Eng. Maths – III

207003 ENGINEERING MATHEMATICS – III (2008 Course)
Teaching Scheme: Examination Scheme:
Lectures: 4 hrs./week Paper: 100 marks
Duration: 3 hrs.
SECTION I
Unit I: Linear Differential Equations (LDE) (09 Hours)
Solution of nth order LDE with Constant Coefficients, Method of Variation of Parameters, Cauchy’s &
Legendre’s DE, Solution of Simultaneous & Symmetric Simultaneous DE, Modeling of Electrical
Circuits.
Unit II: Complex Variables (09 Hours)
Functions of Complex Variables, Analytic Functions, C-R Equations, Conformal Mapping, Bilinear
Transformation, Cauchy’s Theorem, Cauchy’s Integral Formula, Laurent’s Series, Residue Theorem
Unit III: Transforms (09 Hours)
Fourier Transform (FT): Complex Exponential Form of Fourier Series, Fourier Integral Theorem, Sine
& Cosine Integrals, Fourier Transform, Fourier Sine and Cosine Transform and their Inverses,
Application to Wave Equation.
Introductory Z-Transform (ZT): Definition, Standard Properties, ZT of Standard Sequences and their
Inverses. Solution of Simple Difference Equations.
SECTION II
Unit IV: Statistics and Probability (09 Hours)
Measures of Central Tendency, Standard Deviation, Coefficient of Variation, Moments, Skewness and
Kurtosis, Correlation and Regression, Reliability of Regression Estimates
Theorems and Properties of Probability, Probability Density Function, Probability Distributions:
Binomial, Poisson, Normal and Hypergometric; Test of Hypothesis: Chi-Square test.
Unit V: Vector Differential Calculus (09 Hours)
Physical Interpretation of Vector Differentiation, Vector Differential Operator, Gradient, Divergence
and Curl, Directional Derivative, Solenoidal, Irrotational and Conservative Fields, Scalar Potential,
Vector Identities.
Unit VI: Vector Integral Calculus (09 Hours)
Line, Surface and Volume integrals, Work-done, Green’s Lemma, Gauss’s Divergence Theorem,
Stoke’s Theorem, Applications to Problems in Electro-Magnetic Fields.
Text Books:
1. Advanced Engineering Mathematics by Peter V. O'Neil (Cengage Learning).
2. Advanced Engineering Mathematics by Erwin Kreyszig (Wiley Eastern Ltd.).
Reference Books:
1. Engineering Mathematics by B.V. Raman (Tata McGraw-Hill).
2. Advanced Engineering Mathematics, 2e, by M. D. Greenberg (Pearson Education).
3. Advanced Engineering Mathematics, Wylie C.R. & Barrett L.C. (McGraw-Hill, Inc.)
4. Higher Engineering Mathematics by B. S. Grewal (Khanna Publication, Delhi).
5. Applied Mathematics (Volumes I and II) by P. N. Wartikar & J. N. Wartikar
(Pune Vidyarthi Griha Prakashan, Pune).
6. Advanced Engineering Mathematics with MATLAB, 2e, by Thomas L. Harman, James Dabney
and Norman Richert (Brooks/Cole, Thomson Learning).