B.Tech Syllabi Maths
B.TECH SYLLABI FOR MATHEMATICS
Approved syllabus for the batches admitted from 2017
MA 101 
Mathematics – I I B.Tech. I Semester  all sections 
BSC 
300 
3 Credits 
Prerequisites: None
Course Outcomes:At the end of the course, the students will be able to
CO 1 
solve the consistent system of linear equations 
CO 2 
apply orthogonal and congruent transformations to a quadratic form 
CO 3 
determine the power series expansion of a given function 
CO 4 
find the maxima and minima of multivariable functions 
CO 5 
solve arbitrary order linear differential equations with constant coefficients 
CO 6 
apply the concepts in solving physical problems arising in engineering 
Matrix Theory: Linear dependence and independence of vectors; Rank of a matrix; Consistency of the system of linear equations; Eigenvalues and eigenvectors of a matrix; CaleyHamilton theorem and its applications; Reduction to diagonal form; Reduction of a quadratic form to canonical form  orthogonal transformation and congruent transformation; Properties of complex matrices  Hermitian, skewHermitian and Unitary matrices. (14)
Differential Calculus: Taylor's theorem with remainders; Taylor's and Maclaurin's expansions; Asymptotes; Curvature; Curve tracing; Functions of several variables  partial differentiation; total differentiation; Euler's theorem and generalization; Change of variables  Jacobians; maxima and minima of functions of several variables (2 and 3 variables)  Lagrange's method of multipliers. (14)
Ordinary Differential Equations: Geometric interpretation of solutions of first order ODE ; Exact differential equations; integrating factors; orthogonal trajectories; Higher order linear differential equations with constant coefficients  homogeneous and nonhomogeneous; Euler and Cauchy's differential equations; Method of variation of parameters; System of linear differential equations; applications in physical problems  forced oscillations, electric circuits, etc. (14)
 R. K. Jain and S. R. K. Iyengar, "Advanced Engineering Mathematics", Fifth Edition, Narosa Publishing House, 2016
 Erwin Kreyszig, "Advanced Engineering Mathematics", Eighth Edition, John Wiley and Sons, 2015
 B. S. Grewal, "Higher Engineering Mathematics", Khanna Publications, 2015
MA 151 
Mathematics – II I B.Tech. II Semester  all sections 
BSC 
300 
3 Credits 
Prerequisites: MathematicsI
Course Outcomes:At the end of the course, the students will be able to
CO 1 
analyze improper integrals 
CO 2 
evaluate multiple integrals in various coordinate systems 
CO 3 
apply the concepts of gradient, divergence and curl to formulate engineering problems 
CO 4 
convert line integrals into area integrals and surface integrals into volume integrals 
CO 5 
apply Laplace transforms to solve physical problems arising in engineering 
Integral Calculus: Convergence of improper integrals; Beta and Gamma integrals; Differentiation under integral sign; Double and Triple integrals  computation of surface areas and volumes; change of variables in double and triple integrals. (14)
Vector Calculus: Scalar and vector fields; vector differentiation; level surfaces; directional derivative; gradient of a scalar field; divergence and curl of a vector field; Laplacian; Line and Surface integrals; Green's theorem in a plane; Stoke's theorem; Gauss Divergence theorem(14)
Laplace Transforms: Laplace transforms; inverse Laplace transforms; Properties of Laplace transforms; Laplace transforms of unit step function, impulse function, periodic function; Convolution theorem; Applications of Laplace transforms  solving certain initial value problems, solving system of linear differential equations, finding responses of systems to various inputs viz. sinusoidal inputs acting over a time interval, rectangular waves, impulses etc. (14)
 R. K. Jain and S. R. K. Iyengar, "Advanced Engineering Mathematics", Fifth Edition, Narosa Publishing House, 2016
 Erwin Kreyszig, "Advanced Engineering Mathematics", Eighth Edition, John Wiley and Sons, 2015
 B. S. Grewal, "Higher Engineering Mathematics", Khanna Publications, 2015
MA 201 
Mathematics  III II B.Tech. I Semester (Common to EEE, MME, Chemical and BioTech) 
BSC

3  0  0 
3 Credits 
Prerequisites: Mathematics  II (MA 151)
Course Outcomes: At the end of the course, student will be able to:
CO1 
Obtain the Fourier series for a given function 
CO2 
Find the Fourier transform of a function and Z transform of a sequence 
CO3 
Determine the solution of a PDE by variable separable method 
CO4 
Understand and use of complex variables and evaluation of real integrals 
Fourier Series: Expansion of a function in Fourier series for a given range  Half range sine and cosine expansions (6)
Fourier Transforms : Fourier transformation and inverse transforms  sine, cosine transformations and inverse transforms  simple illustrations. (6)
Ztransforms : Z transform and Inverse Ztransforms – Properties – convolution theorem simple illustrations. (6)
Partial Differential Equations: Method of separation of variables  Solution of one dimensional wave equation, one dimensional heat conduction equation and two dimensional steady state heat conduction equation with illustrations. (8)
Complex Variables: Analytic function  Cauchy Riemann equations  Harmonic functions Conjugate functions  complex integration  line integrals in complex plane  Cauchy’s theorem (simple proof only), Cauchy’s integral formula  Taylor’s and Laurent’s series expansions  zeros and singularities  Residues  residue theorem, use of residue theorem to evaluate the real integrals of the type , without poles on the real axis. (16)
Reading:
 R.K.Jain and S.R.K.Iyengar, Advanced Engineering Mathematics, Narosa Pub. House,Fifth edtion, 2016.
 Erwyn Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 8^{th} Edition, 2008.
 B.S.Grewal, Higher Engineering Mathematics, Khanna Publications, 44th edition, 2017.
MA 211

Mathematical Methods (II year B Tech I semester Civil) 
BSC 
3 – 0 – 0 
3 Credits 
Prerequisites: Mathematics  I and Mathematics – II.
Course Outcomes: At the end of the course, student will be able to:
CO1 
Determine Fourier series expansion of a given function 
CO2 
Solve PDEs by variables separable method 
CO3 
Test the hypothesis for large and small samples 
CO4 
Solve numerically algebraic/transcendental and ordinary differential equations 
Fourier series: Expansion of a function in Fourier series for a given range  Half range sine and cosine expansions. (5)
Partial Differential Equations: PDE types, Method of separation of variables  solution of Heat equation. (4)
Complex Variables: Analytic function  Cauchy Riemann equations  Conformal mapping. (5)
Probability and Statistics: Random variables, Discrete and continuous distributions, Mean and Variance, Binomial, Poisson and Normal distributions, Testing of Hypothesis  Ztest for single mean and difference of means  ttest for single mean and difference of means, Ftest for comparison of variances,. Chisquare test for goodness of fit – Karl Pearson Coefficient of correlation – Lines of regression. (16)
Numerical Analysis: Numerical solution of algebraic and transcendental equations by RegulaFalsi method NewtonRaphson’s method –Finite Differences  Newton’s Forward, backward difference interpolation formulae  Lagrange interpolation  Numerical Integration with Trapezoidal rule, Simpson’s 1/3 rule, Simpson’s 3/8 rule  solving first order differential equations –Taylor’s series method, Euler’s method, modified Euler’s method, RungeKutta method of 4^{th} order. (12)
Reading:
 R.K.Jain and S.R.K.Iyengar, Advanced Engineering Mathematics, Narosa Publ., 2016.
 B.S.Grewal, Higher Engineering Mathematics, Khanna Publishers, 2017
 S.C.Gupta and V.K.Kapoor, Fundamentals of Mathematical Statistics, S.Chand & Co, 2006.
MA 236 
Transformation Techniques II year B.Tech. I Semester (Mechanical) 
BSC 
LTP: 300 
3 Credits 
Prerequisites: Mathematics – I and Mathematics  II
Course Outcomes: At the end of the course, student will be able to:
CO1 
Determine Fourier series expansion of functions 
CO2 
Determine solutions of PDE for vibrating string and heat conduction 
CO3 
Evaluate real integrals using residue theorem 
CO4 
Transform a region to another region using conformal mapping 
Fourier Series: Expansion of a function in Fourier series for a given range  Half range sine and cosine expansions (6)
Fourier Transforms : Complex form of Fourier series  Fourier transformation and inverse transforms  sine, cosine transformations and inverse transforms  simple illustrations. (6)
Partial Differential Equations: Solutions of Wave equation, Heat equation and Laplace’s equation by the method of separation of variables and their use in problems of vibrating string, one dimensional unsteady heat flow and two dimensional steady state heat flow including polar form. (10)
Complex Variables: Analytic function  Cauchy Riemann equations  Harmonic functions  Conjugate functions  complex integration  line integrals in complex plane  Cauchy’s theorem (simple proof only), Cauchy’s integral formula  Taylor’s and Laurent’s series expansions  zeros and singularities  Residues  residue theorem, evaluation of real integrals using residue theorem, Bilinear transformations, conformal mapping. (20)
READING :
 R.K.Jain and S.R.K.Iyengar, Advanced Engineering Mathematics, Narosa Pub. House, 2016.
 Erwyn Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 8^{th} Edition, 2008.
 B.S.Grewal, Higher Engineering Mathematics, Khanna Publications, 2017.
MA251 
MATHEMATICS IV II B.Tech. II Semester (Common to EEE, MME, Chemical and BioTech) 
BSC 
3– 0 – 0 
3 Credits 
Prerequisites:
Course Outcomes: At the end of the course, student will be able to:
CO1 
Interpret an experimental data using interpolation / curve fitting 
CO2 
Solve numericallyalgebraic/transcendental and ordinary differential equations 
CO3 
Understand the concepts of probability and statistics 
CO4 
Obtain the series solutions for ordinary differential equations 
Numerical Methods:
Curve fitting by the method of least squares. Fitting of (i) Straight line (ii) Second degree parabola (iii) Exponential curves  GaussSeidal iteration method to solve a system of equations  Numerical solution of algebraic and transcendental equations by RegulaFalsi method and NewtonRaphson’s method  Lagrange interpolation, Forward and backward differences, Newton’s forward and backward interpolation formulae  Numerical differentiationwith forward and backward differences  Numerical Integration with Trapezoidal rule, Simpson’s 1/3 rule and Simpson’s 3/8 rule  Taylor series method, Euler’s method, modified Euler’s method, 4th order RungeKutta method for solving first order ordinary differential equations. (16)
Probability and Statistics: Random variables, discrete and continuous random variables, Mean and variance of Binomial, Poisson and Normal distributions and applications. Testing of Hypothesis – Null and alternate hypothesis, level of significance and critical regionZtest for single mean and difference of means, single proportion and difference of proportions  ttest for single mean and difference of means  Ftest for comparison of variances, Chisquare test for goodness of fit  Karl Pearson coefficient of correlation, lines of regression and examples. (16)
Series Solution: Series solution of Bessel and Legendre’s differential equations  Bessel function of first kind, Recurrence formulae, Generating function, Orthogonality of Bessel functions  Legendre polynomial, Rodrigue’s formula, Generating function, Recurrence formula, Orthogonality of Legendre polynomials. (10)
Reading:
 M. K. Jain, S.R.K.Iyengarand R.K.Jain, Numerical methods for Scientific and Engineering Computation, New Age International Publications, 2008.
 S.C.Gupta and V.K.Kapoor, Fundamentals of Mathematical Statistics, S.Chand & Co, 2006.
 Erwyn Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 8th Edition, 2008.
 B.S.Grewal, Higher Engineering Mathematics, Khanna Publications, 2009.
MA 261 
Numerical and Statistical Methods II year B.Tech. II Semester (Mechanical) 
BSC 
LTP: 300 
3 Credits 
Prerequisites: Mathematics – I and Mathematics  II
Course Outcomes: At the end of the course, student will be able to:
CO1 
Interpret an experimental data using interpolation / curve fitting 
CO2 
Solve numericallyalgebraic/transcendental and ordinary differential equations 
CO3 
Understand the concepts of probability and statistics 
CO4 
Test the hypothesis for large and small samples. 
Numerical Analysis:
Curve fitting by the method of least squares. Fitting of (i) Straight line (ii) Second degree parabola (iii) Exponential curves. Calculation of dominant Eigenvalue by iteration, GaussSeidal iteration method to solve a system of equations and convergence (without proof). Numerical solution of algebraic and transcendental equations by RegulaFalsi method NewtonRaphson’s method.
Lagrange interpolation, Newton’s divided differences, Forward, backward and central differences, Newton’s forward and backward interpolation formulae, Gauss’s forward and backward interpolation formulae, Numerical differentiation at the tabulated points with forward backward and central differences. Numerical Integration with Trapezoidal rule, Simpson’s 1/3 rule, Simpson’s 3/8 rule and Romberg integration. Taylor series method, Euler’s method, modified Euler’s method, RungeKutta method of 2^{nd}& 4^{th} orders for solving first order ordinary differential equations. (22)
Probability and Statistics : Review of fundamental concepts of probability, Moments and Moment generating function of Discrete and continuous distributions, Binomial, Poisson and Normal distributions, fitting these distributions to the given data, Testing of Hypothesis  Ztest for single mean and difference of means, single proportion and difference of proportions  ttest for single mean and difference of means, Ftest for comparison of variances, Chisquare test for goodness of fit. – Correlation, regression. (20)
READING :
 S.C.Gupta and V.K.Kapoor, Fundamentals of Mathematical Statistics, S.Chand & Co, 2006.
 Jain, Iyengar and Jain, Numerical methods for Scientific and Engineering Computation, New Age International Publications, 2008.
 Erwyn Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 8^{th} Edition, 2008.
MA 239 
Probability, Statistics and Queuing Theory (II B.Tech I Semester CSE) 
BSC

3  0  0 
3 Credits 
Prerequisites: Mathematics – I and Mathematics  II
Course Outcomes: At the end of the course, student will be able to:
CO1 
find mean and variance of a given probability distribution 
CO2 
test the hypothesis for small and large samples 
CO3 
find the coefficient of correlation and lines of regression 
CO4 
understand the characteristics of a queuing model 
Random variables and their distributions:
Introduction to Probability, random variables (discrete and continuous), probability functions, density and distribution functions, mean and variance, special distributions (Binomial, Hyper geometric, Poisson, Uniform, exponential and normal), Chebyshev’s inequality, parameter and statistic, estimation of parameters by maximum Likelihood Estimation method (16)
Testing of Hypothesis:
Testing of Hypothesis, Null and alternative hypothesis, level of significance, onetailed and twotailed tests, tests for large samples (tests for single mean, difference of means, single proportion, difference of proportions), tests for small samples (ttest for single mean and difference of means, Ftest for comparison of variances), Chisquare test for goodness of fit, analysis of variance (one way classification with the samples of equal and unequal sizes), Karl Pearson coefficient of correlation, lines of regression. (16)
Queuing theory:
Concepts, applicability, classification, birth and death process, Poisson queues, Characteristics of queuing models  single server (with finite and infinite capacities) model, multiple server (with infinite capacity only) model. (10)
Reading:
1. R. A. Johnson: Miller and Freund’s Probability and Statistics for Engineers, Pearson Publishers, 9^{th} Edition, 2017
2. Freund: Modern elementary statistics, PHI, 2006
3. S.C.Gupta and V.K.Kapoor : Fundamentals of Mathematical Statistics, 2006
4. Kantiswarup, P.K.Gupta and Manmohan Singh : Operations Research, S.Chand & Co, 2010