Engineering Mathematics-I | Syllabus | College Platform - NITH
Mathematics & Scientific ComputingMA-111
MA-111Core Course
Engineering Mathematics-I
4 Credits
5 Modules
Updated 12/31/2024
01
Matrix Algebra
6 Lectures
Matrices Related matrices Complex matrices (Hermitian and skew-Hermitian matrices Unitary matrix) Rank of
a matrix Gauss-Jordan method Normal form of a matrix Linear dependence and independence of vectors
Consistency of linear system of equations Solution of linear system of equations
Characteristic equation
Eigen
values
Eigen vectors
Properties of eigen values
Cayley-Hamilton theorem and its applications
Reduction to
diagonal form
Quadratic form and their reduction to canonical form.
02
Differential Calculus
9 Lectures
Review of Limits Continuity and Differentiability Mean Value Theorem Partial Differentiation and its geometrical
interpretation Homogeneous functions Euler’s theorem and its extension Total differentials Composite function
Jacobian Taylor’s and Maclaurin’s infinite series Indeterminate forms Errors and increments Maxima and
minima of functions of two variables Method of undetermined multipliers. Curve tracing.
03
Integral Calculus
6 Lectures
Double Integrals (Cartesian and Polar) Change of Order of Integration Change of Variables Applications of
Double Integrals.
Triple integrals Change of Variables Applications of Triple Integrals.
Beta and Gamma functions.
04
Vector Calculus
9 Lectures
Differentiation of vectors Curves in space Velocity and acceleration Relative velocity and acceleration Scalar
and vector point functions Vector Operator ‘Del’ - Del Applied to Scalar Point Functions (Gradient) and its
Geometrical Interpretation - Directional Derivative Del Applied to Vector Point Function (Divergence and Curl)
and their Physical Interpretation Del Applied Twice to Point Function Del Applied to Products of Point Functions.
Integration of Vector Tangential Line Integral Normal Surface Integral Volume integrals Theorems of Green
Stokes and Gauss (without proofs) and their verifications and applications Irrotational Fields Solenoidal Fields.
05
Fourier Series
6 Lectures
Euler’s formula Dirichlet’s Conditions Functions Having Points of Discontinuity Change of interval Expansion of
odd and even periodic functions Half-range series Typical wave-forms Parseval’s formula Practical harmonic
analysis
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