Calculus 1 - Full College Course

Learn Calculus 1 in this full college course.

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 ⭐️

⭐️ Lecture Notes ⭐️

⭐️ 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
(9:14:59) Polynomial and Rational Inequalities
(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

Correction:

[doodaks]

Sitting through the entire video AFTER failing calculus feels like watching the evidence unfold in court

[commanderkuplar]

12 hours ago, I was a boy. Now, I’m a man.

[VR-Enthusiast]

I can't believe I'm binge watching calculus

[gkau]

2 and a half hours into this lecture and this is seriously making me question how the hell do some teachers manage to make maths seem so daunting, I never thought to learn trigonometry like you explain it ❤️

[anonymousjose]

And dont forget your calculus exam is at 12 tomorrow.
Me at midnight: its showtime

[bobrowder]

Guys i did it. I DID IT. I actually watched the entire video! I’m proud of myself. Imma take a nap

[bonidel]

4 weeks of attending lectures and recitation and this woman summarized everything I could not understand for exam 1 in just 2 hours. I FEEL MORE CONFIDENT THAN EVER FOR A TEST.

[GodsOath_com]

In high school I got Ds and Cs in math. In College I got an A in Calculus. The difference was an encouraging professor and many hours laboring in the math lab. I was determined to understand it. Your determination determines your future. I became a CPA using algebra everyday. I suppose I should have become a higher paid actuary, but I was not as determined to master statistics. 😊. Good luck to all. The man who invented the jet engine was able to do it because of his determination not because he was deemed smart. The world is your oyster if you dive into the ocean.

[terracotta]

Finally, an ASMR that actually makes me sleep.

[yourdailydoseofstupidity]

Me puts it on 2x speed: CALCULUS IN 6 HOURS

[sharp]

Doing AP Calc over the summer this year. Tracking my progress

(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✔ (theres no audio for this one 😥)
(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✔

[saucypastaman]

If only professors took a few minutes to review the algebra and trig needed to do calc we would do so much better. I remember taking calc the professor refused to review any of that saying "you learned this in highschool" So many students in the class failed. We are not math experts and are using math in our daily lives all the time to remember all these little rules. This video is so much better than a class I payed 1, 000 dollars for

[hurtyjames]

The more you sweat in practice, the less you bleed in war .

[CM-dxxu]

This is what society needs. Great people giving great things to help others. A very kind gesture given without pay, you are one among the heroes of modern education. May god bless.

[SnapScienceOfficial]

I have been looking to brush up on calculus since I left school. I can't believe how well you articulate your ideas. This video and its creators are an invaluable resource for self-guided learning.

[isiahcurry]

I guess this would be considered a “personal” problem, but there are times where I wish I could be at this level of intelligence. I was just horrible at math. I had a learning disability (IEP) which, shamefully, made learning even harder for me. Now at the age of 26 I’m just now starting undergrad, but I’m struggling a bit in Algebra this semester. To put it simply, I have no business ever watching this video.

I just hope no one makes the same mistakes or endures the struggles that I made in school. Good luck to everyone.

[connormichalec]

The fact that this is free on youtube is incredible. Thank you, people who do this make the world a better place (even tho there's no way I'm watching a minute of it)

[sage]

I didn't know that mathematicians do speedruns lmao

[dylansshoes]

Been on a 2 year gap year before college and needed to brush up on Calculus. Half way through and can't thank y'all enough.

[twilightugge]

I am so happy I came across this video. As someone who took precalc 2 years ago and got a C, you're a life saver. You explain things so well and this will legit be my ticket to a good grade in Calc 1