 # ECE Maths Syllabus as per 2020 : The Easy explanation for Exams

ECE Maths Syllabus as per 2020 Simple and Short according to the New Education  Policy. ECE Maths Syllabus as per 2020 Simple and Short According to the All-University Syllabus

Course Code: MTH-S101

## Course Name: Mathematics-I (ECE Maths Syllabus as per 2020 Simple and Short)

Course Details:

Unit I

Applications of Integrals: Areas between curves, Methods of finding volume: Slicing, Solids of revolution, Cylindrical shell, Lengths of plane curves, Areas of the surface of revolution, Moments and Center of mass, Improper integrals.

Unit II

Sequences: Definition, Monotonic sequences, Bounded sequences, Convergent and Divergent Sequences. Series: Infinite series, Oscillating and Geometric series, their Convergence, Divergence. Tests of Convergence: nth Term test of divergence, Integral test, Comparison Test, Limit Comparison Test, Ratio test, nth root test (Cauchy root test), Alternating series, Absolute and Conditional convergence. Power Series: Power series and its convergence, Radius and the interval of convergence, Term by term differentiation, Term by term integration, Product of power series, Taylor and Maclaurin series, The convergence of Taylor series, Error estimates, Taylor’s Theorem with the remainder.

Unit III

Vector Calculus: Vector-valued functions, Arc length, and Unit Tangent vector, Curvature, Torsion and TNB frame. Partial Derivatives: Function of two or more variables (Limit, Continuity, Differentiability, Taylors Theorem , Partial derivatives, Chain Rule, Partial Derivatives of higher orders, Maxima and Minima and Saddle Point, Lagrange Multipliers, Exact differential, Leibniz Theorem. Directional derivatives, Gradient Vectors, Divergence, and Curl, Tangent planes.

Unit IV

Multiple Integrals: Double and triple integrals, Change of order, Jacobian, Change of variables, Application to area and volume, Dirichlet integral, and Applications. Line, surface integrals, Path independence, Statement, and problems of Green’s, Stoke’s, and Gauss divergence theorems (without proof).

Text Books and Reference :

1. G.B.Thomas and R.L.Finney: Calculus and Analytical Geometry, 9th edition,

Pearson Education

Also read this-Engineering mathematics books for Gate

Course Code: MTH-S102

### Course Name: Mathematics-II (ECE Maths Syllabus as per 2020 Simple and Short)

Course Details:

Unit-I

Linear Algebra

Matrices, Elementary row, and Column operations, Echelon form, Determinants, Rank of matrix, Vector spaces, Linear dependence, and Independence, Linear transforms and matrices, Consistency of linear system of equations and their solution, Special Matrices: Symmetric, Hermitian, etc, Characteristic equation, Cayley-Hamilton theorem(statement only), Eigenvalues and Eigenvectors, Diagonalization.

Unit-II (ECE Maths Syllabus as per 2020 Simple and Short)

Differential Equations: Separable, Exact Differential Equation, Integrating Factors, Linear differential equations with constant coefficients, Homogeneous Linear differential equations, Bernoulli Equation, Simultaneous linear differential equations, Clairaut’s equation, Homogeneous linear differential equations of second-order with constant coefficients, Complex root case, Differential operators, Euler-Cauchy-equation,Wronskian, Nonhomogeneous equations, Solution by undetermined coefficients, solution by variation of parameters. Series solution: Ordinary differential equations of 2nd order with variable coefficients (Frobenius Method).

Unit-III: Laplace Transform

Laplace transform, Existence Theorem, Laplace transform of derivatives and integrals, Inverse Laplace

transform, Unit step function, Dirac Delta function, Laplace transform of periodic functions, Convolution

Theorem, Applications to solve simple linear and simultaneous differential equations.

Text Books and Reference :

1. E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 2005.

3. C. Ray Wylie & Louis C. Barrett, Advanced Engineering Mathematics, Tata McGraw-Hill Publishing

Company Ltd. 2003.

4. G.F. Simmons, Differential Equations, Tata McGraw-Hill Publishing Company Ltd. 1981.. Course Code: MTH-S201

#### Course Name: Mathematics – III (ECE Maths Syllabus as per 2020 Simple and Short)

Course Details:

Unit – I: Function of a Complex variable

Complex numbers- power and roots, limits, continuity, and a derivative of functions of a complex

variable, Analytic functions, Cauchy-Reimann equations, Harmonic function, Harmonic conjugate of

analytic function and methods of finding it, Complex Exponential, Trigonometric, Hyperbolic and

Logarithm function.

Unit – II: Complex Integration

Line integral in the complex plane(definite and indefinite), Cauchy’s Integral Theorem, Cauchy’s Integral the formula, Derivatives of analytic functions, Cauchy’s Inequality, Liouville’s theorem, Morera’s theorem, Power series representation of analytic function and radius of convergence, Taylor’s and Laurent’s series, singularities, Residue theorem, evaluation of real integrals, Improper Integrals of rational functions, Fourier integrals.

Unit – III: Fourier Series

Periodic functions, Trigonometric series, Fourier series of period 2π, Euler’s formulae, Functions having

arbitrary period, Change of the interval, Even and odd functions, Half range sine and cosine series, Complex

Fourier series.

Unit – IV: Partial Differential Equations

Linear partial differential equations with constant coefficients of second-order and their classifications – parabolic, elliptic, and hyperbolic with illustrative examples. Methods of finding solutions using the separation of variables method. Wave and Heat equations up to two-dimension (finite length)

Unit – V: Probability and Statistics

Basics of probability, Bayes theorem, Random variables, Probability, and density functions, Binomial,

Poisson and Normal distributions.

Text Books and Reference :

1. E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 2005.

2. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 2005

Course Code: MTH-S301

##### Course Name: Discrete Mathematics

Course Details:

Unit-I

Logic: Introduction to formal logic, Formulae of prepositional logic, Truth tables, Tautology, Satisfiability,

Contradiction, Normal, and principle normal forms, Completeness. Theory of inference. Predicate calculus:

Quantifiers, Inference Theory of predicate logic, Validity, Consistency and Completeness.

Unit-II

Sets, Operations on sets, Ordered pairs, Recursive definitions, Relations and Functions, Equivalence

relations, Composition of relations, Closures, Partially ordered sets, Hasse Diagrams,

Lattices ( Definition and some properties ).

Unit-III

Algebraic Structures: Definition, Semigroups, Groups, Subgroups, Abelian groups, Cyclic groups.

Unit-IV

Graph Theory: Incidence, Degrees, Walks, Paths, Circuits, Characterization theorems, Connectedness, Euler

graphs, Hamiltonian graphs, Travelling salesman problem, Shortest distance algorithm (Dijkstra’s), Trees,

Binary trees, Spanning trees, Spanning tree algorithms Kruskal’s and Prim’s.

Unit-V

Introduction to Combinatorics: Counting techniques, pigeon-hole the principle, Mathematical induction, Strong induction, Permutations, and Combination.

Unit-VI

Generating functions, Recurrence relations, and their solutions.

Text Books and Reference :

1. C.L.Liu: Discrete Mathematics

2. B.Kolman, R.C.Busby, and S.C.Ross, Discrete mathematical structures, 5/e, Prentice Hall, 2004

3. J.L.Mott, A.Kandel and T.P.Baker: Discrete mathematical structures For computer scientists &

Mathematicians, Prentice–Hall India

4. J.P.Trembley, R. Manohar, Discrete mathematical structures with applications to computer science,

McGraw –Hill, Inc. New York, NY,1975