Course Objectives: To learn
Types of matrices and their properties.
Concept of a rank of the matrix and applying this concept to know the consistency and solving
the system of linear equations.
Concept of Eigen values and eigenvectors and to reduce the quadratic form to canonical form.
Concept of Sequence.
Concept of nature of the series.
Geometrical approach to the mean value theorems and their application to the mathematical problems
Evaluation of surface areas and volumes of revolutions of curves.
Evaluation of improper integrals using Beta and Gamma functions.
Partial differentiation, concept of total derivative
Finding maxima and minima of function of two and three variables. Course Outcomes: After learning the contents of this paper the student must be able to
Write the matrix representation of a set of linear equations and to analyse the solution of the system of equations
Find the Eigen values and Eigen vectors
Reduce the quadratic form to canonical form using orthogonal transformations.
Analyse the nature of sequence and series.
Solve the applications on the mean value theorems.
Evaluate the improper integrals using Beta and Gamma functions
Find the extreme values of functions of two variables with/ without constraints. UNIT – I: Matrices
Matrices: Types of Matrices, Symmetric; Hermitian; Skew-symmetric; Skew-Hermitian; orthogonal matrices; Unitary Matrices; rank of a matrix by Echelon form and Normal form, Inverse of Non-singular matrices by Gauss-Jordan method; System of linear equations; solving system of Homogeneous and Non-Homogeneous equations. Gauss elimination method; Gauss Seidel Iteration Method. UNIT – II: Eigen values and Eigen vectors
Linear Transformation and Orthogonal Transformation: Eigen values and Eigenvectors and their properties: Diagonalization of a matrix; Cayley-Hamilton Theorem (without proof); finding inverse and power of a matrix by Cayley-Hamilton Theorem; Quadratic forms and Nature of the Quadratic Forms;Reduction of Quadratic form to canonical forms by Orthogonal Transformation UNIT – III: Sequences & Series
Sequence: Definition of a Sequence, limit; Convergent, Divergent and Oscillatory sequences.Series: Convergent, Divergent and Oscillatory Series; Series of positive terms; Comparison test, p-test,D-Alembert’s ratio test; Raabe’s test; Cauchy’s Integral test; Cauchy’s root test; logarithmic test.Alternating series: Leibnitz test; Alternating Convergent series: Absolute and Conditionally
Convergence. UNIT – IV: Calculus
Mean value theorems: Rolle’s theorem, Lagrange’s Mean value theorem with their Geometrical Interpretation and applications, Cauchy’s Mean value Theorem. Taylor’s Series. Applications of definite integrals to evaluate surface areas and volumes of revolutions of curves (Only in Cartesian coordinates), Definition of Improper Integral: Beta and Gamma functions and their applications. UNIT – V: Multivariable calculus (Partial Differentiation and applications)
Definitions of Limit and continuity.Partial Differentiation; Euler’s Theorem; Total derivative; Jacobian; Functional dependence &independence, Maxima and minima of functions of two variables and three variables using method of
Lagrange multipliers. TEXT BOOKS:
1. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 36th Edition, 2010
2. Erwin kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons, 2006.
3. G.B. Thomas and R.L. Finney, Calculus and Analytic geometry, 9th Edition, Pearson, Reprint,
2002. REFERENCE BOOKS:
1. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, Laxmi Publications,
Reprint, 2008.
2. Ramana B.V., Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th Reprint,
2010.
CSE-AIML
SEMESTER
SUBJECT CODE
SUBJECT
Lession Plan Lecturer Notes & Question Bank
SYLLABUS
I
MA101BS
Mathematics – I
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I
AP102BS
Applied Physics
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I
CS103ES
Programming for Problem Solving
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I
ME104ES
Engineering Graphics
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I
AP105BS
Applied Physics Lab
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I
CS106ES
Programming for Problem Solving Lab
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I
MC109ES
Environmental Science
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II
MA201BS
Mathematics – II
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II
CH202BS
Chemistry
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II
EE203ES
Basic Electrical Engineering
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II
ME205ES
Engineering Workshop
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II
EN205HS
English
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II
CH206BS
Engineering Chemistry Lab
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II
EN207HS
English Language and Communication Skills Lab
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II
EE208ES
Basic Electrical Engineering Lab
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II-I
CS310PC
Discrete Mathematics
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II-I
CS302PC
Data Structures
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II-I
MA313BS
Mathematical and Statistical Foundations
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II-I
CS304PC
Computer Organization and Architecture
II-I
CS311PC
Python Programming
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II-I
SM306MS
Business Economics & Financial Analysis
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II-I
CS307PC
Data Structures Lab
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II-I
CS312PC
Python Programming Lab
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II-I
MC309
Gender Sensitization Lab
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II-II
CS416PC
Formal Language and Automata Theory
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II-II
CS417PC
Software Engineering
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II-II
CS403PC
Operating Systems
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II-II
CS404PC
Database Management Systems
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II-II
CS412PC
Object Oriented Programming using Java
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II-II
CS406PC
Operating Systems Lab
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II-II
CS407PC
Database Management Systems Lab
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II-II
CS408PC
Java Programming Lab
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II-II
MC409
Constitution of India
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III-I
Design and Analysis of Algorithms
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III-I
Machine Learning
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III-I
Computer Networks
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III-I
Compiler Design
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III-I
Graph Theory (PE1)
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III-I
Introduction to Data Science(PE1)
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III-I
Web Programming(PE1)
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III-I
Image Processing(PE1)
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III-I
Computer Graphics(PE1)
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III-I
Software Testing Methodologies(PE2)
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III-I
Information Retrieval Systems(PE2)
III-I
Pattern Recognition(PE2)
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III-I
Computer Vision and Robotics(PE2)
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III-I
Data Warehousing and Business Intelligence(PE2)
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III-I
Machine Learning Lab
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III-I
Computer Networks Lab
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III-I
Advanced Communication Skills Lab
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III-I
Intellectual Property Rights
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III-II
Artificial Intelligence
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III-II
DevOps
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III-II
Natural Language Processing
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III-II
Internet of Things(PE3)
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III-II
Data Mining(PE3)
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III-II
Scripting Languages(PE3)
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III-II
Mobile Application Development(PE3)
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III-II
Cryptography and Network Security(PE3)
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III-II
Artificial Intelligence and Natural Language
Processing Lab
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