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Statistics
Algebra
Trigonometry and Vectors
Calculus (1st Year)
Advanced Math
Trigonometry and Vectors
Course Topic: Mathematical Induction
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-24
Time: 63:20 to 65:10
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video first considers the number of arrangements of 100 coin tosses with 0, 1, and 2 heads. For 2 heads, the professor uses the formula for combinations. Then the professor explains that this relates to gas and entropy. The math is not difficult to follow, but the students may need some explanation of the context of Boltzmann's formula.
Video Link: http://oyc.yale.edu/economics/econ-159/lecture-15
Time: 1:32 - 4:42 for the statement and 12:23 - 31:25 for the full proof
University: Yale
Course: Game Theory
Professor Name: Ben Polak
Teaching Ideas: This video presents Zermelo's Theorem. Which states that in a sequential game where there is a win, loss or tie then either player 1 can either force a win or a tie or player 2 can force a win. This works for checkers or chess. The first three minutes has the statement of the theorem and the second clip is very long but rigorously goes through the steps for mathematical induction. It would be a good idea to first show the students the first clip and then have them work in groups to see if they can provide a mathematical induction argument for the proof.
Course Topic: Radians
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-9
Time: 10:59 to 13:50
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video gives the definition of radians. The professor first finds the length of an arc at θ degrees and argues that the radian is the natural measure of an angle. It is a very simple explanation that all students will understand.
Course Topic: Using the Trigonometric Functions
Video Link: http://oyc.yale.edu/geology-and-geophysics/gg-140/lecture-13
Time: 28:30 - 31:53
University: Yale
Course: The Atmosphere, the Ocean, and Environmental Change
Professor Name: Ronald Smith
Teaching Ideas: This video goes over the Coriolis Force which is a formula that involves the sin of the latitude. This also refers to the force vector and gives the direction. Although no math is done with this formula, but this is an interesting use of the sin function and the Coriolis effect is incredibly important in meteorology but not that well understood by the general public. The professor does go over that since sin 0 = 0 the equator has no Coriolis force and the maximum Coriolis force occurs at the poles since the sin is a maximum there.
Video Link: http://oyc.yale.edu/geology-and-geophysics/gg-140/lecture-17
Time: 40:32 - 42:26
University: Yale
Course: The Atmosphere, the Ocean, and Environmental Change
Professor Name: Ronald Smith
Teaching Ideas: This video explain why the seasons occur. The professor explains that the cos of the solar zenith angle determines what season it is. this is an east to understand use of the cos function to explain something so basic yet something that most do not know the mathematical reason.
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-4
Time: 41:50 to 44:14
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video considers the physics problem of a block moving down an inclined plane where friction is not ignored. The question asks how steep an angle before it slides down. The professor's derivation involves dividing sin by cos to get tan. This is an effective video to play on the day that tan introduced in a trig class.
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-4
Time: 57:34 to 60:06
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video looks at the physics application of a mass spinning around a circle when the mass is attached to a string that is held fixed at the top. The professor derives the acceleration and uses the definition of the tan function. This is an easy to follow example that student should be able to relate to.
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-4
Time: 60:19 to 62:26
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video looks at another physics application that asks what angle should a road bank to keep the car from slipping. This is a very relevant example and makes use of sin, cos, and tan. It can be shown when the students are first learning about the trig functions. He explains it further through 63:17.
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-11
Time: 31:33 to 35:56
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video derives the formula for the force that a wall exerts on a ladder that is leaning on a wall with a given angle. The derivation is lengthy, but it does use the cot function and complementary angles.
Video Link: http://oyc.yale.edu/physics/phys-201/lecture-16
Time: 14:44 to 16:42
University: Yale
Course: Fundamentals of Physics II
Professor Name: Ramamurti Shankar
Teaching Ideas: This video presents Snell's Law. The professor writes down Snell's Law which involves the sin function, but does not go into any detail. This short clip can work as a quick intro to an application of trig functions.
Video Link: http://oyc.yale.edu/physics/phys-201/lecture-22
Time: 71:29 to 75:35
University: Yale
Course: Fundamentals of Physics II
Professor Name: Ramamurti Shankar
Teaching Ideas: This video solves the Schrodinger equation a particle in a well. The clips starts just after the general solution is found and focuses on finding the constants. The derivation finishes with one of the greatest discoveries of physics: that quantized nature of particles. The math is pretty easy to follow and the result is clear.
Video Link: http://oyc.yale.edu/physics/phys-201/lecture-23
Time: 39:05 to 41:18
University: Yale
Course: Fundamentals of Physics II
Professor Name: Ramamurti Shankar
Teaching Ideas: This video investigates the non-redundant solutions to the particle in the well. The professor shows why we can ignore the negative integers. This is due to the fact that one can pull a "-" sign out of the sin function. The professor asks if the students can figure out why. This is a good time to pause the video and see if the any of the instructor's students can answer.
Video Link: https://www.youtube.com/watch?v=9K2Zu-phR4Q&list=PL0A0E275BC354C934&index=6
Time: 58:10 to 1:02:17
University: Missouri University of Science and Technology
Course: Engineering Geology and Geotechnics
Professor Name: David Rogers
Teaching Ideas: This video goes over the driving force and resisting forces that is exerted on a sloped hill. The professor talks about how a road is destroyed by the hill above it and how the Teton dam was destroyed. The equations for these forces involve a cos and tan function. The professor does not go over the equations themselves nor does he use them, so an instructor might want to give an example of how they are used.
Video Link: https://www.youtube.com/watch?v=HmstcE_1ZXU&index=14&list=PL0A0E275BC354C934
Time: 2:02:05 to 2:04:51
University: Missouri University of Science and Technology
Course: Engineering Geology and Geotechnics
Professor Name: David Rogers
Teaching Ideas: This video shows the fundamental period for earthquakes. The background is that if a structure is at the fundamental period then resonance will occur during this earthquake and the structure will collapse. When the period of sin waves are discussed in trigonometry, this video can be shown. It will excite students who are interested in engineering.
Course Topic: SOH CAH TOA
Video Link: http://oyc.yale.edu/astronomy/astr-160/lecture-2
Time: 35:35 - 36:55 and 49:00 - 51:08
University: Yale
Course: Frontiers and Controversies in Astrophysics
Professor Name: Charles Bailyn
Teaching Ideas: This video uses right triangle trigonometry to demonstrate how the sin x can be used to find the difference from a planet to its star. It is a very simple explanation. Afterwards he uses the approximation sin x is close to x. Then at 49:00, he uses it to show why "The idea of looking up and seeing a (exo) planet is going to fail".
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-4
Time: 31:35 to 38:24
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video looks at the classic physics problem of a mass sliding down an inclined plane. It makes extensive use of the trig functions sin and cos which come from looking at the diagram with the xy-plane positioned so that the x-axis corresponds with the incline. The derivation may be difficult for the students at the level of a trig class, but the professor does an excellent job explaining each part. This is a classic example of where math is needed to solve science problems. The clip is a bit long, but may be worth it due to its importance in physics and its heavy reliance on trig.
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-9
Time: 56:00 to 57:47
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video calculates the work done to take a pendulum that begins vertical and bring it to an angle θ0. The professor accomplishes this by looking at the change in energy of the system and makes use of triangle trigonometry. This is a solid example of using the cos function in physics.
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-19
Time: 57:13 to 60:52
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video solves the problem of where to set the boat in the water when there are two holes in the breakwater. It is a great application of triangle trigonometry and the double split experiment and most students will be able to follow.
Video Link: http://oyc.yale.edu/physics/phys-201/lecture-18
Time: 55:03 to 56:14
University: Yale
Course: Fundamentals of Physics II
Professor Name: Ramamurti Shankar
Teaching Ideas: This video looks at the double slit experiment and shows how Young originally came up with the wavelength of light. The professor does the triangle trig part of the derivation, but does not complete the problem. Students can be asked to continue to find the formula for the wavelength.
Video Link: http://oyc.yale.edu/physics/phys-201/lecture-19
Time: 49:34 to 54:04
University: Yale
Course: Fundamentals of Physics II
Professor Name: Ramamurti Shankar
Teaching Ideas: This video explains Heisenberg's uncertainty principle. It uses the sin of the angle of reflection and the fact that it is the opposite over the hypotenuse for the derivation. The math is simple, but the result is famous.
Course Topic: Using Arc Trigonometric Functions to Solve for an Angle
Video Link: http://oyc.yale.edu/chemistry/chem-125a/lecture-4
Time: 18:32 - 23:42 (Skip 19:55 to 21:40 as the professor fumbles with the experiment)
University: Yale
Course: Freshman Organic Chemistry I
Professor Name: Michael McBride
Teaching Ideas: This video shows how an inverse trigonometric function is used to measure lengths at the molecular scale. The professor describes how Newtons used "Newton's Rings" to measure something the size of 30 water molecules. This a a nice application of using sides of a right triangle to find the angle using the cos-1 function.
Video Link: http://oyc.yale.edu/chemistry/chem-125a/lecture-14
Time: 3:30 - 6:37
University: Yale
Course: Freshman Organic Chemistry I
Professor Name: Michael McBride
Teaching Ideas: This video uses a cos-1 function to compute the bond angle for hybridization structures. The professor pauses and has the students figure out the answers. This can be used in a similar way where the trigonometry class is prompted to come up with the bond angle for each.
Course Topic: The Graph of the sin (or cos) Function
Video Link: http://oyc.yale.edu/astronomy/astr-160/lecture-4
Time: 35:00 - 37:00
University: Yale
Course: Frontiers and Controversies in Astrophysics
Professor Name: Charles Bailyn
Teaching Ideas: This video shows how understanding the period and amplitude of the sin function is used to detect and characterize exoplanets. The professor describes how the doppler effect is seen as a sin wave when the hot Jupiter orbits around its star causing the star to wobble in a sin wave. This can be shown when first going over the graph of y = sin x in a trig class.
Video Link: http://oyc.yale.edu/chemistry/chem-125a/lecture-5
Time: 8:37 - 9:28
University: Yale
Course: Freshman Organic Chemistry I
Professor Name: Michael McBride
Teaching Ideas: This video show the sense at which light is a wave. It presents both the graphs of both the time and the position vs. force on a charge that will make it accelerate. The professor uses a nice animation to show the second graph. This can be used when presenting the graphs of y = sin x and y = cos x for the first time to students.
Video Link: http://oyc.yale.edu/chemistry/chem-125b/lecture-20
Time: 5:05 - 7:00
University: Yale
Course: Freshman Organic Chemistry II
Professor Name: Michael McBride
Teaching Ideas: This video shows the way a the electron's time dependent wave function works when there is a 1s and 2p interaction. This motion is a sin wave. In particular the professor explains how the frequency determines the rate that the electron goes up and down.
Video Link: http://oyc.yale.edu/geology-and-geophysics/gg-140/lecture-1
Time: 12:40 - 14:33
University: Yale
Course: The Atmosphere, the Ocean, and Environmental Change
Professor Name: Ronald Smith
Teaching Ideas: This video presents the graphs over time of the predicted tide due to the moon and the sun, the actual tide, and the difference. The predicted is clearly a sin wave. The professor states that there are two high tides each day. An instructor can ask the students what the frequency and period are based on this fact.
Time: 44:55 - 50:11
University: MIT
Course: Circuits
Professor Name: Anant Agarwal
Teaching Ideas: This video shows what it means for there to be a sin wave as a current function. The professor goes through what is happening in a circuit with the current swinging back and forth. The professor is very enthusiastic and gives a demo at the end. This is a very applied approach to explaining the up and down motion of the sin wave.
Time: 19:16 to 22:01
University: MIT
Course: Exploring Black Holes: General Relativity and Astrophysics
Professor Name: Jeffrey McClintock
Teaching Ideas: This video first looks at data that was collected on a star that was orbiting around "something". The professor proves that the "something" must be a black hole. The graph is a clear fit to a sin function. The professor then shows the equation to find the mass of what it is orbiting around. The mass of what it is orbiting around is so large it must be a black hole. It is interesting to note that this is the same method that astronomers use to find exo-planets. This is a nice motivation for studying graphs of sin functions especially since the professor notes that the amplitude and period are all that is needed to determine the mass of the black hole.
Time: 14:26 - 16:46
University: MIT
Course: Principles of Chemical Science
Professor Name: Elizabeth Vogel Taylor
Teaching Ideas: This video presents the wave equation for light. Then the professor sets time to 0 and graphs the equation. The graph demonstrate amplitude and frequency very well. Next the professor goes over how to see the values of x where the amplitude is maximum. This is a simple and clear demonstration of the cos function and is a great way to introduce amplitude and frequency.
Course Topic: Trigonometric Equations
Video Link: http://oyc.yale.edu/physics/phys-201/lecture-18
Time: 45:18 to 50:52
University: Yale
Course: Fundamentals of Physics II
Professor Name: Ramamurti Shankar
Teaching Ideas: This video looks at the double slit experiment and solves a trig equations to find where there is complete destructive and complete constructive interference. The professor sets a cos function equal to 0 and writes down the list of angles. This fundamental application should interest most students and remind them that there are an infinite number of solutions to some trig equations.
Time: 26:55 to 29:15
University: MIT
Course: Principles of Chemical Science
Professor Name: Christopher Cummins
Teaching Ideas: This video finds the angle of the conical nodal surface of the dz2 orbital in chemistry. The equation involves solving for the square of a cos function producing an arccos solution. This is a clear application of needing inverse trig functions to understanding chemistry.
Course Topic: Trigonometric Identities
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-19
Time: 41:10 to 46:45
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video uses the sum to product formula to investigate constructive and destructive interference of waves. The professor explains the physics and manipulates the equation involving a sum of two cos functions. This can be used to motivate the sum to product rule in a trig class.
Video Link: http://oyc.yale.edu/physics/phys-201/lecture-13
Time: 48:09 to 50:00
University: Yale
Course: Fundamentals of Physics II
Professor Name: Ramamurti Shankar
Teaching Ideas: This video uses the sum of angles formula to observe the oscillatory nature of the power required to run a circuit. The professor quickly goes through the math, but does explain what is happening. The video shows that when you run a circuit, the energy usage is not just constant.
Video Link: http://oyc.yale.edu/physics/phys-201/lecture-18
Time: 25:32 to 28:58
University: Yale
Course: Fundamentals of Physics II
Professor Name: Ramamurti Shankar
Teaching Ideas: This video derives the formula for the wave formed when there are two wave equations with the same frequency, but with a shift. It uses the sum to product formula. The professor explains it very well and students should be able to follow the derivation.
Course Topic: Parametric Equations
Time: 33:15 - 40:36
University: MIT
Course: The Early Universe
Professor Name: Alan Guth
Teaching Ideas: This video shows how a cycloid models the Big Crunch theory of the universe. The Big Crunch theory uses the forumal y = 1 - cos(θ) which shows that at the beginning the universe had no volume and after one period, we will be back to no volume (The Big Crunch). It turns out that the most recent evidence shows that the Big Crunch theory is incorrect and in fact we will have an accelerating universe finishing off with a cold dark lonely universe instead.
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-2
Time: 59:11 to 63:11
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video solves the problem of finding the angle one should throw a projectile in order to maximize the horizontal distance that it travels. The professor very clearly goes through the derivation and even uses the double angle formula for sin: sin(2x) = 2sin(x)cos(x). This clip can be used in a trigonometry class as it serves as motivation for parametric equations and using trig formulas.
Course Topic: Vectors
Video Link: http://oyc.yale.edu/economics/econ-251/lecture-2
Time: 65:15 to 66:06
University: Yale
Course: Financial Theory
Professor Name: John Geanakoplos
Teaching Ideas: This video explains using addition of vectors that the sum of the endowments of a product x is equal to the sum of the endowments of a product y. This is a little difficult to follow, but with some explanation from the instructor the students can see why the vectors model the situation.
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-2
Time: 8:05 to 10:43
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video explains what the definition of a vector is in the context of the position of a hiker and then in general two dimensional space. The explanation is very clear and can be used as the direct definition of a vector in math class for a vector described as a direction and a magnitude. The example is just a sketch without numbers shown.
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-2
Time: 10:51 to 12:31
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video shows the graphical definition of addition of two vectors in two dimensional space. The professor draws the vectors tip to tail to first define addition of vectors. Then he shows the commutative law by drawing the standard parallelogram. This is very "mathy" but it does show that math definitions are directly given in other courses. This video can be used to reinforce what is being done in a math class when introducing vectors.
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-2
Time: 16:15 to 17:42
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video proves that the magnitude-direction definition of a vector can always be restated as x and y coordinates. The professor shows this just as a math instructor would, so the clip would help validate what is done in class as vectors are introduced for the first time.
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-2
Time: 17:42 to 19:10
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video begins where the above one left off. It uses trigonometry to derive the formulas that relate the magnitude and angle of a two dimensional vector to its x and y coordinates. It is very easy to follow, but does not give an example. It can substitute for the proof that a math instructor will give in this section.
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-2
Time: 55:50 to 58:38
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video generically solves the problem that asks if a car goes over a cliff, when will it hit the ground. It uses the standard vector valued function. No numbers are given so this is more of a derivation than an example. The professor does not complete the last steps, so it would be a good idea to as the students to fill in the details at the end.
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-6
Time: 20:12 to 21:13
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video uses the definition of the magnitude of a vector to derive the kinetic energy formula in two dimensions. It is clearly stated and can be shown at the pre-calculus level without issue.
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-14
Time: 24:43 to 27:26
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video introduces the concept of four dimensional vectors that correspond to points in the space time continuum. The professor states that numerical subscripts work better then changing letters since with many you will run out of letters. This is a nice way of convincing students that the n-vector has use. If you have extra time you can continue for another few minutes and the professor will mention the 10-vector in string theory.
Video Link: http://oyc.yale.edu/physics/phys-201/lecture-2
Time: 13:22 to 14:15
University: Yale
Course: Fundamentals of Physics II
Professor Name: Ramamurti Shankar
Teaching Ideas: This video looks at two charges in space and considers the displacement vector from the first charge to the second. The professor shows why this displacement vector is just the subtraction of the vector from the origin to the second charge and the vector from the origin to the first charge. The reason why this triangle depicts subtraction is very clearly stated and can be used to remind students how subtraction of vectors works geometrically. If you continue to 16:35, you will see this in use to find the total force between the two charges along with a detailed explanation of the magnitude of a vector and how to find a unit vector in the direction of a given vector.
Course Topic: Dot Product
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-6
Time: 24:13 to 27:14
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video begins by looking at the work done in two dimensions and notices that the form occurs often. This motivates the professor to define the general definition of the dot product in two dimensions. This combination of application and pure math will serve as a great start to the topic of the dot product either in a pre-calculus or a calculus class.
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-6
Time: 28:02 to 30:43
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video looks demonstrates that the dot product of a vector with itself is the square of its magnitude. Then the professor uses the Law of Cosines to derive that A o B = |A| |B| cos θ. This is a very "mathy" clip, but shows that the math is important in physics.
Video Link: http://oyc.yale.edu/physics/phys-201/lecture-6
Time: 38:37 to 40:43
University: Yale
Course: Fundamentals of Physics II
Professor Name: Ramamurti Shankar
Teaching Ideas: This video looks at the potential difference between two nearby points. The professor derives that it is a dot product. Then he uses the geometric definition to come up with the equation that equates the change in potential to a product of the electric field, the change in radius, and the cos of the angle between them.
Time: 36:22 to 41:40
University: MIT
Course: Introduction to Algorithms
Professor Name: Erik Demaine
Teaching Ideas: This video Comes up with a definition of how different word documents are from each other by creating for each document a vector whose components correspond to word frequency. The distance is defined by the dot product between the two vectors. This is a perfect example of the dot product used in ways that students have almost certainly never seen before and can be very effective in getting students interested in the field of computer science and artificial intelligence.
Time: 31:22 - 41:34 (or earlier)
University: MIT
Course: Principles of Chemical Science
Professor Name: Elizabeth Vogel Taylor
Teaching Ideas: This video goes over the angles of various molecules. The professors do not actually work out the angles using the dot product, but an instructor can ask the students to work them out by creating vectors after seeing the physical structures and then taking the dot product. This would be a creative exercise, but the students will need help getting started. There are many example given so an instructor can just have the students work on the first few in order to save time.
Time: 21:27 to 23:02
University: MIT
Course: Artificial Intelligence
Professor Name: Patrick Winston
Teaching Ideas: This video uses the dot product of vectors to come up with a way of measuring closeness between two point in order for a computer to use artificial intelligence to identify what magazine an article might have come from based on the frequency of the word "hack" and "computer". No numbers are given, but the dot product formula is shown for two general n-dimensional vectors. An instructor will have to provide some context unless much more of the video is shown.
Time: 14:42 - 17:09
University: MIT
Course: Artificial Intelligence
Professor Name: Patrick Winston
Teaching Ideas: This video uses uses subtraction of vectors, shown geometrically, and the dot product of find the width of the street that best separates objects that are either + or - type. The context of this video is that this is part of artificial intelligence to differentiate between two different objects. The presentation is very clearly shown geometrically and is appropriate for students who are first learning about vector dot products.
Video Link: https://www.youtube.com/watch?v=KeGCyMy-AWs&list=PL48DE756A5800ED5F&index=6
Time: 23:19 to 25:13
University: UC Berkeley
Course: Environmental Science
Professor Name: (Not Provided in Video)
Teaching Ideas: This video looks at fecundity and survivor schedule for a population of laboratory aphids. The dot product of the two tells us the species will have a population explosion. The professor does not state the words "dot product" but the dot product is clearly being calculated. This is a not very difficult application of the dot product to ecology.
Course Topic: The Cross Product
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-11
Time: 43:27 to 47:13
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video defines the cross product of two vectors in order to define the torque. The professor goes into a long explanation of how to find the angle using the right hand rule. This video can be shown as a replacement to the class explanation since it defines the cross product mathematically.
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-11
Time: 49:27 to 51:01
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video explains three properties of the cross product: AxB = -BxA, AxA = 0 and ixj = k. Although this is a physics class it is straight math. This can be shown to reinforce these three essential properties of the cross product.
Video Link: http://oyc.yale.edu/physics/phys-200/lecture-11
Time: 52:46 to 55:36
University: Yale
Course: Fundamentals of Physics I
Professor Name: Ramamurti Shankar
Teaching Ideas: This video defines the torque as the rate of change of angular momentum. The professor makes use of the product rule for cross products and also the fact that a vector crossed with a parallel vector is 0. This is an excellent example of the use of the product rule for cross products and would accompany the corresponding lecture in a vector calculus class.
Video Link: http://oyc.yale.edu/physics/phys-201/lecture-2
Time: 63:15 to 66:24
University: Yale
Course: Fundamentals of Physics II
Professor Name: Ramamurti Shankar
Teaching Ideas: This video finds the torque that results from a uniform electric field on a dipole. The professor derives the formula for this and then explains that it is just the cross product of the charge and the electric field. This is all done geometrically so no matrices are uses, just magnitudes and angles. This is a simple application of the cross product that students should be able to understand.
Course Topic: The Complex Plane
Video Link: http://oyc.yale.edu/physics/phys-201/lecture-18
Time: 30:14 to 36:22
University: Yale
Course: Fundamentals of Physics II
Professor Name: Ramamurti Shankar
Teaching Ideas: This video derives the formula for the wave formed when there are two wave equations with the same frequency, but with a shift. It uses complex numbers graphed on the complex plane. This is a high level Pre-Calculus argument that will work well as a summary of several key components from the Pre-Calculus course.