BMATS201 Mathematics for CSE Stream

BMATS201 Mathematics for CSE Stream

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Module - 1

Integral Calculus

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.

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Module - 2

Vector Calculus

Introduction to Vector Calculus in Computer Science & Engineering. Scalar and vector fields. Gradient, directional derivative, curl and divergence – physical interpretation, solenoidal and irrotational vector fields. Problems.

Curvilinear coordinates:Scale factors, base vectors, Cylindrical polar coordinates, Spherical polar coordinates, transformation between cartesian and curvilinear systems, orthogonality. Problems.

Self-Study: Vector integration and Vector line integral. 

Applications: Conservation of laws, Electrostatics, Analysis of streamlines

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Module - 3

Vector Space and Linear Transformations

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 dependent sets, Basis and dimension. Problems.

Linear transformations: Definition and examples, Algebra of transformations, Matrix of a linear transformation. 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.

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Module - 4

Numerical Methods -1

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 without proof). Problems.

Numerical integration: Trapezoidal, Simpson’s (1/3)rd and (3/8)th rules(without proof). Problems.

Self-Study: Bisection method, Lagrange’s inverse Interpolation.

Applications: Estimating the approximate roots, extremum values, Area, volume, and surface area. Errors in finite precision

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Module - 5

Numerical Methods – 2

Introduction to various numerical techniques for handling Computer Science & Engineering applications. Numerical Solution of Ordinary Differential Equations (ODE’s): Numerical solution of ordinary differential equations of first order and first degree – Taylor’s series method, Modified Euler’s method, Runge-Kutta method of fourth order and Milne’s predictor-corrector formula (No derivations of formulae). Problems.

Self-Study: Adam-Bashforth method. 

Applications: Estimating the approximate solutions of ODE.

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  133. After I originally commented I appear to have clicked on the -Notify me when new comments are added- checkbox and from now on every time a comment is added I get 4 emails with the same comment. Perhaps there is an easy method you are able to remove me from that service? Thanks.

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  147. May I just say what a comfort to discover somebody who actually understands what they’re discussing on the net. You definitely understand how to bring a problem to light and make it important. A lot more people should read this and understand this side of your story. I was surprised that you aren’t more popular given that you certainly have the gift.

  148. Hello there! I could have sworn I’ve been to this site before but after looking at many of the articles I realized it’s new to me. Anyways, I’m certainly happy I discovered it and I’ll be bookmarking it and checking back often!

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  162. Can I simply just say what a comfort to uncover someone that actually understands what they are discussing on the web. You actually understand how to bring a problem to light and make it important. More and more people have to read this and understand this side of your story. It’s surprising you aren’t more popular because you surely possess the gift.

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  165. Oh my goodness! Incredible article dude! Thanks, However I am having issues with your RSS. I don’t understand the reason why I cannot join it. Is there anybody getting identical RSS issues? Anybody who knows the solution will you kindly respond? Thanx!

  166. Nice post. I learn something new and challenging on sites I stumbleupon on a daily basis. It will always be interesting to read through articles from other writers and practice something from other sites.

  167. An interesting discussion is definitely worth comment. I do think that you should publish more about this subject matter, it might not be a taboo matter but usually people do not speak about these issues. To the next! Cheers!

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