B.Tech Computer Science & Engineering · Sem 2 (Core) · B.Tech Information Technology · Sem 2 (Core) · B.Tech Artificial Intelligence & Machine Learning · Sem 2 (Core) · B.Tech Artificial Intelligence & Data Science · Sem 2 (Core) · B.Tech CSE (Artificial Intelligence) · Sem 2 (Core) · B.Tech CSE (AI & ML) · Sem 2 (Core) · B.Tech CSE (Data Science) · Sem 2 (Core) · B.Tech CSE (Cyber Security) · Sem 2 (Core) · B.Tech CSE (Internet of Things) · Sem 2 (Core) · B.Tech Computer Science & Design · Sem 2 (Core) · B.Tech Computer Science (Hindi) · Sem 2 (Core) · B.Tech Computer Science & Business Systems · Sem 2 (Core) · B.Tech Cyber Security · Sem 2 (Core) · B.Tech Data Science · Sem 2 (Core)
Linear differential equation of nth order with constant coefficients, Cauchy- Euler equation, solution of second order linear differential equations with variable coefficient by the method of variation of parameters, change of independent variable, normal form. Applications: Cloud Computing, Computer Networks, Cyber Security
Functions of Complex Variables, Limit Continuity and Differentiability, Analytic Function, Cauchy-Riemann Equations (Cartesian and Polar Form), Harmonic Function, Milne- Thomson Method, Complex integrals, Cauchy- Integral theorem (without proof), Cauchy integral formula (without proof), Taylor’s series and Laurent’s series, Singularities, Residue of a function, Cauchy Residue Theorem, Evaluating the Real definite integrals. Applications: Image Processing and Computer Design, Quantum Computing
Laplace Transform: Definition of Laplace Transform, Existence Conditions, Linearity Property, Laplace Transform of some standard functions, I and II Shifting theorems (without proof), Change of Scale Property, Laplace transform of derivatives and integrals, Periodic Functions, Unit Step Function, Inverse Laplace Transform, Partial Fraction Method, Convolution theorem (without proof), Application of Laplace transform to solve ordinary differential equation. Applications: Database Systems, Algorithmic Modelling
Periodic function, even and odd function, Dirichlet’s Condition for the Existence of a Fourier Series, Fourier series expansion of a function in the interval c to c+2l,Change of Interval, Half Range Series: Half range sine and cosine series in the interval -l to l, Parseval’s Identity. Fourier Integral theorem, Fourier transform, Inverse Fourier Transform, Finite Fourier Sin and Cosine transform. Applications: Computer Graphics, Cyber Security, Digital Image Processing, Machine Learning Feature Extraction, Image compression.
Applied Linear Algebra: Eigen Value Decomposition and Singular Value Decomposition, Matrix factorization, LU Decomposition (Dolittle method), QR Decomposition, Linear transformation, Matrix representation of Linear Transformation, Kernel and Range, Introduction to inner product space, Norm of a vector. Application: 2D & 3D graphics, Neural Networks, Cryptography
After completion of the course student will be able to:
This subject is on page 17, 18, 19, 20, 21 of the original AKTU PDF.
