CE8301 Notes Strength of Materials 1

CE8301 Notes Strength of Materials 1 Regulation 2017 Anna University free download. Strength of Materials 1 Notes CE8301 pdf free download.

OBJECTIVES: CE8301 Notes Strength of Materials 1

 To learn the fundamental concepts of Stress, Strain and deformation of solids.
 To know the mechanism of load transfer in beams, the induced stress resultants and deformations.
 To understand the effect of torsion on shafts and springs.
 To analyze plane and space trusses

OUTCOMES: CE8301 Notes Strength of Materials 1

Students will be able to

 Understand the concepts of stress and strain, principal stresses and principal planes.

 Determine Shear force and bending moment in beams and understand concept of theory of simple bending.

 Calculate the deflection of beams by different methods and selection of method for determining slope or deflection.

 Apply basic equation of torsion in design of circular shafts and helical springs.

 Analyze the pin jointed plane and space trusses

TEXTBOOKS: CE8301 Notes Strength of Materials 1

1. Rajput.R.K. “Strength of Materials”, S.Chand and Co, New Delhi, 2015.

2. Punmia.B.C., Ashok Kumar Jain and Arun Kumar Jain, SMTS –I Strength of materials, Laxmi publications. New Delhi, 2015

3. Rattan . S. S, “Strength of Materials”, Tata McGraw Hill Education Private Limited, New Delhi, 2012

4. Bansal. R.K. “Strength of Materials”, Laxmi Publications Pvt. Ltd., New Delhi, 2010

REFERENCES : CE8301 Notes Strength of Materials 1

1. Timoshenko.S.B. and Gere.J.M, “Mechanics of Materials”, Van Nos Reinbhold, New Delhi 1999.

2. Vazirani.V.N and Ratwani.M.M, “Analysis of Structures”, Vol I Khanna Publishers, New Delhi,1995.

3. Junnarkar.S.B. and Shah.H.J, “Mechanics of Structures”, Vol I, Charotar Publishing House, New Delhi 2016.

4. Singh. D.K., “ Strength of Materials”, Ane Books Pvt. Ltd., New Delhi, 2016

5. Basavarajaiah, B.S. and Mahadevappa, P., Strength of Materials, Universities Press, Hyderabad, 2010.

6. Gambhir. M.L., “Fundamentals of Solid Mechanics”, PHI Learning Private Limited., New Delhi, 2009.

CE8301 Notes Strength of Materials 1 Unit 1 & Unit 2 Click Here To Download

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CE8301 Syllabus Strength of Materials 1

CE8301 Important questions Strength of Materials 1

CE8301 Question Bank Strength of Materials 1

MA8353 Notes Transforms and Partial Differential Equations

MA8353 Notes Transforms and Partial Differential Equations Regulation 2017 Anna University free download. Transforms and Partial Differential Equations Notes MA8353 pdf free download.

OBJECTIVES : MA8353 Notes Transforms and Partial Differential Equations

To introduce the basic concepts of PDE for solving standard partial differential equations.

To introduce Fourier series analysis which is central to many applications in engineering apart from its use in solving boundary value problems.

To acquaint the student with Fourier series techniques in solving heat flow problems used in various situations.

To acquaint the student with Fourier transform techniques used in wide variety of situations.

To introduce the effective mathematical tools for the solutions of partial differential equations that model several physical processes and to develop Z transform techniques for discrete time systems.

OUTCOMES : MA8353 Notes Transforms and Partial Differential Equations

Upon successful completion of the course, students should be able to:

Understand how to solve the given standard partial differential equations.

Solve differential equations using Fourier series analysis which plays a vital role in engineering applications.

Appreciate the physical significance of Fourier series techniques in solving one and two dimensional heat flow problems and one dimensional wave equations.

Understand the mathematical principles on transforms and partial differential equations would provide them the ability to formulate and solve some of the physical problems of engineering.

Use the effective mathematical tools for the solutions of partial differential equations by using Z transform techniques for discrete time systems.

TEXT BOOKS: MA8353 Notes Transforms and Partial Differential Equations

1. Grewal B.S., “Higher Engineering Mathematics”, 43rd Edition, Khanna Publishers, New Delhi, 2014.

2. Narayanan S., Manicavachagom Pillay.T.K and Ramanaiah.G “Advanced Mathematics for Engineering Students”, Vol. II & III, S.Viswanathan Publishers Pvt. Ltd, Chennai, 1998.

REFERENCES : MA8353 Notes Transforms and Partial Differential Equations

1. Andrews, L.C and Shivamoggi, B, “Integral Transforms for Engineers” SPIE Press, 1999.

2. Bali. N.P and Manish Goyal, “A Textbook of Engineering Mathematics”, 9th Edition, Laxmi Publications Pvt. Ltd, 2014.

3. Erwin Kreyszig, “Advanced Engineering Mathematics “, 10th Edition, John Wiley, India, 2016.

4. James, G., “Advanced Modern Engineering Mathematics”, 3rd Edition, Pearson Education, 2007.

5. Ramana. B.V., “Higher Engineering Mathematics”, McGraw Hill Education Pvt. Ltd, New Delhi, 2016.

6. Wylie, R.C. and Barrett, L.C., “Advanced Engineering Mathematics “Tata McGraw Hill Education Pvt. Ltd, 6th Edition, New Delhi, 2012.

(MA8353 Notes Transforms and Partial Differential Equations)

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MA8353 Syllabus Transforms and Partial Differential Equations

MA8353 Important questions Transforms and Partial Differential Equations

MA8353 Questions Bank Transforms and Partial Differential Equations

MA8251 Notes Engineering Mathematics 2 Unit 5

MA8251 Notes Engineering Mathematics 2 Unit 5 LAPLACE TRANSFORMATION Regulation 2017 For Anna University Free download. ENGINEERING MATHEMATICS 2 MA8251 Unit 5 LAPLACE TRANSFORMATION Notes Pdf Free download.

Content Engineering Mathematics 2 ma8251 Unit 5 LAPLACE TRANSFORMATION

LAPLACE TRANSFORMATION

1. Laplace transformation-Conditions and existence

Definitions 1. Transformation

A “Transformation” is an operation which converts a mathematical expression to a different but equivalent form

2. Laplace Transformation

Let a function f(t) be continuous and defined for positive values of ‘t’. The Laplace transformation of f(t) associates a function s defined by the equation (ma8251 notes engineering mathematics 2 unit 5)

2. Transforms of Elementary functions-Basic Properties

2.1 Problems Based On Transforms Of Elementary Functions- Basic Properties

3. Transforms Of Derivatives And Integrals Of Functions

3.1 Transform of integrals

3.2 Derivatives of transform

3.3 Problems Based On Derivatives Of Transform (ma8251 notes engineering mathematics 2 unit 5)

4 Transforms Of Unit Step Function And Impulse Function

4.1 Problems Based On Unit Step Function (Or) Heaviside’s Unit Step Function

Define the unit step function. Solution: The unit step function, also called Heaviside’s unit function (ma8251 notes engineering mathematics 2 unit 5)

5 Transform Of Periodic Functions Definition:

(Periodic) A function f(x) is said to be “periodic” if and only if f(x+p) = f(x) is true for some value of p and every value of x. The smallest positive value of p for which this equation is true for every value of x will be called the period of the function.

6 Inverse Laplace Transform

a.If L[f(t)] = F(s), then L–1[F(s)] = f(t) where L–1 is called the inverse Laplace transform operator. b.If F1(s) and F2(s) are L.T. of f(t) and g(t) respectively then

7. Convolution theorem (ma8251 notes engineering mathematics 2 unit 5)

8. Initial and final value theorems

8.1 Initial value theorem

8.2 Final value theorem

9. Solution of linear ODE of Second Order with constant coefficients (ma8251 notes engineering mathematics 2 unit 5)

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MA8251 Notes Engineering Mathematics 2 Unit 4

MA8251 Notes Engineering Mathematics 2 Unit 4 COMPLEX INTEGRATION Regulation 2017 For Anna University Free download. ENGINEERING MATHEMATICS 2 MA8251 Unit 4 COMPLEX INTEGRATION Notes Pdf Free download.

Content Engineering Mathematics 2 ma8251 Unit 4 COMPLEX INTEGRATION

COMPLEX INTEGRATION

1. Introduction

2. Cauchy’s Theorem

2.1 Definitions

2.1.1Connected Region

A connected region is one which any two points in it can be connected by a curve which lies entirely with in the region.

2.1.2 Simply connected region

A curve which does not cross itself is called a simple closed curve. A region in which every closed curve in it encloses points of the region only is called a simply connected region. (ma8251 notes engineering mathematics 2 unit 4)

2.1.3 Contour integral

An integral along a simple closed curve is called a contour integral.

2.1.4 Cauchy’s Integral Theorem

If a function f(z) is analytic and its derivative f0(z) is continuous at R all points inside and on a simple closed curve c, then c f(z)dz = 0:

2.1.5 Cauchy’s Integral formula

If f(z) is analytic inside and on a closed curve c of a simply connected region R and if a is any point with in c, then (ma8251 notes engineering mathematics 2 unit 4)

2.1.6 Cauchy’s integral formula for derivative

If a function f(z) is analytic within and on a simple closed curve c and a is any point lying in it, then

3. Taylor’s and Laurent’s

3.1 Taylor’s Series.

A function f(z), analytic inside a circle C with center at a, can be expanded in the series

3.2 Laurent’s Series.

Let C1; C2 be two concentric circles jz aj = R1 and jz aj = R2 where R2 < R1: Let f(z) be analytic on C1andC2 and in the annular region R between them. Then, for any point z in R, (ma8251 notes engineering mathematics 2 unit 4)

4. Singularities

5. Residues

6. Evaluation of real definite Integrals as contour integrals

7. Applications (ma8251 notes engineering mathematics 2 unit 4)

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MA8251 Notes Engineering Mathematics 2 Unit 3

MA8251 Notes Engineering Mathematics 2 Unit 3 ANALYTIC FUNCTIONS Regulation 2017 For Anna University Free download. ENGINEERING MATHEMATICS 2 MA8251 Unit 3 ANALYTIC FUNCTIONS Notes Pdf Free download.

Content Engineering Mathematics 2 ma8251 Unit 3 ANALYTIC FUNCTIONS

ANALYTIC FUNCTIONS

1. Introduction –Function of A Complex Variable

1.1 Function of Complex Variable Many complicated integrals of real functions are solved with the help of complex variable. They are very useful in solving large number of engineering and science problems

1.2 Complex Variable:

1.3 Function of Complex Variable:

z=x+ i y and w=u+ iv are two complex variable. If for each value of z in a given region R of the complex plane there corresponds one or more values of w, then w is called a function of z and it is denoted by w=f(z)=u(x, y)+iv(x, y)where u(x, y) ,v(x ,y) are real functions of the real variable x and y. (ma8251 notes engineering mathematics 2 unit 3)

1.4 Single Valued Function

If for each value of z in R, there is correspondingly only one value of w, the w is called a single valued function of z.

2. Analytic Functions(C-R Equations)

2.1 Limit of The Function:

2.2 Continuity:

3. Harmonic and Orthogonal Properties Of Analytic Functions

3.1 Laplace Equation: (ma8251 notes engineering mathematics 2 unit 3)

3.2 Properties Of Analytic Functions And Harmonic Conjugate

3.3 Problems Based On Harmonic Conjugate

4. Construction of Analytic Functions

5. Conformal Mapping

5.1 Definition:

The transformation w=f(z) is called as conformal mapping if it preserves angle between every pair of curves through a point, both in magnitude and sense The transformation w=f(z) is called as Isogonal mapping if it preserves angle between every pair of curves through a point in magnitude but altered in sense (ma8251 notes engineering mathematics 2 unit 3)

5.2 Standard Transformations

5.3 Problems Based on Transformation

6. Bilinear Transformation (ma8251 notes engineering mathematics 2 unit 3)

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MA8251 Notes Engineering Mathematics 2 Unit 2

MA8251 Notes Engineering Mathematics 2 Unit 2 VECTOR CALCULUS Regulation 2017 For Anna University Free download. ENGINEERING MATHEMATICS 2 MA8251 Unit 2 VECTOR CALCULUS Notes Pdf Free download.

Content Engineering Mathematics 2 ma8251 Unit 2 Vector Calculus

1 Gradient-Directional Derivative

1.1. Gradient

1(a) The Vector Differential Operator

1(b) The Gradient (Or Slope Of A Scalar Point Function)

1.2. Directional Derivative

1.3. Unit Tangent Vector

1.4 Normal Derivative

1.5 Unit Normal Vector

1.6 Angle Between The Suraces

1.7 .Scalar Potential (ma8251 notes engineering mathematics 2 unit 2)

1. 8 The Vector Equation of the Tangent Plane And Normal Line to the Surface

2. Divergence And Curl –Irrotational And Solenoidal Vector Fields Divergence

2.1 Divergence and curl

2.2 SOLENOIDAL VECTOR,IRROTATIONAL VECTOR:

3 Vector Integration

3.1. Line Integral:

3.2. Surface Integral: Definition: Consider a surface S .Let n denote the unit outward normal to the surface S. Let R be the projection of the surface x on xy plane. Let Vec f be a vector function defined in some region containing the surface S, then the surface integral of Vector f is defined to be (ma8251 notes engineering mathematics 2 unit 2)

3.3. Volume Integral:

3.4 Tutorial Problems:

4 Green’s Theorem In A Plane;(Excluding proof)

5 Gauss Divergence Theorem:(Excluding proof)

Statement: The surface integral of the normal component of a vector function F over a closed surface S enclosing volume V is equal to the volume integral of the divergence of F taken throughout the

6 Stoke’s Theorem(Excluding proof)

Statement: The surface integral of the normal component of the curl of a vector function F over an open surface S is equal to the line integral of the tangential component of F around the closed curve C bounding S. (ma8251 notes engineering mathematics 2 unit 2)

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MA8251 Notes Unit 1 ENGINEERING MATHEMATICS 2

MA8251 Notes Unit 3 ENGINEERING MATHEMATICS 2

MA8251 Notes Unit 4 ENGINEERING MATHEMATICS 2

MA8251 Notes Unit 5 ENGINEERING MATHEMATICS 2

MA8251 ENGINEERING MATHEMATICS 2 Syllabus

MA8251 ENGINEERING MATHEMATICS 2 Important questions

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MA8251 Notes Engineering Mathematics 2 Unit 1

MA8251 Notes Engineering Mathematics 2 Unit 1 Matrix Regulation 2017 For Anna University Free download. ENGINEERING MATHEMATICS 2 MA8251 Unit 1 Notes Pdf Free download.

Content MA8251 Notes Engineering Mathematics 2 Unit 1 Matrix:

• MATRIX
• CHARACTERISTIC EQUATION
• EIGEN VALUE
• EIGEN VECTOR
• LINEARLY DEPENDENT AND INDEPENDENT EIGEN VECTOR
• PROPERTIES OF EIGEN VALUES AND EIGEN VECTORS:
• CAYLEY HAMILTON THEOREM:
• DIAGONALISATION OF A MATRIX
• DIAGONALISATION BY ORTHOGONAL
• TRANSFORMATION OR ORTHOGONAL REDUCTION
• QUADRATIC FORMS
• NATURE OF QUADRATIC FORMS:
• RULES FOR FINDING NATURE OF QUADRATIC FORM USING PRINCIPAL SUBDETERMINANTS (ma8251 notes engineering mathematics 2 unit 1)

CHARACTERISTIC EQUATION Let ‘A’ be a given matrix. Let λ be a scalar. The equation det [A- λ I]=0 is called the characteristic equation of the matrix A.

EIGEN VALUE The values of λ obtained from the characteristic equation |A- λ I|=0 are called the Eigen values of A.

EIGEN VECTOR Let A be a square matrix of order ‘n’ and λ be a scalar, X be a non- zero column vector such that AX = λX.  (ma8251 notes engineering mathematics 2 unit 1)

LINEARLY DEPENDENT AND INDEPENDENT EIGEN VECTOR Let ‘A’ be the matrix whose columns are eigen vectors. (i) If |A|=0 then the eigen vectors are linearly dependent. (ii) If |A|=!0 then the eigen vectors are linearly independent.

PROPERTIES OF EIGEN VALUES AND EIGEN VECTORS:

Property 1: (I) The sum of the Eigen values of a matrix is equal to the sum of the elements of the principal diagonal (trace of the matrix). i.e., λ1+ λ2+ λ3=a11+a22+a33 (ii)The product of the Eigen values of a matrix is equal to the determinant of the matrix. i.e., λ1 λ2 λ3=|A|

Property 2: A square matrix A and its transpose ܣ have the same Eigen values.

Property 3: The characteristic roots of a triangular matrix are just the diagonal elements of the matrix.

Property 4: If λ is an Eigen value of a matrix A, then 1/ λ, (λ=!0) is the Eigen value of A-1

Property 5: If λ is an Eigen value of an orthogonal matrix A, then 1/ λ, (λ=!0) is also its Eigen value. (ma8251 notes engineering mathematics 2 unit 1)

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MA8251 Notes ENGINEERING MATHEMATICS 2 

MA8251 Notes ENGINEERING MATHEMATICS 2 Regulation 2017 Anna University free download. ENGINEERING MATHEMATICS 2 MA8251 Notes pdf free download.

OBJECTIVES : MA8251 Notes ENGINEERING MATHEMATICS 2 

This course is designed to cover topics such as Matrix Algebra, Vector Calculus, Complex Analysis and Laplace Transform.

Matrix Algebra is one of the powerful tools to handle practical problems arising in the field of engineering.

Vector calculus can be widely used for modelling the various laws of physics.

The various methods of complex analysis and Laplace transforms can be used for efficiently solving the problems that occur in various branches of engineering disciplines.

OUTCOMES : MA8251 Notes ENGINEERING MATHEMATICS 2

After successfully completing the course, the student will have a good understanding of the following topics and their applications:

Eigenvalues and eigenvectors, diagonalization of a matrix, Symmetric matrices, Positive definite matrices and similar matrices.

Gradient, divergence and curl of a vector point function and related identities.

Evaluation of line, surface and volume integrals using Gauss, Stokes and Green’s
theorems and their verification.

Analytic functions, conformal mapping and complex integration.

Laplace transform and inverse transform of simple functions, properties, various related theorems and application to differential equations with constant coefficients.

TEXT BOOKS : MA8251 Notes ENGINEERING MATHEMATICS 2

1. Grewal B.S., “Higher Engineering Mathematics”, Khanna Publishers, New Delhi, 43rd Edition, 2014.

2. Kreyszig Erwin, “Advanced Engineering Mathematics “, John Wiley and Sons,
10th Edition, New Delhi, 2016.

REFERENCES : MA8251 Notes ENGINEERING MATHEMATICS 2

1. Bali N., Goyal M. and Watkins C., “Advanced Engineering Mathematics”, Firewall Media (An imprint of Lakshmi Publications Pvt., Ltd.,), New Delhi, 7th Edition, 2009.

2. Jain R.K. and Iyengar S.R.K., “ Advanced Engineering Mathematics”, Narosa
Publications, New Delhi , 3rd Edition, 2007.

3. O’Neil, P.V. “Advanced Engineering Mathematics”, Cengage Learning India Pvt., Ltd, New Delhi, 2007.

4. Sastry, S.S, “Engineering Mathematics”, Vol. I & II, PHI Learning Pvt. Ltd, 4
th Edition, New Delhi, 2014.

5. Wylie, R.C. and Barrett, L.C., “Advanced Engineering Mathematics “Tata McGraw Hill Education Pvt. Ltd, 6th Edition, New Delhi, 2012.

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