Courses Catalogue

Engineering Mathematics I

COURSE CODE: MAT1211
COURSE CREDIT UNIT: 4
ACADEMIC PROGRAMME: Mechanical Engineering, Bsc
COLLEGE/SCHOOL/FACULTY: School of Engineering and Applied Sciences
STATUS: Core
PROGRAMME TYPE: Undergraduate

Course Content and Outline



Unit I: Complex Numbers            (10 Hours)

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 a square, rectangle, rhombus. Simple Problems. Demoivre’s Theorem (statement only) – simple problems. Demoivre’s Theorem related problems.

Unit II: Infinite Series & Fourier series

Infinite Series                                             (7 Hours)

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) forseries of positive terms. Alternating series. Absolute and conditional convergence, Leibnitz’s test (without proof)

Fourier series                                                        (7 Hours)

Definition,  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.

Uni III: Vector Calculus              (10 Hours)

Introduction, Vector addition &  subtraction, Resolution of  vectors,  combination of  two

perodic   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

Unit IV: Matrices

Introductions:                                            (7 Hours)

Addition, 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.

Solutions of Linear Systems                     (10 Hours)

Simple  systems,  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.

Transition matrices

Diagonalizable Matrices                           (5 Hours)

Diagonalization criterion, the diagonalizing matrix, Cayley-Hamilton theorem, Annihilating

polynomials, Minimal Polynomial, Diagonalizability and Minimal polynomial, Projections & Decomposition of the matrix in terms of projections.

Applications of Matrices               (4 Hours)

Optimization and Linear Programming, Network models, Game Theory & Control Theory.

At 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

  •   Lectures
  •    Reading assignments
  •    Practical assignments

INSTRUCTIONAL MATERIALS

  •   Whiteboard and Markers
  •   Flip Charts