Dear students, if you are a student of Polytechnic Second Year Third Semester of Electrical & Electronics Engineering and you want to know what are the units in Applied Mathematics 3, then you have reached the right place. Today’s post , we will tell you in detail about the Applied Mathematics 3 Syllabus which is approved by BTEUP and this is the Applied Mathematics 3 new syllabus .
Before we start the post one thing you were must know which is, Applied Mathematics 3 is a common with all Polytechnic branch. So let’s start the post and read about Applied Mathematics 3 detailed syllabus.
DETAILED CONTENTS OF POLYTECHNIC THIRD SEMESTER APPLIED MATHEMATICS 3 FOR ELECTRICAL & ELECTRONICS ENGINEERING
1.) Matrices
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 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 eigen values and eigen vectors of a matrix of order two and three, Caley-Hamilton theorem (without proof) and its verification, Use in finding inverse and powers of a matrix.
2.) Differential Calculus
2.1) Function of two variables, identification of surface in space, conicoids.
2.2) Partial Differntiation
- Directional derivative, Gradient, Use of gradient f, Partial derivatives, Chain rule, Higher order derivatives, Euler’s theorem for homogenous functions, Jacobians.
2.3) Vector Calculus
- Vectors function, Introduction to double and triple integral, differentiation and integration of vectors functions, gradient, divergence and curl, differntial derivatives.
3.) Differntial Equation
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 seperable, equations reducible to seperable forms, Homogeneous equtions, 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= e^ax , Sinax, Cosax, X^n, e^axV, XV).
3.4) Simple Applications
LCR circuit, Motion under gravity, Newton’s law of cooling, radioactive decay, Population growth, Force vibration of a mass point attached to spring with and without damping effect. Equivalence of electrical and mechanical system.
4.) Integral Calculus-II
4.1) Beta and Gamma Functions ( Definition, use, relation between the two, their use in evaliating 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 functiond, inverse laplace transform,Sloution of ordinary differential equations).
5.) Probability and Statistics
5.1) Probability (Introduction, Addition and Multiplication theorem and simple problem.)
5.2) Distribution (Discrete and continuous distribution, Bionimal Distribution, Poisson distribution, Normal distribution.)
LEARNING OUTCOMES
After undergoing this course, the students will be able to:
• Understand matrix operations and uses of matrix in different problems.
• Apply elementary row and column operations in finding inverse of a matrix.
• Find Eigen values, Eigen vectors of a matrix and their different properties.
• Understand degree/order of differential equations and their solution techniques.
• Use differential equations in engineering problems of different areas.
• Find Fourier series expansion of a function.
• Apply Laplace transform and their applications in solving engineering problems.
• Understand concept of probability distribution and their applications.
INSTRUCTIONAL STRATEGY
The content of Applied Mathematics 3 is to be taught on conceptual basis with plenty of real world examples. The basic elements of Laplace transform, Differential equations and Applications of differential equations can be taught with engineering applications of relevant branch.
MEANS OF ASSESSMENT
- Assignments and Quiz/Class Tests
- Mid-term and End-term Written Tests
- Model/Prototype Making
RECOMMENDED BOOKS
1. Elementary Engineering Mathematics by BS Grewal, Khanna Publishers, New Delhi.
2. Engineering Mathematics, Vol I & II by SS Sastry, Prentice Hall of India Pvt. Ltd.,
3. Applied Mathematics-III by Chauhan and Chauhan, Krishna Publications, Meerut.
4. Applied Mathematics-II by Kailash Sinha and Varun Kumar; Aarti Publication, Meerut.
5. E-books/e-tools/relevant software to be used as recommended by AICTE/ NITTTR, Chandigarh.
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