[PDF ]Diploma Applied Mathematics-III Book Pdf download [UP Polytechnic pdf download]

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BTEUP Applied Mathematics – III book

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Applied Mathematics-III

APPLIED MATHEMATICS –III में आप इस पाठ्यक्रम की सामग्री के बारे में जानेंगे, कुछ प्राथमिक और उन्नत गणित एल्गोरिदम और इंजीनियरिंग समस्याओं को सुलझाने के उनके अनुप्रयोगों की समझ प्रदान करते हैं।

Matrices
Differential Calculus
Differential Equation
Integral Calculus-II
Probability and Statistics

Only 5 Chapters That You Have to read in Applied Mathematics – III

And here are the marking scheme according to Chapters in Applied Math – III

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Topic in Applied Mathematics III

Matrices
Differential Calculus
Differential Equations
Integral Calculus
Probability & Statistics

MATRICES : (12 Marks)

1.1 Algebra of Matrices, Inverse :

Addition, Multiplication of matrices, Null matrix and a unit matrix, Square matrix, Symmetric, Skew symmetric, Hermitian, Skew hermition, Orthagonal, Unitary, diagonal and Triangular matrix, Determinant of a matrix. Definition and Computation of inverse of a matrix.

1.2 Elementary Row/Column Transformation :

Meaning and use in computing inverse and rank of a matrix.

1.3 Linear Dependence, Rank of a Matrix

Linear dependence/independence of vectors, Definition and computation of a rank of matrix. Computing rank through determinants, Elementary row transformation and through the concept of a set of independent vectors, Consistency of equations.

1.4 Eigen Pairs, Cayley-Hamilton Theorem :

Definition and evaluation of eign values and eign vectors of a matrix of order two and three, Cayley-Hamilton theorem (without Proof) and its verification, Use in finding inverse and powers of a matrix.

DIFFERENTIAL CALCULUS : (10 Marks)

2.1 Function of two variables, identification of surfaces in space, conicoids

2.2 Partial Differentiation :

Directional derivative, Gradient, Use of gradient f, Partial derivatives, Chain rule, higher order derivatives, Eulens theorem for homogeneous functions, Jacobians.

2.3 Vector Calculus :

Vector function, Introduction to double and triple integral, differentiation and integration of vector functions, gradient, divergence and curl, differential derivatives.

DIFFERENTIAL EQUATION : (10 Marks)

3.1 Formation, Order, Degree, Types, Solution :

Formation of differential equations through physical, geometrical, mechanical and electrical considerations, Order, Degree of a differential equation, Linear, Nonlinear equation.

3.2 First Order Equations :

Variable separable, equations reducible to separable forms, Homogeneous equations, equations reducible to homogeneous forms, Linear and Bernoulli form exact equation and their solutions.

3.3 Higher Order Linear Equation :

Property of solution, Linear differential equation with constant coefficients (PI for X=eax, Sin ax, Cos ax, Xn, eaxV, XV.

INTEGRAL CALCULUS – II: (12 Marks)

4.1 Beta and Gamma Functions :

Definition, Use, Relation between the two, their use in evaluating integrals.

4.2 Fourier Series : Fourier series of f(x),-n<x

<n, Odd and even function,Half range series. 4.3 Laplace Transform : Definition, Basic theorem and properties, Unit step and Periodic functions, inverse laplace transform, Solution of ordinary differential equations. >

4.3 Laplace Transform :

Definition, Basic theorem and properties, Unit step and Periodic functions, inverse laplace transform, Solution of ordinary differential equations.

PROBABILITY AND STATISTICS : ( 6 Marks)

5.1 Probability :

Introduction, Addition and Multiplication theorem and simple problem.

5.2 Distribution :

5.3 Discrete and continuous distribution, Binomial Distribution, Poisson Distribution, Normal Distribution..

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