Mathematics I:

I: Ordinary Differential Equations :

Basic concepts and definitions of 1st order differential equations; Formation of differential equations; solution of
differential equations: variable separable, homogeneous, equations reducible to comparable form, exact differential equation, equations reducible to exact form, linear differential equation, equations reducible to linear form (Bernoulli’s equation); orthogonal trajectories, applications of differential equations.

II: Linear Differential equations of 2nd and higher order 

Second order linear homogeneous equations with constant coefficients; differential operators; solution of similar equations; Euler-Cauchy equation; linear dependence and independence; Wronskian; Solution of nonhomogeneous equations: general solution, complementary function, particular integral; solution by variation of parameters; undetermined coefficients; higher order linear homogeneous equations; applications.

III: Differential Calculus(Two and Three variables)

Taylor’s Theorem, Maxima, and Minima, Lagrange’s multipliers

IV: Matrices, determinants, linear system of equations

Basic concepts of algebra of matrices; types of matrices; Vector Space, Sub-space, Basis and dimension, linear the system of equations; consistency of linear systems; rank of matrix; Gauss elimination; inverse of a matrix by Gauss Jordan method; linear dependence and independence, linear transformation; inverse transformation ; applications of matrices; determinants; Cramer’s rule.

V: Matrix-Eigen value problems

Eigenvalues, Eigenvectors, Cayley Hamilton theorem, basis, complex matrices; quadratic form; Hermitian, SkewHermitian forms; similar matrices; diagonalization of matrices; the transformation of structures to principal axis (conic section).

MATHEMATICS-II

I: Laplace Transforms

Laplace Transform, Inverse Laplace Transform, Linearity, transform of derivatives and Integrals, Unit Step function, Dirac delta function, Second Shifting theorem, Differentiation and Integration of Transforms, Convolution, Integral Equation, Application to solve differential and integral equations, Systems of differential equations.

II: Series Solution of Differential Equations

Power series; the radius of convergence, power series method, Frobenius method; Special functions: Gamma function,
Beta function; Legendre’s and Bessel’s equations; Legendre’s function, Bessel’s function, orthogonal functions;
generating functions.

III: Fourier series, Integrals and Transforms

Periodic functions, Even and Odd functions, Fourier series, Half Range Expansion, Fourier Integrals, Fourier sine, and cosine transforms, Fourier Transform

IV: Vector Differential Calculus

Vector and Scalar functions and fields, Derivatives, Gradient of a scalar field, Directional derivative, Divergence of a vector field, Curl of a vector field.

V: Vector Integral Calculus

Line integral, Double Integral, Green’s theorem, Surface Integral, Triple Integral, Divergence Theorem for Gauss, Stoke’s Theorem

Engineering Mathematics III:

UNIT I: Linear systems of equations:

Rank-Echelon form-Normal form – Solution of linear systems – Gauss elimination – Gauss Jordon- Gauss Jacobi and Gauss-Seidel methods. Applications: Finding the current in electrical circuits.

UNIT II: Eigenvalues – Eigenvectors and Quadratic forms:

Eigenvalues – Eigenvectors– Properties – Cayley-Hamilton theorem Inverse and powers of a matrix by using Cayley-Hamilton theorem- Diagonalization- Quadratic forms- Reduction of quadratic form to canonical form – Rank – Positive, negative and semidefinite – Index – Signature. Applications: Free vibration of a two-mass system.

UNIT III: Multiple integrals:

Curve tracing: Cartesian, Polar and Parametric forms. Multiple integrals: Double and triple integrals – Change of variables –Change of order of integration. Applications: Finding Areas and Volumes.

UNIT IV: Special functions:

Beta and Gamma functions- Properties – Relation between Beta and Gamma functions- Evaluation of improper integrals.
Applications: Evaluation of integrals.

UNIT V: Vector Differentiation:

Gradient- Divergence- Curl – Laplacian and second order operators -Vector identities. Applications: Equation of continuity, potential surfaces

UNIT VI: Vector Integration:

Line integral – Work was done – Potential function – Area- Surface and volume integrals Vector integral theorems: Greens, Stokes, and Gauss Divergence theorems (without proof) and related problems.
Applications: Work is done, Force.

The Main Unit of the book are:
1 Algebra
1.1 Introduction
1.2 Revision of basic laws
1.3 Revision of equations
1.4 Polynomial division
1.5 The factor theorem
1.6 The remainder theorem
2 Partial fractions
2.1 Introduction to partial fractions
2.2 Worked problems on partial fractions with
linear factors
2.3 Worked problems on partial fractions with
repeated linear elements
2.4 Worked problems on partial fractions with
quadratic factors
3 Logarithms
3.1 Introduction to logarithms
3.2 Laws of logarithms
3.3 Indicial equations
3.4 Graphs of logarithmic functions
4 Exponential functions
4.1 Introduction to exponential functions
4.2 The power series for ex
4.3 Graphs of exponential functions
4.4 Napierian logarithms
4.5 Laws of growth and decay

Engineering Mathematics 1st-year pdf Notes

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Suggested Books for Engineering Mathematics -1st year

•  Kreyszig E., Advanced Engineering Mathematics, Wiley, 9th edition.
• Grewal B.S., Higher Engineering Mathematics, Khanna Publishers, 36th edition
•  Dass H.K., Introduction to engineering Mathematics, S.Chand & Co Ltd, 11th edition
•  Ramana B.V., Higher Engineering Mathematics, TMH, Ist edition
•  J.Sinha Roy and S Padhy, A course on ordinary and partial differential Equation, Kalyani Publication, 3rd edition
•  Kreyszig E., Advanced Engineering Mathematics, Wiley, 9th edition.
•  Shanti Narayan and P.K.Mittal, Differential Calculus, S. Chand, reprint 2009
•  Grewal B.S., Higher Engineering Mathematics, Khanna Publishers,36th edition
•  Dass H.K., Introduction to engineering Mathematics, S.Chand & Co Ltd, 11th edition
• Ramana B.V., Higher Engineering Mathematics, TMH, 1st edition
• J.Sinha Roy and S Padhy, A course on ordinary and partial differential Equation, Kalyani Publication, 3rd edition
• chakraborty and Das; Principles of transportation engineering; Phi
• Rangwala SC; Railway Engineering; charotar publication House, Anand
•  Rangwala sc; Bridge Engineering; charotar publication House, Anand
•  Ponnuswamy; Bridge Engineering; TMH

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