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**Matching Problem and conditional probability**

3 Pages |3954 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 ...

4 Pages|2526 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**

3 Pages |1844 Views

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

3 Pages|2324 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**

8 Pages |2462 Views

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

2 Pages|1354 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.**

4 Pages |1952 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.**

5 Pages|1423 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**

2 Pages |3579 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 ...

6 Pages|2349 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**

4 Pages |1255 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 ...

6 Pages|3837 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...

5 Pages |1857 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...

4 Pages|1773 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.**

4 Pages |1661 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**

5 Pages|1555 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.**

4 Pages |2697 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.**

5 Pages|1413 Views

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

5 Pages |1532 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...

5 Pages|1569 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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