Courses Catalogue

Engineering Mathematics I

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

Course Content and Outline

CONTENT

 

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 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) for series 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, Halfrange series, Typical waveforms, Parseval's formula, Practical harmonic analysis and Applications to Problems in Engineering.

 

Unit III: Vector calculus                                                                                        (10 Hours)

Introduction, 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

 

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

INSTRUCTIONAL MATERIALS

·        Whiteboard and Markers

·        Flip Charts