Other university all, Electrical & Electronics Engineering , Engineering Mathematics - III Syllabus

207005: Engineering Mathematics - III

Credit 04 + 01 = 05

Unit I Linear Differential Equations (LDE) and Applications
LDE of nth order with constant coefficients, Complementary Function, Particular Integral, General method,
Short methods, Method of variation of parameters, Cauchy‟s and Legendre‟s DE, Simultaneous and
Symmetric simultaneous DE. Modeling of Electrical circuits.

Mapping of Course Outcomes for Unit I CO1: Solve higher order linear differential equation using appropriate techniques for modelling, analyzing of electrical circuits and control systems.

Unit II Transforms 
Fourier Transform (FT): Complex exponential form of Fourier series, Fourier integral theorem, Fourier
Sine & Cosine integrals, Fourier transform, Fourier Sine and Cosine transforms and their inverses.
Z - Transform (ZT): Introduction, Definition, Standard properties, ZT of standard sequences and their
inverses. Solution of difference equations.
Mapping of Course Outcomes for Unit II CO2: Apply concept of Fourier transform & Z-transform and its applications to continuous & discrete systems, signal & image processing and communication systems.

Unit III Numerical Methods
Interpolation: Finite Differences, Newton‟s and Lagrange‟s Interpolation formulae, Numerical
Differentiation.
Numerical Integration: Trapezoidal and Simpson‟s rules, Bound of truncation error,
Solution of Ordinary differential equations: Euler‟s, Modified Euler‟s, Runge-Kutta 4th order methods and Predictor-Corrector methods.
Mapping of Course
Outcomes for Unit III CO3: Obtain Interpolating polynomials, numerically differentiate and integrate functions, numerical solutions of differential equations using single step and multi-step iterative methods used in modern scientific computing.

Unit IV Vector Differential Calculus 
Physical interpretation of Vector differentiation, Vector differential operator, Gradient, Divergence and
Curl, Directional derivative, Solenoidal, Irrotational and Conservative fields, Scalar potential, Vector
identities.
Mapping of Course Outcomes for Unit IV CO4: Perform vector differentiation & integration, analyze the vector fields and apply to electro- magnetic fields & wave theory.

Unit V Vector Integral Calculus & Applications 
Line, Surface and Volume integrals, Work-done, Green‟s Lemma, Gauss‟s Divergence theorem, Stoke‟s
theorem. Applications to problems in Electro-magnetic fields.
Mapping of Course Outcomes for Unit V CO4: Perform vector differentiation & integration, analyze the vector fields and apply to electro- magnetic fields & wave theory.

Unit VI Complex Variables 
Functions of a Complex variable, Analytic functions, Cauchy-Riemann equations, Conformal mapping,
Bilinear transformation, Cauchy‟s integral theorem, Cauchy‟s integral formula and Residue theorem.

Mapping of Course Outcomes for Unit VI CO5: Analyze Complex functions, Conformal mappings, Contour
integration applicable to electrostatics, digital filters, signal and image processing.

Learning Resources

Text Books:
1. B.V. Ramana, “Higher Engineering Mathematics”, Tata McGraw Hill.
2. B.S. Grewal, “Higher Engineering Mathematics”, Khanna Publication, New Delhi.
Reference Books:
1. Erwin Kreyszig, “Advanced Engineering Mathematics”, Wiley India,10th Edition.
2. M.D. Greenberg, “Advanced Engineering Mathematics”, Pearson Education, 2nd Edition.
3. Peter. V and O‟Neil, “Advanced Engineering Mathematics”, Cengage Learning,7th Edition.

4. S.L. Ross, “Differential Equations”, Wiley India, 3rd Edition.

5. S. C. Chapra and R. P. Canale, “Numerical Methods for Engineers”, McGraw-Hill, 7th Edition.
6. J. W. Brown and R. V. Churchill, “Complex Variables and Applications”, McGraw-Hill Inc, 8thEdition.