Engineering Mathematics I
Course Content and Outline
Unit I: Complex Numbers (10
Definition – Conjugates - Algebra of complex numbers
(geometrical proof not needed) – Real and Imaginary parts. Simple Problems.
Polar form of complex number – Modulus and amplitude form multiplication and
division of complex numbers in polar form. Simple Problems Argand plane –
Collinear points, four points forming square, rectangle, rhombus. Simple problems.
Demoivre’s Theorem (statement only) – simple problems. Demoivre’s Theorem
II: Infinite Series & Fourier series
Convergence, divergence and oscillation of an infinite
series, comparison Test, Pseries, D’Alembert’s ratio test, Raabe’s test,
Cauchy’s root test, Cauchy’s integral test (All tests without proof) for series
of positive terms. Alternating series. Absolute and conditional convergence,
Leibnitz’s test (without proof)
Euler's formula, Conditions (Dirichlet's) for a Fourier expansion, Functions
having points of discontinuity, Change of interval, Odd and even periodic
functions, Expansion of odd and even periodic functions, Half‐range series, Typical wave‐forms, Parseval's formula, Practical harmonic analysis
and Applications to Problems in Engineering.
Unit III: Vector
Vector addition & subtraction, Resolution of vectors, combination of two
periodic waveforms, plotting periodic functions, determining resultant phasors
by calculation.Arithmetic with scalars and vectors, unit vectors. Dot product
of two vectors (scalar& vector products). Reciprocal System of vectors. Application
of vectors: Lines and planes. Derivatives – Velocity and acceleration. Divergence
and curl operations. Find tangent and normal vectors (to a curve or surface).
How to apply Divergence and Green's theorems
subtraction &multiplication, their properties.The transpose of a
matrix.Special matrices. Minors, the adjoint of matrix, the inverse of a
matrix,2 × 2 and 3 × 3 determinants, properties, Cramers’s rule. Consistency of
a system of linear equations.
of Linear Systems (10
Homogeneous and Non-homogeneous systems, Gaussian elimination& Gauss-Jordan
elimination, Null Space and Range, Rank and nullity, Consistency conditions in
terms of rank, General Solution of a linear system, Elementary Row and Column
operations, Row Reduced Form& Row Reduced Echelon Form, Triangular Matrix
Factorization and Transition Matrices.
criterion, the diagonalizing matrix, Cayley-Hamilton theorem, Annihilating
polynomials, Minimal Polynomial, Diagonalizability and Minimal polynomial,
Projections & Decomposition of the matrix in terms of projections.
of Matrices (4
Linear Programming, Network models, Game Theory & Control Theory.
least a question MUST be set from each unit. Seven questions MUST be set from
which five questions are attempted by the students.
MODE OF DELIVERY
Whiteboard and Markers