This 7-minute video lessonn looks at approximating a function around a non-zero x value
- Author:
- Khan, Salman
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This video looks at Generalizing what we did in the last video for f(x) to get the "formula" for using the disc method around the x-axis.
- Author:
- Khan, Salman
This video looks at Generalizing a left Riemann sum with equally spaced rectangles.
- Author:
- Khan, Salman
This video looks at Looking at the example from the last video in a more generalized way.
- Author:
- Khan, Salman
This 10-minute video lesson provides an introduction to the gradient.
- Author:
- Khan, Salman
This 11-minute video lesson examines intuition of the gradient of a scalar field (temperature in a room) in 3 dimensions.
- Author:
- Khan, Salman
This 21-minute video lesson looks at Graphing functions using derivatives.
- Author:
- Khan, Salman
This 11-minute video lesson uses Green's Theorem to solve a line integral of a vector field.
- Author:
- Khan, Salman
This 7-minute video lesson provides Another example of applying Green's Theorem.
- Author:
- Khan, Salman
This 14-minute video lesson provides part 1 of the proof of Green's Theorem.
- Author:
- Khan, Salman
This 19-minute video lesson provides part 2 of the proof of Green's Theorem.
- Author:
- Khan, Salman
This video looks at seeing that Green's Theorem is just a special case of stokes' Theorem.
- Author:
- Khan, Salman
This course begins with a review of algebra specifically designed to help and prepare the student for the study of calculus, and continues with discussion of functions, graphs, limits, continuity, and derivatives. The appendix provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over. Upon successful completion of this course, the student will be able to: calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and LĺÎĺ_ĺĚĺ_hopitalĺÎĺ_ĺĚĺ_s Rule; state whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval and justify the answer; calculate average and instantaneous rates of change in context, and state the meaning and units of the derivative for functions given graphically; calculate derivatives of polynomial, rational, common transcendental functions, and implicitly defined functions; apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems, and calculate slopes and rates for function given as parametric equations; find extreme values of modeling functions given by formulas or graphs; predict, construct, and interpret the shapes of graphs; solve equations using NewtonĺÎĺ_ĺĚĺ_s Method; find linear approximations to functions using differentials; festate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer; state which parts of a mathematical statement are assumptions, such as hypotheses, and which parts are conclusions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 005)
This video looks at identifying minima and maxima for x^3 - 12x - 5.
- Author:
- Khan, Salman
This video looks at the implicit derivative of e^(xy^2) = x - y.
- Author:
- Khan, Salman
This video looks at the implicit derivative of y = cos(5x - 3y).
- Author:
- Khan, Salman
This video looks at the implicit derivative of (x^2+y^2)^3 = 5x^2y^2.
- Author:
- Khan, Salman
This video looks at the implicit derivative of (x-y)^2 = x + y + 1.
- Author:
- Khan, Salman
Like people, mathematical relations are not always explicit about their intentions. In this tutorial, we'll be able to take the derivative of one variable with respect to another even when they are implicitly defined (like "x^2 + y^2 = 1").
This video looks at the improper integral with two infinite bounds.
- Author:
- Khan, Salman