Introduction to Integral Calculus in Computer Science &Engineering.
Multiple Integrals: Evaluation of double and triple integrals, evaluation of double integrals by
change of order of integration, changing into polar coordinates. Applications to find Area and
Volume by double integral.Problems.
Beta and Gamma functions: Definitions, properties, relation between Beta and Gamma functions.
Problems.
Self-Study: Center of gravity, Duplication formula.
Applications: Antenna and wave propagation, Calculation of optimum value in various geometries.
Analysis of probabilistic models.
Importance of Vector Space and Linear Transformations in the field of Computer Science &
Engineering.
Vector spaces: Definition and examples, subspace, linear span, Linearly independent and dependentsets, Basis and dimension. Problems.
Linear transformations: Definition and examples, Algebra of transformations, Matrix of a lineartransformation. Change of coordinates, Rank and nullity of a linear operator, rank-nullity theorem.Inner product spaces and orthogonality. Problems.
Self-study: Angles and Projections.Rotation, Reflection, Contraction and Expansion.
Applications: Image processing, AI & ML, Graphs and networks, Computer graphics
Importance of numerical methods for discrete data in the field of computer science &
engineering.
Solution of algebraic and transcendental equations - Regula-Falsi and Newton-Raphson methods(only formulae). Problems.Finite differences, Interpolation using Newton’s forward and backward difference formulae,Newton’s divided difference formula and Lagrange’s interpolation formula (All formulae withoutproof). Problems.
Numerical integration: Trapezoidal, Simpson's (1/3)rd and (3/8)th rules(without proof). Problems.
Introduction to various numerical techniques for handling Computer Science & Engineering
applications.
Numerical Solution of Ordinary Differential Equations (ODE’s): Numerical solution of ordinarydifferential equations of first order and first degree - Taylor’s series method, Modified Euler’smethod, Runge-Kutta method of fourth order and Milne’s predictor-corrector formula (No
