__MT-441 ADVANCED MATHEMATICAL TECHNIQUES__

__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 |

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:**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.__Error Analysis:__Functions of operators, difference operators and the derivative operators, identities, linear homogeneous and non-homogeneous difference equations.**Finite Difference:**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,__Interpolation & Curve Fitting:__Forward Difference Method, Backward Difference Method, Central Difference Method,__Numerical Differentiation:__Computation of integrals using simple Trapezoidal rule, Simpson’s rule 1/3__Numerical Integration:__^{rd}, Simpson’s 3/8^{th}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.Introduction and identification of elementary elliptic integrals of first, second and third kinds, Simple applications__Elliptic Integration:__

**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*

*For details of Taxonomy Levels **CLICK HERE!**