## Course Detail

 Course Name Mathematics for Intelligent Systems 2 Course Code 19MAT117 Program B. Tech. in Computer Science and Engineering (Artificial Intelligence) Semester 2 Year Taught 2019

### Syllabus

Gaussian elimination, LU decomposition. Vector Spaces , Bases, Orthogonal bases Infinite dimensional vector spaces Fourier Series and Fourier Transform and its properties Convolution Vector spaces associated with Matrices Projection matrices and its properties Cayley Hamilton theorem Diagonalizability of matrices Eigenvalues and Eigenvectors of Symmetric matrices Eigenvalues and Eigen vectors of ATA, AAT Relationship between vector spaces associated with A, ATA, AAT. Formulation of ordinary differential equation with constant coefficients in various engineering domains, Converting higher order into first order equations Numerical solution with Rungekutta method. Taylor series expansion of multivariate functions, conditions for maxima , minima and saddle points, Concept of gradient and hessian matrices Multivariate regression and regularized regression , Newton methods for optimization, Signal processing with regularized regression. Random variables and distributions, Expectation, variance , moments cumulants, Sampling from univariate distribution- various methods, Concept of Jacobian and its use in finding pdf of functions of Random variables(RVs), boxmuller formula for sampling normal distribution, Concept of correlation and Covariance of two linearly related RVs, Multivariate Gaussian distribution, Bayes theorem, Introduction to Bayesian estimation process, Markov chain, Markov decision process.

### Objectives and Outcomes

Course Objectives

The course will lay down the basic concepts and techniques of linear algebras applied to signal processing. It will explore the concepts initially through computational experiments and then try to understand the concepts/theory behind it. At the same time, it will provide an appreciation of the wide application of these disciplines within the scientific field. Another goal of the course is to provide connection between the concepts of linear algebra, differential equation and probability theory.

Course Outcomes

 CO1 To develop an understanding of the basic concepts and techniques of linear algebra as applied to signal processing. CO2 To provide an appreciation of these disciplines within the scientific field. CO3 To provide connection between the concepts of linear algebra, differential equation and probability theory. CO4 To develop an insight into the applicability of linear algebra in business and scientific domains. CO5 To enable the students to understand the use of calculus and Linear algebra in modelling electrical and mechanical elements. CO6 To equip the students to understand the role of probability theory in providing data sets for computational experiments in data science.

 PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12 CO1 3 3 2 2 3 3 2 3 3 CO2 3 3 3 3 3 2 3 2 3 3 CO3 3 2 3 3 3 3 2 3 3 CO4 3 3 3 2 3 3 2 3 3 CO5 3 2 3 3 3 3 2 3 3 CO6 3 3 3 3 3 2 3 2 3 3

Course Evaluation Pattern:

Internal – 75%

• Assignments – 50% (20 assignments with equal credit)
• Quiz- 25% (5 Quizzes with equal credit)

External – 25%

• Project – 25%

### Text Books / References

1. Gilbert Strang, Linear Algebra and Learning from Data, Wellesley, Cambridge press, 2019.
2. William Flannery, “Mathematical Modeling and Computational Calculus”, Vol-1, Berkeley Science Books, 2013.

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