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Matching Problem and conditional probability

Matching Problem and conditional probability

3 Pages |3704 Views

Matching Problems of probability are discussed. If n letters are randomly stuffed into the n envelopes, then the probability that at least one letter ...

Multinomial Coefficients

Multinomial Coefficients

4 Pages|2368 Views

Multinomial Coefficients are defined and explained. These values are used to split objects into groups of various sizes. The use of multinomial variabl...

Properties of Probability and sampling

Properties of Probability and sampling

3 Pages |1657 Views

Properties of Probability are discussed. Numerical problems based on these are solved.The probability of a union of disjoint events is explained. Fini...

Probability and Sets

Probability and Sets

3 Pages|2090 Views

Probability is defined. Classical, Frequency and Subjective Interpretations of probability is discussed here with examples. Experiment, Sample Space,...

An application of the Dirac delta function

An application of the Dirac delta function

8 Pages |2267 Views

A continuously differentiable function is defined and analysed by the help of multivariable calculus. Theorems on continuously differentiable function...

Plotting functions

Plotting functions

2 Pages|1198 Views

Functions are defined on an interval called the domain. To plot the function in MATLAB, the domain is to be  specified. The  left endpoint and the righ...

Cauchy sequences and complete metric spaces.

Cauchy sequences and complete metric spaces.

4 Pages |1775 Views

"Cauchy sequences and complete metric spaces. A metric space is complete if it “has no holes”. A metric space “has a <br/>hole” if there is...

Terminologies related to calculus are defined.

Terminologies related to calculus are defined.

5 Pages|1248 Views

Open region and closed regions are defined, bounded and open sets are discussed. The maximal solution of a real valued function is explained. Theorem ...

Differential equation of a mixing problem

Differential equation of a mixing problem

2 Pages |3388 Views

Set-up model for a mixing problem is explained. The differential equation is set up for the rate of mass of a chemical in a tank for time t under the ...

Limit cycles

Limit cycles

6 Pages|2152 Views

Stable, unstable, semi stable and neutrally stable limit cycles are defined and explained. Poincare Bendixson theorem is stated and illustrated by dia...

Trajectories of non linear systems

Trajectories of non linear systems

4 Pages |1141 Views

"In this note we continue the study of the behavior of the trajectories of At all points on y = mx, where m is a constant, the orbits passing ...

Phase plane and trajectories.

Phase plane and trajectories.

6 Pages|3610 Views

The (u, v)-plane associated to a differential equation this way is called the phase plane. The (parameterized) solution curve (u(t), v(t)) is called a...

Repeated eigenvalues

Repeated eigenvalues

5 Pages |1694 Views

An eigenvalue is repeated if it is a multiple root. Repeated eigenvalues are explained with the help of numerical examples. The matrix exponential is...

Complex eigenvalues

Complex eigenvalues

4 Pages|1614 Views

Complex eigenvalues are defined and discussed. The fundamental matrix and the linear operator are discussed here. A linear operator is defined on the...

Definition and theorems on eigenvector and eigenvalue.

Definition and theorems on eigenvector and eigenvalue.

4 Pages |1489 Views

"Eigenvector, eigenvalue of a constant matrix are defined and explained with examples. Characteristic polynomial of a matrix is defined. Importa...

Linear systems and its solution

Linear systems and its solution

5 Pages|1388 Views

" In this lecture note we study linear systems of n first-order differential equations. They are related to first-order matrix differential equati...

Convolution integral and the Convolution Theorem.

Convolution integral and the Convolution Theorem.

4 Pages |2492 Views

A convolution integral is defined. The properties of convolution are stated and discussed. The convolution operator acts like ordinary multiplication ...

Application of transform function.

Application of transform function.

5 Pages|1237 Views

The transfer Function is defined and discussed.A function transforming the input signal to the output is called the transfer function. Application of ...

Theory of distributions

Theory of distributions

5 Pages |1374 Views

A signal which acts for a very short time but produces a large effect is called impulsive function. Impulsive function is discussed elaborately in thi...

Input-output system

Input-output system

5 Pages|1411 Views

"The differential equation is sometimes viewed as an input-output system. The simpler the input signal is, the clearer we should expect the sign...

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OpenCourseWare (OCW) is a web-based publication of virtually all MIT course content. OCW is open and available to the world and is a permanent MIT activity.

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*Materials may not reflect entire content of the course.

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