ENGINEERING MATHEMATICS (M1)
About M1 : This course is mostly continuation of the concepts you learned in class 12th but the focus is shifted towards the application part of concepts. So easy if compared with M-II and M-III. But the learning methodology includes regular practice of the concepts. To equip students with techniques to understand advanced level mathematics and its application part.
Examination Scheme
In-Semester Exam :30 Marks
End-Semester Exam :70 Marks
Team Work (TW) :25 Marks
Unit I
Differential Calculus
Rolle’s Theorem, Mean Value Theorems, Taylor’s Series and Maclaurin’s Series, Expansion of
functions using standard expansions, Indeterminate Forms, L’ Hospital’s Rule, Evaluation of
Limits and Applications.
Unit II
Fourier Series
Definition, Dirichlet’s conditions, Full range Fourier series, Half range Fourier series,
Harmonic analysis, Parseval’s identity and Applications to problems in Engineering.
Unit III
Partial Differentiation
Introduction to functions of several variables, Partial Derivatives, Euler’s Theorem on
Homogeneous functions, Partial derivative of Composite Function, Total Derivative, Change
of Independent variables.
Unit IV
Applications of Partial Differentiation
Jacobian and its applications, Errors and Approximations, Maxima and Minima of functions
of two variables, Lagrange’s method of undetermined multipliers.
Unit V
Linear Algebra-Matrices, System of Linear Equations
Rank of a Matrix, System of Linear Equations, Linear Dependence and Independence, Linear
and Orthogonal Transformations, Application to problems in Engineering.
Unit VI: Linear Algebra-Eigen Values and Eigen Vectors, Diagonaliztion
Eigen Values and Eigen Vectors, Cayley Hamilton theorem, Diagonaliztion of a matrix,
Reduction of Quadratic forms to Canonical form by Linear and Orthogonal transformations.
ENGINEERING MATHEMATICS (M2)
About : If you are able to understand the concepts of M-I, the concepts of M-II will be easier to understand as it is the continuation but on advance level. The learning methodology includes rigorous practice of the concepts. To equip students with techniques to understand the mathematical models of physical system.
Examination Scheme
In-Semester Exam :30 Marks
End-Semester Exam :70 Marks
Team Work (TW) :25 Marks
Unit I: First Order Ordinary Differential Equations
Exact differential equations, Equations reducible to exact form. Linear differential equations,
Equations reducible to linear form, Bernoulli’s equation.
Unit II: Applications of Differential Equations
Applications of Differential Equations to Orthogonal Trajectories, Newton’s Law of Cooling,
Kirchhoff’s Law of Electrical Circuits, Rectilinear Motion, Simple Harmonic Motion, One
dimensional Conduction of Heat.
Unit III: Integral Calculus
Reduction Formulae, Beta and Gamma functions, Differentiation Under Integral Sign and Error
functions.
Unit IV: Curve Tracing
Tracing of Curves – Cartesian, Polar and Parametric curves, Rectification of curves.
Unit V: Solid Geometry
Cartesian, Spherical polar and cylindrical coordinate systems, Sphere, Cone and Cylinder.
Unit VI: Multiple Integrals and their Applications
Double and Triple integrations, change of order of integration, Applications to find Area,
Volume, Mass, Centre of Gravity and Moment of Inertia.
ENGINEERING MATHEMATICS (M3)
(Second Year of Electronics / E & Tc Engineering)
About M3: This is also application based and has different syllabus for different branches. The learning methodology includes lots and lots of practice of the concepts. To equip students with techniques to understand the advance level mathematics and its application that would enhance analytical thinking in their core area.
Examination Scheme
In-Semester Exam :30 Marks
End-Semester Exam :70 Marks
Team Work (TW) :25 Marks
Unit I: Linear Differential Equations (LDE) and Applications
LDE of nth order with constant coefficients, Complementary Function, Particular Integral,
General method, Short methods, Method of variation of parameters, Cauchy’s and Legendre’s
DE, Simultaneous and Symmetric simultaneous DE. Modeling of Electrical circuits.
Unit II: Transforms Fourier Transform (FT):
Complex exponential form of Fourier series, Fourier integral theorem,
Fourier Sine & Cosine integrals, Fourier transform, Fourier Sine and Cosine transforms and
their inverses. Z – Transform (ZT): Introduction, Definition, Standard properties, ZT of
standard sequences and their inverses. Solution of difference equations.
Unit III: Numerical Methods
Interpolation: Finite Differences, Newton’s and Lagrange’s Interpolation formulae, Numerical
Differentiation. Numerical Integration: Trapezoidal and Simpson’s rules, Bound of truncation
error, Solution of Ordinary differential equations: Euler’s, Modified Euler’s, Runge-Kutta 4th
order methods and Predictor-Corrector methods.
Unit IV: Vector Differential Calculus
Physical interpretation of Vector differentiation, Vector differential operator, Gradient,
Divergence and Curl, Directional derivative, Solenoidal, Irrotational and Conservative fields,
Scalar potential, Vector identities.
Unit V: Vector Integral Calculus & Applications
Line, Surface and Volume integrals, Work-done, Green’s Lemma, Gauss’s Divergence theorem,
Stoke’s theorem. Applications to problems in Electro-magnetic fields.
Unit: VI Complex Variables
Functions of a Complex variable, Analytic functions, Cauchy-Riemann equations, Conformal
mapping, Bilinear transformation, Cauchy’s integral theorem, Cauchy’s integral formula and
Residue theorem.
Unit VI : Complex Variables
Functions of a Complex variable, Analytic functions, Cauchy-Riemann equations, Conformal
mapping, Bilinear transformation, Cauchy’s integral theorem, Cauchy’s integral formula and
Residue theorem.
Operations Research (OR)
About Operations Research (OR): Operations Research is a multidisciplinary field that applies mathematical and analytical methods to help organizations make better decisions. Operations Research and Engineering combines two disciplines focused on the operation of complex systems. To equip students to learn statistically rooted frameworks to model and solve systems-level engineering problems. This also helps them for optimum utilization of resources in the organization.
Examination Scheme
In-Semester Exam :30 Marks
End-Semester Exam :70 Marks
Team Work (TW) :25 Marks
Unit I: Introduction of Operations Research
Introduction to operations research and optimization techniques, applications of operations
research in civil engineering, introduction to linear and non-linear programming methods,
formulation of linear optimization models for civil engineering applications (objective
function, constraints), graphical solutions to L P problems, local & global optima, unimodal
function, convex and concave function.
Unit II: Stochastic Programming
Sequencing: n jobs through 2, 3 and M machines, queuing theory: elements of queuing system
and its operating characteristics, waiting time and ideal time costs, Kendall‘s notation,
classification of Queuing models, single channel Queuing theory: Model I (Single channel
Poisson Arrival with exponential services times, Infinite population (M/M/1): (FCFS/ /),
simulation: Monte Carlo simulation.
Unit III: Linear programming
The transportation model and its variants, assignment model and its variants
Unit IV: Linear programming
The simplex method, method of big M, two phase method, duality
Unit V: Nonlinear programming
Single variable unconstrained optimization: sequential search techniques-dichotomous,
Fibonacci, golden section, multivariable optimization without constraints: the gradient vector
and hessian matrix, gradient techniques, steepest ascent/decent technique, Newton’s Method,
Multivariable optimization with equality constraints: Lagrange multiplier technique
Unit VI: Dynamic programming, Games Theory and Replacement Model
Dynamic programming: multi stage decision processes, principle of optimality, recursive
equation, applications, Games theory: 2 persons games theory, various definitions, application
of games theory, replacement of items whose maintenance and repair cost increase with time
ignoring time value of money
Discrete Mathematics(DM)
About this course: This course combines part of logic, computer science, operation research and statistical techniques. The learning methodology includes providing students with some tools to understand these concepts better. To equip students with techniques to understand the application of mathematical concepts in computer core.
Examination Scheme
In-Semester Exam :30 Marks
End-Semester Exam :70 Marks
Team Work (TW) :25 Marks
Unit I: Set Theory and Logic
Introduction and significance of Discrete Mathematics, Sets– Naïve Set Theory (Cantorian Set
Theory), Axiomatic Set Theory, Set Operations, Cardinality of set, Principle of inclusion and
exclusion. Types of Sets – Bounded and Unbounded Sets, Diagonalization Argument,
Countable and Uncountable Sets, Finite and Infinite Sets, Countably Infinite and Uncountably
Infinite Sets, Power set, Propositional Logic- logic, Propositional Equivalences, Application of
Propositional LogicTranslating English Sentences, Proof by Mathematical Induction and
Strong Mathematical Induction
Unit II: Relations and Functions
Relations and their Properties, n-ary relations and their applications, Representing relations ,
Closures of relations, Equivalence relations, Partial orderings, Partitions, Hasse diagram,
Lattices, Chains and Anti-Chains, Transitive closure and Warshall‘s algorithm. Functions-
Surjective, Injective and Bijective functions, Identity function, Partial function, Invertible
function, Constant function, Inverse functions and Compositions of functions, The Pigeonhole
Principle.
Unit III: Counting Principles
The Basics of Counting, rule of Sum and Product, Permutations and Combinations, Binomial
Coefficients and Identities, Generalized Permutations and Combinations, Algorithms for
generating Permutations and Combinations.
Unit IV: Graph Theory
Graph Terminology and Special Types of Graphs, Representing Graphs and Graph
Isomorphism, Connectivity, Euler and Hamilton Paths, the handshaking lemma, Single source
shortest path Dijkstra’s Algorithm, Planar Graphs, Graph Colouring
Unit V: Trees
Introduction, properties of trees, Binary search tree, tree traversal, decision tree, prefix codes
and Huffman coding, cut sets, Spanning Trees and Minimum Spanning Tree, Kruskal‘s and
Prim‘s algorithms, The Max flow- Min Cut Theorem (Transport network).
Unit VI: Algebraic Structures and Coding Theory
The structure of algebra, Algebraic Systems, Semi Groups, Monoids, Groups, Homomorphism
and Normal Subgroups, and Congruence relations, Rings, Integral Domains and Fields, Coding
theory, Polynomial Rings and polynomial Codes, Galois Theory –Field Theory and Group
Theory.
