I want the syllabus of B.Tech First Year program of National Institute of Technology NIT Calicut so can you provide me?

[ReenaK]

I am providing you the syllabus of B.Tech First Year program of National Institute of Technology NIT Calicut

NIT Calicut B.Tech First Year syllabus

MA1001D MATHEMATICS I

Total hours: 39

Course Outcomes:
Students will be able to:
CO1: Find the limits, check for the continuity and differentiability of functions of a single variable as
well as several variables.
CO2: Test for the convergence of sequences and series of numbers as well as functions.
CO3: Formulate different mensuration problems as multiple integrals and evaluate them.
CO4: Use techniques in vector differential calculus to solve problems related to curvature, surface
normal and directional derivative.
CO5: Find the parametric representation of curves and surfaces in space and will be able to evaluate
the integral of functions over curves and surfaces.

Module 1: (13 Lecture hours)

Real valued function of real variable: Limit, Continuity, Differentiability, Local maxima and local minima,
Curve sketching, Mean value theorems, Higher order derivatives, Taylors theorem, Integration, Area
under the curve, Improper integrals.
Function of several variables: Limit, Continuity, Partial derivatives, Partial differentiation of composite
functions, Differentiation under the integral sign, Local maxima and local minima, Saddle point, Taylors
theorem, Hessian, Method of Lagrange multipliers.

Module 2: (13 Lecture hours)

Numerical sequences, Cauchy sequence, Convergence, Numerical series, Convergence, Tests for
convergence, Absolute convergence, Sequence and series of functions, point-wise and uniform
convergence, Power series, Radius of convergence, Taylor series.
Double integral, Triple integral, Change of variables, Jacobian, Polar coordinates, Applications of
multipleintegrals.

Module 3: (13 Lecture hours)

Parameterised curves in space, Arc length, Tangent and normal vectors, Curvature and torsion, Line
integral, Gradient, Directional derivatives, Tangent pla ne and normal vector, Vector field, Divergence,
Curl, Related identities, Scalar potential, Parameterised surface, Surface integral, Applications of
surface integral, Integral theorems: Green's Theorem, Stokes' theorem, Gauss divergence theorem,
Applications of vector integrals.
References:
1. H. Anton, I. Bivensand S. Davis, Calculus, 10th edition, New York: John Wiley & Sons, 2015.
2. G. B. Thomas, M.D. Weirand J. Hass, Thomas’ Calculus, 12th edition, New Delhi, India: Pearson Education, 2015.
3. E. Kreyszig, Advanced Engineering Mathematics, 10th edition, New York: John Wiley & Sons, 2015.
4. Apostol, CalculusVol 1, 1st ed. New Delhi: Wiley, 2014.

MA1002D MATHEMATICS II

Total hours: 39

Course Outcomes

Students will be able to:
CO1: T est the consistency of system of linear equations and then solve it.
CO2: Test for linear independence of vectors and perform orthogonalisation of basis vectors.
CO3: Diagonalise symmetric matrices and use it to find the nature of quadratic forms.
CO4: Formulate some engineering problems as ODEs and hence solve them.
CO5: Use Laplace transform and its properties to solve differential equations and integral equations.

Module 1: (16 Lecture hours)

System of Linear equations, Gauss elimination, Solution by LU decomposition, Determinant, Rank of a
matrix, Linear independence, Consistency of linear system, General form of solution.
Vector spaces, Subspaces, Basis and dimension, Linear transformation, Rank-nullity theorem, Innerproduct, Orthogonal set, Gram-Schmidt orthogonalisation, Matrix representation of linear
transformation, Basis changing rule.
Types of matrices and their properties, Eigenvalue, Eigenvector, Eigenvalue problems, CayleyHamiltonian theorem and its applications, Similarity of matrices, Diagonalisation, Quadratic form ,
Reduction to canonical form.

Module 2: (13 Lecture hours)

Ordinary Differential Equations (ODE): Formation of ODE, Existence and uniqueness solution of first
order ODE using examples, Methods of solutions of first order ODE, Applications of first order ODE.
Linear ODE: Homogenous equations, Fundamental system of solutions, Wronskian, Solution of second
order non-homogeneous ODE with constant coefficients: Method of variation of parameters, Method of
undetermined coefficients, Euler-Cauchy equations, Applications to engineering problems, System of
linear ODEs with constant coefficients.

Module 3: (10 Lecture hours)

Gamma function, Beta function: Properties and evaluation of integrals.
Laplace transform, Necessary condition for existence, General properties, Inverse Laplace transform,
Transforms of derivatives and integrals, Differentiation and Integration of transform, Unit-step function,
Shifting theorems, Transforms of periodic functions, Convolution, Solution of differential equations and
integral equations using Laplace transform.
References:
1. E. Kreyszig, Advanced Engineering Mathematics, 10th edition, New Delhi, India: Wiley , 2015.
2. G. Strang, Introduction to Linear Algebra, Wellesley MA: Cambridge Press, 2016.
3. R. P. Agarwal and D. O Regan, An Introduction to Ordinary Differential Equations, New York: Springer, 2008.
4. V. I. Arnold, Ordinary Differential Equations, New York: Springer, 2006.
5. P. Dyke, An Introduction to Laplace Transforms and Fourier Series, New York: Springer,2014.

For complete syllabus here is the attachment

NIT Calicut B.Tech First Year syllabus








Contact-

National Institute of Technology, Calicut, Kerala
Calicut Mukkam Road, Kattangal, Kerala 673601
0495 228 6106