric Limits and Derivatives

(5:54:38) Rectilinear Motion

(6:11:41) Marginal Cost

(6:16:51) [Corequisite] Logarithms: Introduction

(6:25:32) [Corequisite] Log Functions and Their Graphs

(6:36:17) [Corequisite] Combining Logs and Exponents

(6:40:55) [Corequisite] Log Rules

(6:49:27) The Chain Rule

(6:58:44) More Chain Rule Examples and Justification

(7:07:43) Justification of the Chain Rule

(7:10:00) Implicit Differentiation

(7:20:28) Derivatives of Exponential Functions

(7:25:38) Derivatives of Log Functions

(7:29:38) Logarithmic Differentiation

(7:37:08) [Corequisite] Inverse Functions

(7:51:22) Inverse Trig Functions

(8:00:56) Derivatives of Inverse Trigonometric Functions

(8:12:11) Related Rates – Distances

(8:17:55) Related Rates – Volume and Flow

(8:22:21) Related Rates – Angle and Rotation

(8:28:20) [Corequisite] Solving Right Triangles

(8:34:54) Maximums and Minimums

(8:46:18) First Derivative Test and Second Derivative Test

(8:51:37) Extreme Value Examples

(9:01:33) Mean Value Theorem

(9:09:09) Proof of Mean Value Theorem

(0:14:59) [Corequisite] Solving Right Triangles

(9:25:20) Derivatives and the Shape of the Graph

(9:33:31) Linear Approximation

(9:48:28) The Differential

(9:59:11) L’Hospital’s Rule

(10:06:27) L’Hospital’s Rule on Other Indeterminate Forms

(10:16:13) Newtons Method

(10:27:45) Antiderivatives

(10:33:24) Finding Antiderivatives Using Initial Conditions

(10:41:59) Any Two Antiderivatives Differ by a Constant

(10:45:19) Summation Notation

(10:49:12) Approximating Area

(11:04:22) The Fundamental Theorem of Calculus, Part 1

(11:15:02) The Fundamental Theorem of Calculus, Part 2

(11:22:17) Proof of the Fundamental Theorem of Calculus

(11:29:18) The Substitution Method

(11:38:07) Why U-Substitution Works

(11:40:23) Average Value of a Function

(11:47:57) Proof of the Mean Value Theorem for Integrals

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## Comments (38)

## @kapil_das221

JUST LOVE YOUR TEACHING METHOD.

IT'S SO EASY AND SIMPLE ❤

## @kapil_das221

ALL MY LIFE I WAS RUNNING AWAY FROM MATHEMATICS JUST TO REALISE LATER THAT IT'S THE MOST PRETTY SUBJECT ❤.

## @kapil_das221

IT'S BEAUTIFUL ❤️

## @PraveenSrJ01

Thank you so much 😊

## @ManthanPureLife

This is so helpful, mam the way u teach is so awesome , i love it and grateful for it , thank you guys frm India

## @jaigowrershgovindan4857

Literally we indian people completed like 70 to 80 percent of this lecture at our grade 11 / class 11 at the age of 16 and coming in terms of jee advanced those who cleared it , this lecture is just like a piece of cake as a student

## @MAHIR_FAISAL

Best way to become a man is to master calculus

## @pro123chess

tysm for this masterpeice

## @bpascualamadeop.6696

Starting to learn cal good luck to me

## @pichooooo

If all professors are like this, then I would actually have the motivation to go to class

## @nasimahmad8768

Took Cal1/Cal2, it helps me in Finance,

## @user-rq6ly9jt3b

tracking my progress

I already had cal 1 and cal 2 at university and currentily taking calc 3 and wanted to revise the subject

Day 1: 1:30:35

Day 2: 3:07:40 trigonometry part got kinda hard but i finished that subejct

Day 3: 4:46:57

Day 4: 6:09:03

## @aquarocket8165

1:23:35 h(x) is equal to 12/7 not 12/9 you added 2 to the sum of the denominator

## @Slow-Biden9

Can someone please explain the castle-wall problem at 2:03:15 ? It's bothering me now that she left out the solution for this and I can't seem to figure it out

## @hika_00_x

Can you guys make a in depth video on logrithimic functions

## @fnjamth

good luck..

## @isyaht

I play this video for background noise before I sleep. And yes, I have a good night sleep.

## @muzzammilsajid

2:03:02 To prove that somewhere on the wall there must be two diametrically opposite places with the same height using the Intermediate Value Theorem, let's outline the steps clearly.

1. Define the Wall's Height as a Function:Let h(θ) be the height of the wall at angle θ where θ is measured from a fixed reference direction (e.g., north). Since the height varies continuously, h(θ) is a continuous function on [0, 2π).

2. Consider the Function g(θ):Define a new function g(θ) as follows:

g(θ) = h(θ) – h(θ + π)

Here, g(θ) represents the difference in height between two diametrically opposite points on the wall.

3. Properties of g(θ):Since h(θ) is continuous, the function g(θ) is also continuous because it is composed of continuous functions.

4. Evaluating g(θ) at Specific Points:– Evaluate g(0):

g(0) = h(0) – h(π)

– Evaluate g(π):

g(π) = h(π) – h(0) [Since h(2π) is essentially equal to h(0)]

Notice that g(π) = -g(0). This relationship comes from the fact that g(θ) measures the difference in height at points θ and θ + π.

5. Application of the Intermediate Value Theorem:Since g(0) and g(π) are negatives of each other, one of them is positive and the other is negative (unless they are both zero, which we will consider later). Thus, if g(0) ≠ 0:

-g(0) and g(θ) are of opposite signs.

By the Intermediate Value Theorem, because g(θ) is continuous and changes sign over the interval [0, π], there must be some angle θ in [0, π] such that:

g(θ) = 0

This means:

h(θ) = h(θ + π)

6. Case When g(0) = 0:If g(0) = 0 , then h(0) = h(π), which already satisfies the condition we are trying to prove.

7. Conclusion:Whether g(0) ≠ 0 or g(0) = 0, in either case, there exists an angle θ such that:

h(θ) = h(θ + π)

Hence, there are two diametrically opposite points on the wall with the same height.

This completes the proof using the Intermediate Value Theorem.

## @aymantadros9182

Handwriting is awful and confusing

## @diesireaf8667

1:45:00

## @robertsumbrasko3591

Day 1: 1:08:40

Day 2: 3:22:02

Day 3: tomorrow ( i will finish this course)

## @tidalfriction5301

I haven’t taken calculus since 1998. I really enjoy the burn this has put into my brain, and I’m ready to go back to school.

## @______Sugar_______2

Can anyone explain me first slide of the video second question in detail plzzz❤

## @sigmaeditzzz857

3 days before exam is wild

## @royreber526

Have you considered the "holes in the graph"? One should mention that a variable in the denominator limits the answer.

## @NapoleonThabethe

I can hear and feel numbers☄️🪐🌠

## @elpollolocoman119

I love it, but I still have much more to learn before I reach here, please keep these videos up as long as possible. Thank you very much.

## @JuanRamirez-xw3gc

Watching college algebra, trigonometry, pre-cal, and then Calculus 1 freeCodeCamp videos is equivalent to Thanos collecting the infinity stones. I feel unstoppable.

## @Laffedd_

Binge watching calc during summer

## @Gardiencotier13

This isn’t calculus is algebra with co-ordinate geometry

## @user-td6qw2mj4y

And I'm not even gay

## @user-td6qw2mj4y

But what is x?? X of what v. Tell you what give me a quantum computer if ai is so bad ass. Fine. If Ai is really that good. Let me have a keyboard 1 with all of fraction signs. Let's teach American people how to think again. Let's say that you had a board game called the table of elements. Not a nomoply game think outside of the the box that we are living in. Milt @bradly. Wow. That is good. I want thT board game Lazar had to play with. Thata ok Let's dumb the people down

## @user-td6qw2mj4y

What is the product #??

## @user-td6qw2mj4y

Thank you

## @vikashnara6887

We learn this in highschool to get admission in IIT's 😅

## @arandomperson8640

I just turned 16 some months ago (will try to watch this full video) (don't know if I will lose motivation)

12 June 2024: till 9:39

7:12 I learnt it a bit different but answer same bec things cancel out. I was taught to cross multiply(multiply the denominator of the second fraction with first numerator and multiply the denominator of first fraction with second numerator and just multiply the denominators

But at the end it cancels out (I think ma'am's method is easier as we can avoid one step)

9:40 (I think I have to learn what a function is first before hearing all this) (I saw it in my textbook as second chapter but it is vacation so no teachers)(I might have to first find a vid which explains that in yt byeeee)

## @carlosjoyeux4722

9:10

## @jlm357

this video make my insomnia disappear. big thanks 🙂