IV Semester Bridge Course for Diploma Students

BASIC MATHEMATICS - II

(Common to all branches of Engineering)

(Audit Course)

Subject: Basic Mathematics - II Subject Code: MATDIP401

Hours / week: 3 Total hours: 40

COURSE CONTENTS:

PART A
Unit 1 / Differential Equations-I: Solution of first order first degree differential equations- Variable separable methods, Homogeneous Equations, Exact differential equations Illustrative examples from engineering field. (Without I.F direct problems). / (5 hours)
Unit 2 / Differential Equations-II: Linear & Bernoulli’s differential equations, Illustrative examples from engineering field. / (5 hours)
PART B
Unit 3 / Differential Equations-III: Solution of second and higher order equations with constant coefficient by inverse differential operator method,,, , (Simple problems). Illustrative examples from engineering field. / (5 hours)
Unit 4 / Laplace Transforms-I: Definitions, Laplace transforms of elementary functions, Laplace transforms of derivatives and integrals (without proof), illustrative examples. / (5 hours)
PART C
Unit 5 / Laplace Transforms-II: Periodic functions, Unit step function, Unit impulse function, Illustrative examples from engineering field. / (5 hours)
Unit 6 / Laplace Transforms-III: Inverse transforms simple problems, Applications of Laplace transforms to differential equations. Illustrative examples from engineering field. / (5 hours)
PART D
Unit 7 / Vector Algebra: vector addition, Multiplication (Dot and Cross product), Triple products, vector differentiation, velocity, acceleration of a vector point function, Gradient, divergence, curl / (5 hours)
UNIT 8 / Vector integration – Evaluation of Line integrals, surface integrals and volume integrals simple problems, Statement of Green’s theorem, Stokes theorem and Gauss Divergence theorem, Illustrative examples from engineering field. / (5 hours)
Note - Theorems and properties without proof. Applicable to all the units.
TEXT BOOK:
  1. Dr. B. S. Grewal, Higher Engineering Mathematics, Khanna Publications,
40 thedition (2007).
  1. Erwin Kreyezig, Advanced Engineering Mathematics, Tata McGraw Hill
Publications, 8th edition (2007).