Syllabus
SYLLABUS PRESCRIBED FOR
FOUR YEAR DEGREE COURSE IN
B.E./ B.TEXT. E./B.TECH. (CHEM.ENGG.)/B.TECH. (CHEM. TECH.)
POLYMER (PLASTIC) TECH.
SEMESTER-I / II “GROUP A”
I A 1 ENGINEERING MATHEMATICS-I
Aim :
The course is aimed at developing the basic Mathematical skills of engineering students that are
imperative for effective understanding of engineering subjects. The topics introduced will serve as basic
tools for specialized studies in many fields of engineering and technology.
Objectives :
On completion of the course the students are expected:
-to identify algebraic problems from practical areas and obtain the solutions in certain cases
-to understand maxima and minima concept.
-to solve differential equations of certain types, including systems of differential equations that they might
encounter in the same or higher semesters.
-to understand double and triple integration and enable them to handle integrals of higher orders.
SECTION-A
Unit I : Successive differentiation, Leibnitz's theorem on the nth derivative of a product, Expansion of a
function by using Taylor's theorem and Maclaurin's theorem, Indeterminate forms. (10)
Unit II: Partial differentiation, total differential coefficients, exact differential, Euler's theorem on
homogeneous function, Transformation of independent variables. (10)
Unit III : Jacobians of explicit functions and implicit function with properties, functional dependence,
Maxima and Minima of a function of two independent variables, Maxima and Minima of a
function of several independent connected variables by Lagrange's method of undetermined
multipliers. (10)
SECTION-B
Unit IV : Complex Numbers : Demoiver's theorem and its applications, Hyperbolic and inverse
hyperbolic functions, separation of real and imaginary parts, Logarithm of complex numbers.
(10)
Unit V : Ordinary differential equations of first order and first degree in various forms;
(Variable separable, linear differential equation, homogeneous differential equation, exact
differential equation) and reducible to above forms, methods of substitution. (10)
Unit VI : Solution of differential equation of first order and higher degree by various methods.
application of differential equations of first order and first degree to the problems on orthogonal
trajectories and electrical engineering. (10)
TEXT BOOK :-
(1) Wartikar P.N. & Wartikar J.N.- A Text Book of Applied Mathematics, Vol.-I, & II, Pune V.G.
Prakashan, Pune.
REFERENCE BOOKS :-
1) Grewal B.S. - Higher Engineering Mathematics, 40/e, Khanna Publishers.
2) Kreyszig E.K. - Advanced Engineering Mathematics, John Wiley.
3) Ramana B.V. - Higher Engineering Mathematics, (TMH)
4) Singh R.R. & Bhatt M. - Engineering Mathematics, (TMH)
SYLLABUS PRESCRIBED FOR
FOUR YEAR DEGREE COURSE IN
B.E./ B.TEXT. E./B.TECH. (CHEM.ENGG.)/B.TECH. (CHEM. TECH.)
POLYMER (PLASTIC) TECH.
SEMESTER-I / II “GROUP B”
I B 1 ENGINEERING MATHEMATICS-II
Aim :
The course is aimed at developing the basic Mathematical skills of engineering students that are
imperative for effective understanding of engineering subjects. The topics introduced will serve as basic
tools for specialized studies in many fields of engineering and technology.
Objectives :
On completion of the course the students are expected:
-Solution of simultaneous equations by matrix method
-Fourier series
-to know the basics of vector calculus comprising of gradient, divergence & curl and line, surface
-to grasp the basics of complex integration and the concept of contour integration which is important for
evaluation of certain integrals encountered in practice
SECTION-A
Unit I: Matrices : Inverse of matrix by adjoint method, Inverse of matrix by partitioning, Rank of a
matrix, solution of simultaneous equations by matrix method, Eigen values and Eigen vectors,
Cayley-Hamilton theorem (without proof)
(10)
Unit II: Fourier series: Periodic function, Fourier expansion of periodic function in (C, C+2L), even and
odd functions, half range Fourier series, Harmonic Analysis. (10)
Unit III: (a) Scalar Triple Product, vector triple product and their properties, multiple products.
(b) Rule of differentiation under integral sign.
(c) Tracing of curves in Cartesian, polar and parametric forms. (10)
SECTION-B
Unit IV: Reduction formulae, Beta and Gamma function, Rectification. (10)
Unit V: Double integration, change of order of integration, transformation to polar coordinates,
Evaluation of area by double integration (10)
Unit VI: Triple integration, transformation to spherical polar coordinates, volume of solid by triple
integration. Mean and RMS values. (10)
TEXT BOOK :-
(1) Wartikar P.N. & Wartikar J.N.- A Text Book of Applied Mathematics, Vol.-I, & II, Pune V.G.
Prakashan, Pune.
REFERENCE BOOKS :-
1) Grewal B.S. - Higher Engineering Mathematics, 40/e, Khanna Publishers.
2) Kreyszig E.K. - Advanced Engineering Mathematics, John Wiley.
3) Ramana B.V. - Higher Engineering Mathematics, (TMH)
4) Singh R.R. & Bhatt M. - Engineering Mathematics, (TMH)
SYLLABUS PRESCRIBED FOR FOUR YEAR DEGREE COURSE
IN BACHELOR OF ENGINEERING MECHANICAL ENGINEERING
SEMESTER PATTERN (CREDIT GRADE SYSTEM) SEMESTER : THIRD 3ME01
MATHEMATICS-III
Section-A
UNIT-I : Ordinary differential equations:- Complete solution, Operator D, Rules for finding complementary function, the inverse operator, Rules for finding the particular integral, Method of variations of parameters, Cauchy’s and Legendre’s linear differential equations. (10 Hrs)
UNIT-II Laplace transforms : Definition, standard forms, properties of Laplace transform, inverse Laplace transform, initial and final value theorem, convolution theorem, Laplace transform of impulse function, Unit step function, Laplace transforms of periodic function. Solution of Linear differential equations. (10 Hrs.)
UNIT-IIIa) Partial differential equation of first order of following form- (i) f (p,q)=0; (ii) f (p,q,z)=0; (iii)f (x,p)=g(y,q); (iv) Pp+Qq=R (Lagranges form); (v) z=px+qy+f (p,q) (Clairaut form) b) Statistics : Curve fitting by method of least squares (Straight and parabola only), Correlation, Regression. c) Probability Distribution:– Binomial distribution, Poisson and normal Distribution. (10 Hrs.)
Section-B
UNIT-IV Complex Analysis :- Functions of complex variables, Analytic function, Cauchy-Reimann conditions, Harmonic function, Harmonic conjugate functions, Milne’s method, conformal mappings (translation, rotation, magnification, inversion, bilinear transformation), singular points, expansion of function in Tayler’s and Laurent’s series. Cauchy’s integral theorem and formula, Residue theorem. (12 Hrs.)
UNIT-V Numerical Analysis : Solution of algebric and transcendental equations by Newton-Raphson method & method of false position. Solution of system of linear equations by GaussSeidal method, Relaxation method. Solution of first order ordinary differential equations by Picard’s, modified Euler’s, Runge-Kutta and Taylor’s method. (10 Hrs.)
UNIT-VI Vector Calculus :- Scalar and vector point functions, Differentiation of vectors, Gradient of a scalar point function, Directional derivatives, Divergence and curl of a vector point function and their physical meaning, line, surface, volume integrals, irrotational and solenoidal vector fields, Stoke’s and Divergence theorem (without proof). (10 Hrs.)
Books Recommended:- Text Books: 1. Text book on Applied Engineering Mathematics, Vol. II, J.N. Wartikar and P.N. Wartikar, Pune Vidyarthi Griha Prakashan, Pune. 2. Higher Engineering Mathematics, B.S Grewal, Himalaya Publishing House. 3. Applied Mathematics, Vol. III, J.N. Wartikar and P.N. Wartikar, Pune Vidyarthi Griha Prakashan, Pune. Reference Book : 1. Advanced Engineering Mathematics, Erwin Kreyzig, John Wiley
SYLLABUS PRESCRIBED FOR FOUR YEAE B.E. DEGREE COURSE
IN ELECTRICAL ENGINEERING (ELECTRONICS & POWER) / ELECTRICAL & ELECTRONICS ENGINEERING / ELECTRICAL ENGINEERING (ELECTRICAL & POWER) / ELECTRICAL ENGINEERING
SEMESTER PATTERN (CREDIT GRADE SYSTEM) THIRD SEMESTER :
MATHEMATICS-III
SECTION-A
UNIT-I: Ordinary differential equations:- Completer solution, Operator D,Rules for finding complementary function, the inverse oprator, Rules for finding the particular integral, Method of variations of parameters, Cauchy’s and Legendre’s linear differential equations. Simultaneous linear differential equations with constant co-efficient, Applications to electrical circuits.
UNIT-II : Laplace transforms: definition, standard forms, properties of Laplace transform, inverse Laplace transform, initial and final value theorem, Convolution theorem, Laplace transform of impulse function, Unit step function, Laplace transforms of periodic function.
UNIT-III : a) Application of L.T. to linear differential equations with constant coefficients & Simultaneous linear differential equations. b) Fourier transforms- Definition, standard forms, inverse Fourier transform, Properties of Fourier transforms, Convolution theorem, Fourier sine and Fourier cosine transforms and integrals.
SECTION-B
UNIT-IV : a) Difference equation:- solution of difference equations of first order, Solution of difference equations of higher order with constant co-efficients. b) Z-transform: Definition, standard forms, Z-transform of impulse function, Unit step functions, Properties of Ztransforms (Linearity, shifting, multiplication by k, change of scale), initial and final values, inverse Z-transforms (by direct division and partial fraction), Solution of difference equation by Z-transforms.
UNIT-V : Vector calculus: Scalar and vector point functions, Differentiation of vectors, Curves in space,Gradient of a scalar point function, and their physical meaning, expansion formulae (without proof).
UNIT-VI : Line,surface,volume integrals, irrotational and solenoidal vector fields, Stoke’s and Divergence theorem (without proof).
BOOKS RECOMMENDED:-
1) Advanced Engineering Mathematics, 3 edi – Potter, Oxford University Press, 2008
2) Mathematical Techniques – Jordan and Smith 4/e – Oxford University Press, 2008
3) A Mathematical Companion for Science and Engineering Students – Brettenbach, Oxford University Press, 2008
4) Elements of Applied Mathematics by P.N.Wartikar and J.N.Wartikar 5) Advancing Engg. Mathematics by E.K.Kreyzig.
SYLLABUS PRESCRIBED FOR FOUR YEAR DEGREE COURSE
IN BACHELOR OF ENGINEERING COMPUTER SCIENCE & ENGINEERING / COMPUTER ENGINEERING SEMESTER PATTERN (CREDIT GRADE SYSTEM)
SEMESTER : THIRD 3KS01/3KE01
MATHEMATICS – III
SECTION-A
UNIT-I: Ordinary differential equations:- Complete solution, Operator D, Rules for finding complementary function, the inverse operator, Rules for finding the particular integral, Method of variations of parameters, Cauchy’s and Legendre’s linear differential equations.
UNIT-II: Laplace transforms:- definition, standard forms, properties of Laplace transform, inverse Laplace transform, initial and final value theorem, convolution theorem, Laplace transform of impulse function, Unit step function, Laplace transforms of periodic function Solution of Linear differential equations, Simultaneous differential equation by Laplace transform method.
UNIT-III: a) Difference equation:- solution of difference equations of first order Solution of difference equations of higher order with constant co-efficients b) Z-transform:- Definition, standard forms, Z-transform of impulse function, Unit step functions, Properties of Z transforms (linearity, shifting, multiplication by k, change of scale), initial and final values, inverse Ztransforms (by direct division and partial fraction), Solution of difference equation by Z-transforms.
SECTION-B
UNIT-IV: a) Fourier transforms:- Definition, standard forms, inverse Fourier trnasforms, properties of Fourier transforms, convolution theorem, Fourier sine and Fourier cosine transforms and integrals. b) Partial differential equation of first order of following form:- (i) f (p,q)=0; (ii) f (p,q,z)=0; (iii) f (x,p)=g (y,q); (iv) Pp+Qq=R (Lagranges Form); (v) Z=px+qy+f(p,q) (Clairaut form)
UNIT-V: Complex Analysis :- Functions of complex variables, Analytic function, Cauchy-Reimann conditions, Harmonic function, Harmonic conjugate functions, Milne’s method conformal mappings (translation, rotation, magnification and bilineartransformation),singular points, expansion of function in Taylor’s and Laurent’s series.
UNIT –VI: Vector calculus:- Scalar and vector point functions, Differentiation of vectors, Curves in space, Gradient of a scalar point function, Directional derivatives, Divergence and curl of a vector point function and their physical meaning, expansion formulae (with out proof), line, surface, volume integrals, irrotational and solenoidal vetor fields.
BOOKS RECOMMENDED:-
1) Elements of Applied Mathematics by P.N.Wartikar and J.N.Wartikar
2) A Text Book of Differential Calculas by Gorakh Prasad.
3) Engg. Mathematics by Chandrika prasad.
4) Advancing Engg. Mathematics by E.K.Kreyzig.
5) A Text Book of Applied Mathematics by P.N.Wartikar and J.N.Wartikar. 6) Higher Engg. Mathematics by B.S.Grewal.
7) Control System by Gopal and Nagrath.
8) Integral transforms by Goyal & Gupta.
SECTION-A
UNIT-I: Ordinary differential equations:- Complete solution, Operator D, Rules for finding complementary function, the inverse operator, Rules for finding the particular integral, Method of variations of parameters, Cauchy’s and Legendre’s linear differential equations.
UNIT-II: Laplace transforms:- definition, standard forms, properties of Laplace transform, inverse Laplace transform, initial and final value theorem, convolution theorem, Laplace transform of impulse function, Unit step function, Laplace transforms of periodic function Solution of Linear differential equations, Simultaneous differential equation by Laplace transform method.
UNIT-III: a) Difference equation:-solution of difference equations of first order Solution of difference equations of higher order with constant coefficients, b) Z-transform:- Definition, standard forms, Z-transform of impulse function, Unit step functions, Properties of Z transforms (linearity, shifting, multiplication by k, change of scale), initial and final values, inverse Z-transforms (by direct division and partial fraction), Solution of difference equation by Z-transforms.
SECTION-B
UNIT-IV: a) Fourier transforms:- Definition, standard forms, inverse Fourier transforms, properties of Fourier transforms, convolution theorem, Fourier sine and Fourier cosine transforms and integrals. b) Partial differential equation of first order of following form:- (i) f (p, q)=0; (ii)f (p, q, z)=0; (iii) f (x, p)=g (y, q); (iv) Pp + Qq = R (Lagranges Form); (v) Z = px+qy+f (p,q) (Clairaut form) UNIT-V: Complex Analysis :- Functions of complex variables, Analytic function, Cauchy-Reimann conditions, Harmonic function, Harmonic conjugate functions, Milne’s method conformal mappings (translation, rotation, magnification and bilineartransformation),singular points, expansion of function in Taylor’s and Laurent’s series.
UNIT –VI: Vector calculus:- Scalar and vector point functions, Differentiation of vectors, Curves in space, Gradient of a scalar point function, Directional derivatives, Divergence and curl of a vector point function and their physical meaning, expansion formulae (with out proof), line, surface, volume integrals, irrotational and solenoidal vetor fields.
BOOKS RECOMMENDED:-
1) Elements of Applied Mathematics, Vol. II by P.N.Wartikar and J.N.Wartikar
2) Applied Mathematics, Vol. III, J.N. Wartikar and P.N. Wartikar, Pune Vidyarthi Griha Prakashan, Pune. 3) Advancing Engg. Mathematics by E.K.Kreyzig.
4) A Text Book of Applied Mathematics by P.N.Wartikar and J.N.Wartikar.
5) Higher Engg. Mathematics by B.S.Grewal.
6) Control System by Gopal and Nagrath.
7) Integral Transforms by Goyal & Gupta.
MATHEMATICS-III
SECTION-A
UNIT –I: Ordinary differential equations:- Complete solution, Operator D, Rules for finding complementary function, the inverse operator, Rules for finding the particular integral, Method of variations of parameters, Cauchy’s and Legendre’s linear differential equations. (7 Hrs.)
UNIT-II: Laplace transforms:Definition, standard forms, properties of Laplacetransform,Inverse Laplace transform, Laplace convolution theorem,Laplace transforms and Unit step function, Solution of Linear differential equations. (7 Hrs.)
UNIT-III: Probability & Probability Distribution Probability: definition, axioms of mathematical probability, complementation rule,Theorem of total probability, Theorem of compound probability, Independent Events, subjective probability, Baye’s Theorem, Probability Distribution:– Binomial distribution, Poisson and normal Distribution. (7 Hrs.)
SECTION-B
UNIT-IV: Complex Analysis :-Functions of complex variables, Analytic function, Cauchy-Reimann conditions, Harmonic conjugate functions, Milne’s method, singular points, expansion of function in Taylor’s and Laurent’s series, Cauchy’s integral theorem and formula,Residue theorem.(7Hrs.)
UNIT-V: Numerical Analysis:Solution of algebric and transcendental equations by method & method of false position, Newton-Raphson method Solution of system of linear equations by Gauss Seidal method,Relaxation method. Solution of first order ordinary differential equations by modified Euler’s,method Runge - Kutta method.(7Hrs.)
UNIT-VI: Vector Calculus :-Scalar and vector point functions, Differentiation of vectors,Gradient of a scalar point function, Directional derivatives,Divergence and curl of a vector point function and their physical meaning, line, surface, volume integrals, irrotational and solenoidal vector fields, Stoke’s and Divergence theorem (without proof). (7Hrs.)
Text Books:
1. Higher Engineering. Mathematics by B.S. Grewal, Khanna Publication.
2. A Text Book of Applied Mathematics, Volume-II by P. N. Wartikar and
J.N. Wartikar, Pune Vidyarthi Griha Prakashan, Pune.
3. Applied Mathematics, Vol. III, J.N. Wartikar and P.N. Wartikar, Pune
Vidyarthi Griha Prakashan, Pune.
Reference Books:
1. Numerical Analysis- S.S. Sastry.
2. Advancing Engg. Mathematics by E.K.Kreyzig.