# B.Tech Engineering Mathematics Syllabus 1st Semester                          (Computer science and Engg.)

Course Objectives:
1. To give adequate exposure of basics of Engineering Mathematics so as to
enable them to visualize engineering problems by using Mathematical tools and to support
their subsequent engineering studies.
2. To familiarize the students with techniques in basic calculus and linear algebra.
3. To equip the students with standard concepts and tools at an intermediate to
4. To know the advanced level of mathematics and applications that they would find
useful in their disciplines.
5. Students will demonstrate the ability to apply the techniques of multivariable
Calculus to problems in mathematics, the physical sciences, and engineering.

Unit-I (12 Lectures)

Matrices addition and scalar multiplication, matrix multiplication; Linear systems of equations,
linear Independence, rank of a matrix, determinants, Cramer's Rule, inverse of a matrix, Gauss
elimination and Gauss-Jordan elimination.

Unit-II (12 Lectures)

Eigen values, Eigen vectors, Cayley Hamiltan Theorem symmetric, skew-symmetric, and
orthogonal Matrices, Eigen space. Diagonalization; Inner product spaces, Gram-Schmidt
orthogonalization.

Unit-III (12 Lectures)

Taylor's and Maclaurin theorems with remainders; Maxima and minma of function of single
independent variable.
Curvature & Asymptotes (Cartesian and polar form), Evolutes and involutes; Evaluation
of definite and improper integrals; Beta and Gamma functions and their properties; Applications
of definite integrals to evaluate surface areas and volumes of revolutions.

Unit-IV (12 Lectures)

Vector space, linear dependence and independence of vectors, basis, dimension; Linear
transformations (maps), range and kernel of a linear map, rank and nullity, Inverse of a linear
transformation, rank-nullity theorem, composition of linear Maps, Matrix associated with a linear map.

Text Books:
1. Erwin Kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons, 2006.
2. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, Laxmi
Publications, Reprint, 2008.
3. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 36th Edition, 2010.

Reference Books:
1. G.B. Thomas and R.L. Finney, Calculus and Analytic Geometry, 9th Edition, Pearson
Education.
2. D. Poole, Linear Algebra: A Modern Intaiduction, 2nd Edition, Brooks/Cole, 2005.
3. Veerarajan T., Engineering Mathematics for firstyear, Tata McGraw-Hill, New Delhi, 2008.
4. Ramana B.V., Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th Reprint,
2010.
5. V. Krishnamurthy, V.P. Mainra and J.L. Arora, An introduction to Linear Algebra,
Affiliated East-West press, Reprint 2005.

Course Outcomes:
1. The students will learn to apply differential and integral calculus to notions of curvature
and to improper integrals.
2. They will have a basic understanding of Beta and Gamma functions.
3. They will understand essential tools of matrices and determinant to solve system of
algebraic equation.
4. To know the basic concepts of linear algebra i.e., linear transformations, eigen values,
diagonalization and orthogonalization to solve engineering problems.
5. Apply Taylor series to approximate functions and estimate the error of
approximation

Note:
1. The paper setter will set two questions (with/without parts) from each units, & a
ninth compulsory question comprising of 6 to 10 sub-parts, covering the entire
syllabus. The examinee will attempt 5 questions in all, along with the compulsory
question (with all it sub-parts), selecting one question from each unit.
2. The use of programmable devices such as programmable calculators, etc. is not
allowed during the exam.

# (Common for all branches except Computer science and BioTech.)

Course objectives:
1. To familiarize the students with tools and Techniques in calculus and analysis.
2. To equip the students with standard concepts towards tackling various applications that are
useful in several disciplines.
3. To understand liner algebra concepts and their application in different fields of engineering.
4. To have the idea of vector calculus and its applications
5. To give adequate exposure of basics of Engineering Mathematics so as to
enable them to visualize engineering problems by using Mathematical tools and
to support their subsequent engineering studies.
6. To introduce to students the concept of convergence of sequences and series.
.

Unit-I (12 Lectures)

Determinants; Inverse and rank of a matrix, System of linear equations; Symmetric, skew-
symmetric and orthogonal matrices; Eigenvalues and eigen vectors; Diagonalization of matrices;

Cayley-Hamilton Theorem, Matrix representation, Rank-nullity theorem of a Linear
Transformation, Orthogonal transformation.

Unit –II (12 Lectures)

Convergence of sequence and series, tests for convergence of sequence and series ; Power series,
Taylor's and Maclaurin series, series for exponential, trigonometric and logarithm functions;
Fourier series: Half range sine and cosine series, Parseval's theorem.

Unit-III (12 Lectures)

Taylor's and Maclaurin theorems with remainders; (one variable).Asymptotes, Curvature
,Evolutes and involutes, Curve Tracing; Evaluation of definite and improper integrals; Beta and
Gamma functions and their properties; Applications of definite integrals to evaluate surface areas
and volumes of revolutions.

Unit-IV (12 Lectures)

Function of several variables: Limit, continuity and partial derivatives, Total derivative; Maxima, minima and saddle points; Method of Lagrange multipliers; Differentiation under Integral Sign. ,Vector Calculus: Gradient, Directional derivative,  curl and divergence.

Text Books:
1. Erwin Kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons,
2006.
2. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, Laxmi
Publications, Reprint, 2008.
3. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 36th Edition, 2010.
Reference Books:
1. G.B. Thomas and R.L. Finney, Calculus and Analytic Geometry, 9th Edition, Pearson
Education.
2. Veerarajan T., Engineering Mathematics for first year, Tata McGraw-Hill, New Delhi,
2008.
3. Ramana B.V., Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11th
Reprint, 2010.
4. D. Poole, Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/Cole, 2005.

Course outcomes:
1. The students will understand the basic properties of Determinants and matrices & apply
these concepts in solving linear simultaneous equations.
2.They will learn the basic concepts regarding convergence of series.
3. The students will learn concepts of vector calculus and apply it in most of the
branches of engineering.
4. They will be able to solve Eigen value problems and apply Cayley-Hamilton
theorem.
Note:
1. The paper setter will set two questions (with/without parts) from each units, & a
ninth compulsory question comprising of 6 to 10 sub-parts, covering the entire
syllabus. The examinee will attempt 5 questions in all, along with the compulsory
question (with all it sub-parts), selecting one question from each unit.
2. The use of programmable devices such as programmable calculators, etc. is not
allowed during the exam.

# ​

Course objectives:

1. To familiarize the students with techniques in multivariate integration, ordinary and   partial differential equations and complex variables.

2. To equip the students to deal with advanced level of mathematics and applications   that would be essential for their disciplines

Unit-I (12 Lectures)

Multiple Integration: Double integrals, change of order of integration, Triple integral and application, Change of variables, Applications to areas and volumes, Centre of mass and Gravity (constant and variable densities) of solids of revolution, orthogonal curvilinear coordinates, vector line integrals, surface integrals, Volume integral Theorems of Green, Gauss and Stokes.

Unit II (12 Lectures)

Ordinary differential Equations of first order and first degree: Exact, linear and Bernoulli's equations, Equations of first order but not of first degree, equation solvable for p, equations solvable for y, equations solvable for x and Clairaut's type. Second order linear differential equations with variable coefficients, method of variation of parameters, Cauchy-Euler equation; Power series solutions; Legendre polynomials, Bessel functions of the first kind and their properties.

Unit III (12 Lectures)

Cauchy-Riemann equations, analytic functions, harmonic functions, finding harmonic conjugate; elementary analytic functions (exponential, trigonometric, logarithm) and their properties; Conformal mappings, Mobius transformations and their properties.

Unit IV (12 Lectures)

Contour integrals, Cauchy-Goursat theorem (without proof), Cauchy Integral formula (without proof), Liouville's theorem and Maximum-Modulus theorem (without proof); Taylor's series, Laurent's series; zeros of analytic functions, singularities, Residues, Cauchy Residue theorem (without proof), Evaluation of definite integral involving sine and cosine, Evaluation of certain improper integrals using the Bromwich contour.

# B.Tech Engineering Mathematics Syllabus 3rd Semester

UNIT- I

First order Partial Differential Equations, Solutions of First order Linear and Non-Linear PDEs. Solution to Homogenous and Non-Homogenous Linear Partial Differential Equations of second and higher order by complimentary function and particular integral method.

UNIT-II

Flows, Vibrations and Diffusions, Second-order Linear equations and their classification, Initial and, Boundary conditions (with an informal description of well-posed problems), D'Alembert's solution of the Wave equation; Duhamel's principle for One Dimensional Wave Equation. Separation of variables, Method to Simple Problems in Cartesian coordinates.

UNIT-III

Basic Statistics, Measures of Central Tendency: Moments, Skewness and Kurtosis, Probability distributions: Binomial, Poisson and Normal, Evaluation of Statistical Parameters for these three distributions, Correlation and Regression, Rank Correlation. Curve fitting by the Method of Least Squares, Fitting of Straight Lines, Second Degree Parabolas and more general curves.

UNIT-IV

Probability spaces, Conditional Probability, Independence; Discrete random variables, Independent random variables, the Multinomial Distribution, Poisson Approximation to the Binomial Distribution, Infinite sequences of Bernoulli Trials, Sums of independent random variables; Expectation of Discrete Random Variables, Moments, Variance of a sum, Correlation coefficient, Chebyshev's Inequality.

REFERENCE BOOKS:

1. S. J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Publications, 1993.

2. R. Haberman; Elementary Applied Partial Differential equations with Fourier Series And Boundary Value Problem, 4th Ed., Prentice Hall, 1998.

3. Ian Sneddon, Elements of Partial Deferential Equation, McGraw Hill, 1964.

4. S.S. Sastry, Engineering Mathematics, PHI, Vol. I & II.

Note:

1. In Semester Examinations, the examiner will set two questions from each unit (total 8 questions in all) covering the entire syllabus.  The students will be required to attend only five questions selecting atleast one question from each unit.

2. The use of scientific calculator will be allowed in the examination.  However, programmable calculator and cellular phone will not be allowed.