CREDIT HOURS

Theory = 3
Practical = 0

COURSE LEARNING OUTCOMES (CLOs)

 S. No. CLOs PLO Taxonomy 1 Discuss numerical differentiation, numerical integration, and complex variable PLO-2 Coginitive Level 2* 2 Discuss numerical differentiation, numerical integration, and complex variable PLO-1 Coginitive Level 3* 3 Apply numerical differentiation and numerical integration in relevant engineering problems PLO-2 Coginitive Level 3*

COURSE CONTENT

• Function of Complex Variable: Limit, continuity, zeros and poles of a complex function, Laplace equation and Cauchy-Reimann equation, conformal transformation, contour integration.
• Error Analysis: Types of errors (relative, Absolute, inherent, round off, truncation), significant digits and numerical instability, flow chart. Use any Computational tools to Analysis the Numerical Solutions.
• Finite Difference: Functions of operators, difference operators and the derivative operators, identities, linear homogeneous and non-homogeneous difference equations.
• Interpolation & Curve Fitting: Interpolating polynomials for equal space and unequal space data, Newton’s Forward difference and backward difference interpolation, Lagrange’s, Newton, Hermit, Spline, least squares approximation, (Linear and non-linear curve), with numerical problem in engineering,
• Numerical Differentiation: Forward Difference Method, Backward Difference Method, Central Difference Method,
• Numerical Integration: Computation of integrals using simple Trapezoidal rule, Simpson’s rule 1/3rd , Simpson’s 3/8th rule, Composite Simpson’s and Trapezoidal rules, computation of solutions of differential equations using (Euler method, Euler modified method, Runge Kutta method of order 4). Special types of integration: Improper Integrals Definitions, Types of improper integral and their convergence.
• Elliptic Integration: Introduction and identification of elementary elliptic integrals of first, second and third kinds, Simple applications

RECOMMENDED BOOKS

(01) Complex Analysis for Mathematics and Engineering by John H. Mathews

(02) Advance Engineering Mathematics by Erwin Kreyszig

(03) Applied Numerical Analysis by Gerald

(04) Calculus & Analytical Geometry Howard Anton