Latest Engineering Mathematics Syllabus – First Year BTech

If you are looking for a detailed syllabus of Engineering mathematics then you are on the right page. Here, we have updated an Engineering Maths 1st year Syllabus in a full-fledged way. Plan your preparation by covering all these concepts and clear the exam. Having prior knowledge of the topics helps you in clearing the exam easily. So, refer to the below sections and collect all MI, MII, MIII Syllabus and start your preparation.

Mathematics M1 Syllabus – 1st Year M1 PDF Notes 

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 homogeneous 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 homogeneous 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 an algebra of matrices; types of matrices; Vector Space, Sub-space, Basis, and dimension, linear the system of equations; consistency of linear systems; the rank of a matrix; Gauss elimination; the 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; transformation of forms to principal axis (conic section).

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# Kreyszig- Advanced Engineering Mathematics

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Syllabus of Engg. Maths M2 – Mathematics II Books Pdf

Unit 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.

Unit 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.

Unit 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

Unit 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.

Unit V: Vector Integral Calculus

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

Engg. Mathematics M3 Syllabus – Best Books for 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 is 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.