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Open Courseware
Exponential Decay Formula Proof
Showing that N(t)=Ne^(-kt) describes the amount of a radioactive substance we have at time T. For students with background in Calculus. Not necessary for intro chemistry class.
http://www.youtube.com/watch?v=H7nrVDV8ahc -
Open Courseware
Exponential Growth
Exponential growth involving bacteria (some calculus in part c).
http://www.youtube.com/watch?v=JWfTckls59k -
Open Courseware
Differential Equations
Topics covered in a first year course in differential equations. Need to understand basic differentiation and integration from Calculus before starting here.
https://academicearth.org/courses/differential-equations-khan/ -
Open Courseware
Big Picture: Integrals
The second half of calculus looks for the distance traveled even when the speed is changing. Finding this integral is the opposite of finding the derivative. Professor Strang explains how the integral adds up little pieces to recover the total distance.
http://www.youtube.com/watch?v=2qxY859dzzQ -
Open Courseware
The Exponential Function
Professor Strang explains how the magic number e connects to ordinary things like the interest on a bank account. The graph of y = e^x has the special property that its slope equals its height (it goes up exponentially fast!). This is the great function of calculus.
http://www.youtube.com/watch?v=oo1ZZlvT2LQ -
Open Courseware
Big Picture: Derivatives
Calculus finds the relationship between the distance traveled and the speed — easy for constant speed, not so easy for changing speed. Professor Strang is finding the rate of change, the slope of a curve, and the derivative of a function.
http://www.youtube.com/watch?v=T_I-CUOc_bk -
Open Courseware
Curl
This lecture gently introduces the idea of a the “curl” of a vector field. The curl is one of the basic operations of vector calculus. Dr Chris Tisdell discusses the definition of the curl and how to compute it. Plently of examples are provided. A physical interpretation of the curl is also presented in terms […]
http://www.youtube.com/watch?v=tOyzmdnYEWA -
Open Courseware
Applications of Line Integrals
This lecture discusses the applications of line integrals, including calculating work; flux (flow) in the plane over curves; and also circulation around curves in the plane. A number of examples are presented to illustrate the theory. The fundamental theorem of line integrals may be thought of as one of the basic theorems of vector calculus.
http://www.youtube.com/watch?v=MK9AVLamII8 -
Open Courseware
Divergence
This video discusses the ‘divergence’ of a vector field. Divergence is one of the basic operations of vector calculus and, loosely speaking, may be thought of as a type of derivative in vector calculus.
http://www.youtube.com/watch?v=9Qf1PIggBhA -
Open Courseware
Einstein’s General Theory of Relativity IV
October 13, 2008, Stanford’s Felix Bloch Professor of Physics, Leonard Susskind, discusses covariant and contra variant indices, tensor arithmetic, algebra and calculus, and the geometry of expanding space time.
http://www.youtube.com/watch?v=ttMI0dmmkrE