1st and 2nd Sem Engineering Mathematics 2022 scheme M1 and M2 VTU University 2nd SEM 1st SEM & 2nd SEM physics/Chemistry Cycle | BMATE101/BMATE201 notes

Scheme & Syllabus Copy of 1st and 2nd Sem Engineering Mathematics 2022 scheme M1 and M2

Syllabus copy 1st and 2nd Sem Engineering Mathematics 2022 scheme M1 and M2 BMATE101/BMATE201

Module-1:Calculus (8 hours)

Introduction to polar coordinates and curvature relating to Computer Science and Engineering. Polar coordinates, Polar curves, angle between the radius vector and the tangent, angle between two curves. Pedal equations. Curvature and Radius of curvature - Cartesian, Parametric, Polar and Pedal forms. Problems. Self-study: Center and circle of curvature, evolutes and involutes. Applications: Computer graphics, Image processing. (RBT Levels: L1, L2 and L3)

Module-2:Series Expansion and Multivariable Calculus (8 hours) 

Introduction of series expansion and partial differentiation in Computer Science & Engineering applications. Taylor’s and Maclaurin’s series expansion for one variable (Statement only) – problems. Indeterminate forms - L’Hospital’s rule-Problems. Partial differentiation, total derivative - differentiation of composite functions. Jacobian and problems. Maxima and minima for a function of two variables. Problems. Self-study: Euler’s theorem and problems. Method of Lagrange’s undetermined multipliers with single constraint. Applications: Series expansion in computer programming, Computing errors and approximations. (RBT Levels: L1, L2 and L3)

Module-3: Ordinary Differential Equations (ODEs) of First Order (8 hours)

Introduction to first-order ordinary differential equations pertaining to the applications for Computer Science & Engineering. Linear and Bernoulli’s differential equations. Exact and reducible to exact differential equations - Integrating factors on 1 ? ( ?? ?? − ?? ??) ??? 1 ? ( ?? ?? − ?? ??). Orthogonal trajectories, L-R & C-R circuits. Problems. Non-linear differential equations: Introduction to general and singular solutions, Solvable for p only, Clairaut’s equations,reducible to Clairaut’s equations. Problems. Self-Study: Applications of ODEs, Solvable for x and y. Applications of ordinary differential equations: Rate of Growth or Decay, Conduction of heat. (RBT Levels: L1, L2 and L3)

Module-4: Modular Arithmetic (8 hours)

Introduction of modular arithmetic and its applications in Computer Science and Engineering. Introduction to Congruences, Linear Congruences, The Remainder theorem, Solving Polynomials, Linear Diophantine Equation, System of Linear Congruences, Euler’s Theorem, Wilson Theorem and Fermat’s little theorem. Applications of Congruences-RSA algorithm. Self-Study: Divisibility, GCD, Properties of Prime Numbers, Fundamental theorem of Arithmetic. Applications: Cryptography, encoding and decoding, RSA applications in public key encryption. (RBT Levels: L1, L2 and L3)

Module-5: Linear Algebra (8 hours)

Introduction of linear algebra related to Computer Science &Engineering. Elementary row transformationofa matrix, Rank of a matrix. Consistency and Solution of system of linear equations - Gauss-elimination method, Gauss-Jordan method and approximate solution by Gauss-Seidel method. Eigenvalues and Eigenvectors, Rayleigh’s power method to find the dominant Eigenvalue and Eigenvector. Self-Study: Solution of system of equations by Gauss-Jacobi iterative method. Inverse of a square matrix by Cayley- Hamilton theorem. Applications: Boolean matrix, Network Analysis, Markov Analysis, Critical point of a network system. Optimum solution. (RBT Levels: L1, L2 and L3).