Determinant of a square matrix - Minors and cofactors – Procedures for evaluation Properties of determinants (no deduction) Evaluation of determinant by Ohio's method (4th order) - Problems.
Concept of vector -Addition and subtraction of vectors - Multiplication of a vector by a scalar - Position vector of a point - Ratio formula - Rectangular resolution of a vector - Dot and cross product - Geometrical interpretation - Distributive law -Applications.
Introduction to numerical integration - Formulae for composite trapezoidal and Simpson's 1/3 rule (no deduction) Related problems
Numerical solution of non-linear equations - Formula for Newton-Raphson method (no deduction) - Problems.
Numerical solution of system of linear equation - Gauss-Elimination Method (no deduction) - Problems.
Homogeneous differential equations - Equations reducible to the homogeneous form - Problems.
functions - Euler's theorem on homogeneous functions (no deduction) - Problems.
Exact differential equations - equations reducible to the exact form - problems Linear equations - Bernoulli's equations.
Differential equations of 2nd order with constant co-efficients - Complementary function and particular integral - Problems.
Measure of central tendency - Mean - Median - Mode - Standard deviation - Simple problems
Basic Principle of: Storage cell, DC. motors, Transformer, A.C. generators & motors (No deduction & problems).
Various components of computer (brief knowledge)
Hardware-CPU, inputs output system, primary memory, secondary memory.
Peripherals devices - Printers, plotter, scanners, digitals cameras, web cam sound card & systems, dicta phone speaker
Software Operating system, system software like compilers and device drivers, and various application software (definitions only).
Conversion of number systems, signed and unsigned representation
Binary arithmetic & compliments
Character codes : ASCII. BCD & Gray codes
Basic concepts of compilers, interpreters, assemblers and device drives
Operating system - Single user, multi user, graphical user interfaces and characters user
Case studies : MS-DOS, Windows interfaces.
Different types of programming languages - machine level, assembly level and high-level(concepts only)
Brief introduction to different high-level languages including C
Basics of C-Language
Branching and loping statements
Arrays and user-defined functions languages
Client - Server architecture (elementary level)
Internetworking concepts of World Wide Web, domain name system emails
Web browsing, use of search engines, web site hosting (elementary level)
Methods of finding out centroids of simple area by :(i) Geometrical consideration and (ii) Method of Moments. [** Method of integration should be learnt in Strength of materials on 2nd Semester]
Finding the centroid of the following areas by any method :(i) uniform triangular lamina, (ii) uniform rectangular lamina, (iii) uniform circular lamina
6.3 Finding the centriod of the following sections using the method of moment:(i) T-section, (ii) equal and unequal angle-sections, (iii) equal and unequal l-sections, (iv) different cut-out sections as shown in the following figures.
MI of a lamina
Theorems of finding out M I by :(i) Parallel axis theorem, and, (ii) Perpendicular axis theorem.
Radius of Gyration
Finding out M I of the following sections using formula only.(i) rectangular section, (ii) Square section , (iii) circular section, (iv) triangular section
M I of irregular areas such as l-sections, T-sections, - Related simple problems.
Newton's Second Law of linear motion P - mf (deduction) -Conservation of momentum of a body -No Numerical problems
Engineering materials: Definitions and examples
Definition and Types of beams, supports and loads.
Problems on bending stress about axis parallel to the plane of bending For rectangular circular & l – section.
Differential equation of elastic curve — Relation among deflection, slope, shear force, bending moment and rate of loading — Sign convention of slope and deflection
Standard formula (no proof, only simple problems) for maximum slope of deflection of (a) cantilever beam subjected to point load at free end, uniformly distributed load en entire span; (b) simply supported beam carrying a point load at mid span, uniformly distributed toad on entire span.
Stress and strain Tensile, Compressive, Shear
Stress-strain diagram: Principles of tensile testing m universal testing machine's showing salient points such as elastic limit, proportional limit, yield points, breaking points etc., ultimate stress, working stress and factor of safety.
Stress - Strain relations: Hooke's law, Young's Modulus, Modulus of rigidity, Poission's ratio.
Shear force and bending moment diagrams (with simple problems): (i) Cantilever beams with point loads and Uniformly Distributed Loads (UDL); (ii) Simply supported beams with point loads and UDL. (iii) Simply supported overhanging beam with point load
Types of Stresses: Tensile Stress and Compressive Stress.
Elastic Limit — Hook's' Law — Modulus of Elasticity (Young's Modulus) Deformation of a body due to Force acting on it — Simple problems.
Principle of Superposition — Simple problems on uniform cross-section.
Belt & pulley drive Different types belt and pulley drive — Open belt drive and cross belt drive. Types of belt and types of pulley — Velocity ratio. Simple problems.
Mott Theory chemistry of photographic development fixing photographic reduction and chemistry intensification, chemical reversal, elementary idea of silverless films.