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The First & Zeroth Laws of Thermodynamics: Crash Course Engineering #9
00:10:05
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11 Views · 5 months ago

In today’s episode we’ll explore thermodynamics and some of the ways it shows up in our daily lives. We’ll learn the zeroth law of thermodynamics, what it means to reach a thermal equilibrium, and define the first law of thermodynamics. We’ll also explore how stationary, adiabatic, and isochoric processes can make our lives as engineers a little easier.

Note: Different branches of engineering sometimes define the first law of thermodynamics differently, depending on how work is defined. Essentially, work released from a system might be defined as a positive value or a negative value, and thus the first law can be defined as either Q-W or Q+W. Both are acceptable forms, depending on how the system is defined! We chose to focus on only one definition here to limit the confusion.

Crash Course Engineering is produced in association with PBS Digital Studios: https://www.youtube.com/playli....st?list=PL1mtdjDVOoO

***

RESOURCES:
Çengel, Yunus A., and Michael A. Boles. Thermodynamics: An Engineering Approach. 8th ed., McGraw-Hill Education.
http://web.mit.edu/16.unified/....www/FALL/thermodynam
https://www.livescience.com/50....776-thermodynamics.h
https://www.khanacademy.org/te....st-prep/mcat/chemica
https://www.wired.com/2014/12/....whats-inside-hot-han
http://www.chemistryislife.com..../the-chemistry-of-ha
http://hyperphysics.phy-astr.g....su.edu/hbase/thermo/
https://www.grc.nasa.gov/www/k....-12/airplane/thermo0
http://hyperphysics.phy-astr.g....su.edu/hbase/thermo/
http://www.physicsclassroom.co....m/class/energy/Lesso
http://www.physicsclassroom.co....m/class/energy/Lesso
https://www.realclearscience.c....om/blog/2014/01/the_
http://hyperphysics.phy-astr.g....su.edu/hbase/thermo/
https://www.britannica.com/science/internal-energy
https://www.nuclear-power.net/....nuclear-engineering/
https://www.britannica.com/science/enthalpy
http://pillars.che.pitt.edu/student/slide.cgi?course_id=12&slide_id=35.0
https://courses.lumenlearning.....com/boundless-physic
https://www.khanacademy.org/sc....ience/biology/energy
http://www.ftexploring.com/ene....rgy/first-law_p2.htm
https://water.usgs.gov/edu/hyhowworks.html

***

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Physics Electro Magnetic Induction | Practice #18 | AIRFORCE | NAVY | NDA | Defence Exams | R.S SIR
00:00:00
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11 Views · 5 months ago

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SEMICONDUCTORS in One Shot : All Concepts, Tricks and PYQs || NEET Physics Crash Course
07:17:41
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9 Views · 5 months ago

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The Physics and Philosophy of Time - with Carlo Rovelli
00:54:54
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8 Views · 5 months ago

From Boltzmann to quantum theory, from Einstein to loop quantum gravity, our understanding of time has been undergoing radical transformations. Carlo Rovelli brings together physics, philosophy and art to unravel the mystery of time.
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Watch the Q&A: https://youtu.be/NXcu0BlbTrM

Time is a mystery that does not cease to puzzle us. Philosophers, artists and poets have long explored its meaning while scientists have found that its structure is different from the simple intuition we have of it. Time flows at a different speed in different places, the past and the future differ far less than we might think, and the very notion of the present evaporates in the vast universe.

Carlo Rovelli is a theoretical physicist who has made significant contributions to the physics of space and time. He has worked in Italy and the US, and is currently directing the quantum gravity research group of the Centre de physique théorique in Marseille, France. His books 'Seven Brief Lessons on Physics' and 'Reality Is Not What It Seems' are international bestsellers translated into forty-one languages.

This talk and Q&A was filmed in the Ri on 30 April 2018.

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For the Love of Physics - Walter Lewin - May 16, 2011
01:01:26
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7 Views · 5 months ago

This lecture has been viewed about 14 million times. About 1 million times on MIT's OCW, more than 6.7 million times in the channel "For the Allure of Physics" and more than 6 million times in this channel. Walter Lewin put his life on the line to demonstrate that he is a strong believer in the conservation of energy. He explained why the sky is blue, why the clouds are white and why sunsets are red. Great demonstrations! MIT video streamed this lecture in real time. It was viewed live by about 25 thousand people all over the world.

Supernovas and Magnetars: The Most Frightening Things in the Universe | How The Universe Works
00:09:55
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6 Views · 5 months ago

White dwarfs can cause both types of supernovas and magnetars, the most frightening things in the universe. However, scientists are still sure how these gigantic explosions occur.

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Dr. Michio Kaku Answers Physics Questions From Twitter | Tech Support | WIRED
00:16:19
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6 Views · 5 months ago

Dr. Michio Kaku, a professor of theoretical physics, answers the internet's burning questions about physics. Can Michio explain "string theory" to the layperson? What is a quark? What is the "God Equation"? How do black holes distort time? Is the best physicist ever Albert Einstein or Richard Feynman? Or someone else? Michio answers all these questions and much more!

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Dr. Michio Kaku Answers Physics Questions From Twitter | Tech Support | WIRED

What Triggered the Big Bang? | How the Universe Works
00:07:45
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6 Views · 5 months ago

The Big Bang is one of science's most famous theories, but we now know it wasn't big and it wasn't a bang.

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If You Don't Understand Quantum Physics, Try This!
00:12:45
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5 Views · 5 months ago

A simple and clear explanation of all the important features of quantum physics that you need to know. Check out this video's sponsor https://brilliant.org/dos
I have spent a lot of time thinking about how best to explain quantum physics and this is the result of all my hours of pondering, and I’m really happy with how it turned out. I decided to just explain it as it actually is, rather than rely on analogies. The video explains the quantum wavefunction, particle-wave duality, the measurement problem, the double-slit experiment, superposition, entanglement, quantum tunnelling, the Heisenberg uncertainty principle, and energy quantisation. Let me know if it was helpful! Cheers Dx

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Further reading
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Calculus - Introduction to Calculus
00:04:11
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5 Views · 5 months ago

This video will give you a brief introduction to calculus. It does this by explaining that calculus is the mathematics of change. A couple of examples are presented, and then limits, derivatives, and integrals are introduced. For more videos please visit http://www.mysecretmathtutor.com

3 Perplexing Physics Problems
00:14:00
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5 Views · 5 months ago

Why does shaken soda explode? Does ice melt first in fresh or salt water?
Thank you Squarespace for sponsoring this video. Go to https://squarespace.com to save 10% off your first purchase of a website or domain using code: VERITASIUM

This video features experiments that have been shown to me by science teachers over the years. Does ice melt fast in salt water or fresh water was an experiment introduced to me at the Utah Science Teachers' conference. The ring of metal over a chain demo came from a teachers event in Florida. The idea shaking a carbonated drink increases pressure came from an email.

Special thanks to Petr Lebedev for building the pressure gauge.

Links to literature are below:
Victims of the pop bottle, by Ted Willhoft. New Scientist, 21 August 1986 p.28

Carbonation speculation
The Physics Teacher 30, 173 (1992); https://doi.org/10.1119/1.2343501

Agitation solution
The Physics Teacher 30, 325 (1992); https://doi.org/10.1119/1.2343556

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All physics explained in 15 minutes (worth remembering)
00:17:15
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4 Views · 5 months ago

Signup for your FREE trial to The Great Courses Plus here: http://ow.ly/s2UK30r2D3q
Five areas of physics worth remembering: Classical mechanics, energy and thermodynamics, electromagnetism, Relativity, and Quantum Mechanics. Classical mechanics - two main concepts worth knowing. The first is Newton’s second law: F= ma: Force equals mass times acceleration. If you apply a force to a fixed mass, it tells you how much acceleration you will get. And knowing acceleration which is the change in velocity, you can make predictions.

The second equation is the law of universal gravitation. it allows us to determine the motion of heavenly bodies. It says that the gravitational attraction between two bodies is the product of their masses divided by the distance between them squared, times a constant, called Newton’s gravitational constant.

Energy is not a vector like force or momentum, but it is just a number. Work is closely related to energy. It is force times distance traveled. Energy for most objects consists of kinetic energy plus potential energy. KE is the energy of motion, It is KE = ½ M V^2 – the more mass you have and/or the more velocity you have, the more energy you have.

Gravitational potential energy is expressed as PE = m g h – mass times the gravitational acceleration times the height. The total energy of an object is both Kinetic energy plus potential energy. Potential energy can take many forms. Gasoline or petrol has chemical potential energy. Important: Energy is always conserved. It is not created or destroyed. It only changes form.

Thermodynamics is the study of work, heat, and energy on a system. We showed energy is how much work you could do. But another form of energy is thermal energy. If a car is moving and you apply the brakes, the kinetic energy of the car gets converted to thermal energy, created by friction of the car’s brakes. Temperature is the average kinetic energy of atoms in a system. Thermal energy is the total kinetic energy of atoms in a system.

Entropy is a measure of disorder, or more accurately, the information required to describe the micro states of a system. The 2nd law of thermodynamics states that entropy of an isolated system can never decrease. Energy at lower entropy can do more work than energy at high entropy. The one way flow of Entropy seems to be the only reason we have a forward flow of time.

Electromagnetism is the study of the interaction between electrically charged particles. The essentials are in Maxwell’s equations. If you have a static object with a charge, it will affect only other charges. If you have a static magnet, it will affect only other magnets. It will not affect charges. But if you have a moving charge, it will affect a magnet. And if you have a moving magnet, it will affect a charge. The constants mu naught and epsilon naught are the permeability and permittivity of free space. These two constants determine the speed of light because they measure the resistance of space to changing electric and magnetic fields.

Special Relativity: Einstein presumed that the speed is the same in any frame of reference. This was one of the postulates.
The second postulate was principle of relativity - the laws of physics are the same for all observes who are moving at the same velocity relative to each other. Einstein showed that the only way these can be true is if time was not fixed, but was relative.

General relativity: Later Einstein showed using the same assumptions, there would be no way to tell if you were in an accelerating reference frame or standing stationary on earth. A flashlight beam will bend in gravity. But since light always takes the shortest path between any two points, this means that space-time itself is bending.

Quantum mechanics: Three principles are important. First by Max Planck, says that energy is not continuous, but is quantized. The amount of energy equals the frequency of the radiation times Planck's constant. Using this, Einstein later showed that a photon is both a wave and a particle.

The second is the Heisenberg's uncertainty principle: you cannot know both a particle’s exact position and it’s exact momentum at the same time. For a particle with mass, this means if you know exactly where a particle is, you don’t know how fast going. If you know exactly how fast it’s going, you don’t know where it is.
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Schrodinger's equation: prior to measurement, quantum systems are in superposed states. This means that their properties can only be expressed as a wave function. A wave function simplified, is a set of probabilities. So in a hydrogen atom, you can’t know where to find the electron in advance. All you can know is the probability of where you might find it, if you measured it. Prior to measurement, all quantum systems are waves of probabilities. This is not a limitation of our measuring devices. It is a limitation of reality.
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FIRST LAW OF THERMODYNAMICS | Easy and Short
00:02:09
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4 Views · 5 months ago

First Law of Thermodynamics

The first of law of thermodynamic says that heat is a form of energy, and as what all other forms of energy is subject to, it follows the law of conservation of energy.
So what does this mean? It means that Heat Energy also cannot be created nor destroyed and can only be transferred to one form or another.

Don’t overthink this too much, this law is all about HEAT as energy, and follows the law of conservation of energy and that’s it.
Now to appreciate the application of this law let’s try a very good one example.

This Coal is just a type of rock but for scientists this rock contains an energy that produced HEAT Energy when it undergoes a complete combustion. Actually some powerplant utilizes this coal to generate electrical energy or what we call as electricity.

What they do is that they feed this coal into a boiler furnace and with an assistance of oxygen and a little heat, this creates a combustion in a form of heat energy.
Now the heat energy, will transfer its energy to a water above it making it into a steam, and this steam will rotate a Turbine (and that’s a Mechanical Energy right there) and then this Turbine will rotate a Generator which converts that energy into Electrical Energy.

See that just by knowing this law you can do so much.

And that’s it! This is Easy Engineering.

7 AMAZING Physics Tricks That You Must See
00:06:47
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4 Views · 5 months ago

7 Amazing physics tricks that you can try at home!

Watch part two here https://www.youtube.com/watch?v=2YD_WyT-n5s

00:12 Mould effect
It's obvious that the weight of the heavy falling beads is pulling the remaining beads from the pot. However, it's not so obvious whats causing the large arc and why the beads don't just slide directly over the edge of the pot. It's said that you should view the chain as a series of short ridged rods rather than a flexible string of isolated beads.
When the beads are pulled out of the pot by the weight of the falling beads it causes the ridged rods not only to be lifted but also to rotate. The combination of these two forces causes the end that is not being picked up to push down on the pot which in turn creates a kick. It's this kick that sort of pushes the beads up out of the jar while they are also being pulled down from the other-side and thus the arc is formed. Check out the full explanation here if you're still not satisfied. https://goo.gl/QaRyZZ

00:47 Cool pressure trick
Heating air causes it to expand and cooling it causes it to contract. The boiling water in the bottle causes the glass to get very hot so the air inside the glass also gets hot causing it to expand. When the bottle is put into the cold water it quickly cools causing the air inside to contract rapidly which creates a vacuum and sucks the water up.

01:54 The lenz effect
"Lenz's law states that the current induced in a circuit due to a change or a motion in a magnetic field is so directed as to oppose the change in flux and to exert a mechanical force opposing the motion." When the magnet is dropped into the conductive alloy pipe it causes a change in magnetic flux. This change in magnetic flux creates a current in the Aluminium pipe which opposes the change and slows the magnet down in order to reduce the change in flux.
This video explains things way more thoroughly. https://goo.gl/idAvZs

02:56 Anti-gravity water trick
There are a couple of forces at work here, air pressure and surface tension. The atmospheric pressure all around us helps to hold the plastic in place. In addition to this, there is a small pocket of air at the top of the bottle. Because no more air can get to this pocket an area of low pressure is formed. A combination of low air pressure inside the glass and higher air pressure outside of it help to keep the plastic in place.
Next is surface tension and adhesion. Water molecules are attracted to each-other like little tiny magnets with a positive and negative end. On the surface of the water, the molecules are able to get closer to each-other than below the surface, this creates a sort of elastic surface layer.
Adhesion occurs because of the water molecules positive and negative ends are not only attracted to each-other, but also to other materials such as the plastic circle in this experiment. This causes the water molecules to adhere to the plastic whilst maintaining the surface tension with the other water molecules. It is a combination of all these factors that keep the plastic in place and stop the water gushing out. Check out this post for a more detailed explanation. https://goo.gl/crM6Xy

04:16 Water on a string surface tension trick
^^^This trick works on the same surface tension and adhesion principles as the one above ^^^

04:52 Ring catch chain trick
The trick with this one is in how you drop the ring. If you let go of the ring with both fingers at the same time it would just drop to the floor. What you need to do is just release your thumb and keep your finger still. When you do this it causes the ring to fall at an angle which in-turn causes the chain to loop itself over the ring and get caught.

05:43 Fork and spoon center of gravity trick
Every object has a center of gravity. This is the central point at which gravity acts upon the object. When you position a fork, spoon and tooth pick in this way, the center of gravity or the pivot point happens to be completely central and towards the far end of the tooth pick which just looks so wrong. It looks even more impressive when you burn the toothpick at both ends, this has no effect on the center of gravity so everything remains balanced. The reason the toothpick does not continue to burn past the metal of the fork or the glass is that when it reaches these points its robbed of its heat and goes out.

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What Are Neutrinos? | How The Universe Works
00:09:58
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4 Views · 5 months ago

What are neutrinos? Where do they come from? Why can't we feel then and how do we detect them? Find out on How The Universe Works.

🇬🇧 Catch full episodes of your favourite Discovery Channel shows on discovery+: https://bit.ly/38dyTev

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Big Stars | How the Universe Works
00:01:33
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4 Views · 5 months ago

The sun has been lighting our planet for 4.6 billion years and dominates all life on Earth -- but it's a speck in comparison to the other stars in the universe. | For more How the Universe Works, visit http://science.discovery.com/t....v-shows/how-the-univ

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Calculus 1 Review -  Basic Introduction
00:26:44
tutorsmediavideos
4 Views · 5 months ago

This back to school calculus 1 review video tutorial provides a basic introduction into a few core concepts taught in a typical AP calculus ab course or a first semester of college calculus.

Full 1 Hour 30 Minute Video:
https://www.youtube.com/watch?v=B-v_lb7kE70

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What is the First Law of Thermodynamics?
00:04:09
tutorsmediavideos
3 Views · 5 months ago

With the a little hydrogen, a few balloons and a couple of makeshift rockets, Valeska Ting launches into an explanation of what the first law of thermodynamics is, and why it matters to our lives.
Day 5 of our 2016 advent calendar. Open each day here: https://rigb.org/advent?utm_source=youtube&utm_medium=social&utm_campaign=201612_channel_advent
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We've all heard the rule that states that ‘energy cannot be created or destroyed’, or ‘energy is always conserved’. But what does that mean? Chemical engineer Valeska Ting explains.

The 2016 advent calendar explores the four laws of thermodynamics with a new short film each day, with explosive demonstrations, unique animations, and even a musical number. Open the calendar at http://rigb.org/advent?utm_source=youtube&utm_medium=social&utm_campaign=201612_channel_advent

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Neil deGrasse Tyson Explains The Weirdness of Quantum Physics
00:10:24
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3 Views · 5 months ago

Quantum mechanics is the area of physics that deals with the behaviour of atoms and particles on microscopic scales. Since its inception, the many counter-intuitive aspects and results of quantum mechanics have provoked strong philosophical debates and many interpretations.

Neil deGrasse Tyson explains quantum physics in a way that is understandable even for the lay person. In Quantum Mechanics there is no such thing as absolute certainty when looking for something. This phenomenon is known as Uncertainty Principle and was Introduced first in 1927 by the German physicist Werner Heisenberg. Heisenberg realized that one implication of quantum physics is that the act of measurement always disturbs the object measured.

Neil deGrasse Tyson explains that the whole computer world is based on the principle of Quantum Physics. We are able to manipulate the electrical properties of silicon only because we can study the wave nature of electrons.

Our daily routines are often governed by technology that is directly related to Quantum Physics, thus our lives rest upon these fundamental scientific discoveries.

Another hard concept to grasp is Quantum entanglement. Einstein referred to it as "spooky action at a distance. It occurs when a pair or group of particles is generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the pair or group cannot be described independently of the state of the others. But Neil deGrasse Tyson and Lawrence Krauss explain this concept with everyday life examples which makes it a little bit easier to understand.

As Neil deGrasse Tyson points out, the first quantum phenomena were observed more than a century ago. However scientists are still learning about this realm of our universe.

#neiltyson #quantumphysics #science

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Sources:
House Science & National Labs Caucus: Neil deGrasse Tyson
https://www.youtube.com/watch?v=joARXZagTuM Accessed 01.03.2021

Lawrence Krauss - Connoway Hall - https://www.youtube.com/watch?v=BRNtcj6YRuc Accessed 12.03.2021

In the Blink of Bird’s Eye, a Model for Quantum Navigation
https://www.ks.uiuc.edu/Public....ations/pdfs/2011-01- retrieved 10.03.2021

Satellite-to-ground quantum-limited communication using a 50-kg-class microsatellite
https://www.nature.com/articles/nphoton.2017.107 Accessed 11.03.2021

NASA's Cold Atom Lab Takes One Giant Leap for Quantum Science
https://www.nasa.gov/feature/j....pl/nasas-cold-atom-l Accessed 09.03.2021

NASA’s Cold Atom Lab: The Coolest Experiment in the Universe
https://coldatomlab.jpl.nasa.g....ov/videos/coolest-ex Accessed 02.03.2021

Why do quantum effects only happen on the atomic scale?
https://wtamu.edu/~cbaird/sq/2....014/04/22/why-do-qua retrieved 01.03.2021

Neil deGrasse Tyson JRE #919
https://www.youtube.com/watch?v=PhHtBqsGAoA retrieved 26.02.2017

Calculus 1 - Full College Course
11:53:48
tutorsmediavideos
3 Views · 5 months ago

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/channe....l/UCkyLJh6hQS1TlhUZx

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

⭐ 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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