Anna University R2025 Maths Syllabus — which book covers which course

4 credits · 3L–1T–0P · BS — Basic Science (Mathematics) · Semester 1 · 50 of 53 programmes

• Differential Calculus — functions and their graphs, limits and continuity, limits at infinity, the derivative as a function, maxima & minima of single-variable functions, mean value theorem, effect of derivatives on the shape of a graph
• Functions of Several Variables — partial derivatives, chain rule, total derivative, maxima & minima of functions of two variables, method of Lagrange’s multipliers, engineering application problems
• Integral Calculus — fundamental theorem of calculus, indefinite integrals and the net change theorem, improper integrals, arc length, area of a region, area of a surface of revolution
• Multiple Integrals — iterated integrals and Fubini’s theorem, evaluation of double integrals, change of order of integration, change of variables between Cartesian and polar coordinates, triple integrals with cylindrical and spherical coordinates

Engineering Mathematics-I

Covers: The whole course — mean value theorems and Taylor/Maclaurin, partial differentiation with maxima–minima and Lagrange multipliers, definite and improper integrals with Beta & Gamma functions, and multiple integrals for surface and volume calculations.

4 credits · 3L–1T–0P · BS — Basic Science (Mathematics) · 46 of 53 programmes

• Vector Spaces — subspaces, linear combinations, span, generating sets, linear dependence & independence, basis and dimension, dimension of subspaces
• Linear Transformations and Diagonalization — null space, range, dimension theorem, matrix representation of a linear transformation, eigenvalues & eigenvectors, diagonalizability
• Inner Product Spaces — inner product, norms, Cauchy–Schwarz inequality, Gram–Schmidt orthogonalization
• Matrix Decomposition — orthogonal transformation of a symmetric matrix to diagonal form, positive definite matrices, QR decomposition, singular value decomposition (SVD), least-squares solutions

Engineering Mathematics-I

Covers: The vector-space and diagonalization core — basis and dimension, linear dependence & independence, linear transformations, rank, eigenvalues & eigenvectors, diagonalisation and the Cayley–Hamilton theorem.

Introduction to Discrete Structure & Linear Algebra

Covers: The matrix-decomposition unit — determinant and trace, eigenvalue decomposition, singular value decomposition (SVD) and Cholesky factorization.

4 credits · 3L–1T–0P · BS — Basic Science (Mathematics) · 23 of 53 programmes

• First Order Ordinary Differential Equations — formation from physical problems, variables separable, exact equations, Leibnitz’s and Bernoulli’s equations; numerical solution by Euler’s formula, Taylor series and fourth-order Runge–Kutta
• Higher Order Ordinary Differential Equations — linear equations of second and higher order with constant coefficients, Euler’s linear equations, method of variation of parameters; numerical solution by Runge–Kutta and finite-difference methods
• First Order Partial Differential Equations — formation by elimination of arbitrary constants and functions, solution by variable separable method, standard types, Lagrange’s linear equation; numerical solution by the method of lines
• Higher Order Partial Differential Equations — linear homogeneous PDEs of second and higher order with constant coefficients; finite-difference solution of two-dimensional Laplace and Poisson equations, one-dimensional heat equation by Bender–Schmidt and Crank–Nicolson schemes, and the wave equation by an explicit scheme

Engineering Mathematics-II

Covers: The analytical half in full — first-order ODEs (Leibnitz linear, Bernoulli, exact), higher-order equations with constant coefficients, variation of parameters, and the formation and solution of linear and non-linear partial differential equations.

Engineering Mathematics-III

Covers: The computational half — Euler and modified Euler, Taylor series, Runge–Kutta and Milne’s methods, plus finite-difference solutions of the Laplace, heat and wave equations, which is exactly what this course’s numerical units ask for.

4 credits · 3L–1T–0P · BS — Basic Science (Mathematics) · 19 of 53 programmes

• Descriptive Statistics — collection, classification and tabulation of data, bar and pie charts, measures of central tendency (mean, median, mode), measures of variation (range, quartile deviation, standard deviation, coefficient of variation), five-number summary and box plots
• Probability and Random Variables — axioms of probability, conditional and total probability, Bayes’ theorem, distribution functions, probability mass & density functions, moments, and the binomial, Poisson, normal, uniform and exponential distributions
• Two-Dimensional Random Variables — joint, marginal and conditional distributions, expected values of functions of two variables, correlation and regression, central limit theorem
• Testing of Hypothesis — large-sample tests for a single mean and difference of means, small-sample t and F tests (paired t-test, variance ratio test), chi-square tests for independence of attributes and goodness of fit
• Design of Experiments — analysis of variance (ANOVA), completely randomized design (CRD), randomized block design (RBD) and Latin square design (LSD)

Probability & Statistics for Data Science

Covers: Most of the course — central tendency and dispersion, skewness & kurtosis, Bayes’ theorem and conditional probability, the standard distributions, correlation & regression, and the full hypothesis-test set (t, F, chi-square, Z).

Introduction to Probability & Statistics

Covers: A parallel route through probability spaces, conditional densities, Bayes’ rule, curve fitting by least squares, and both large- and small-sample significance tests.

Introduction to Discrete Structure & Linear Algebra

Covers: The analysis-of-variance (ANOVA) content of the design-of-experiments unit.

4 credits · 3L–1T–0P · BS — Basic Science (Mathematics) · 10 computing programmes

• Set Theory, Relations and Functions — inductive definition of sets and proof by induction, Peano postulates, equivalence relations and partitions, injective/surjective/bijective functions, composition and inverse functions, permutation functions, recurrence relations and solving linear recurrences
• Logic — propositions, logical operators, normal forms, rules of inference, consistency, propositional logic and proofs, predicates and quantifiers, universe of discourse, logical equivalences for quantified statements, rules of specification and generalization, validity of arguments
• Boolean Algebra and Lattice Theory — partial ordering, posets, lattices as posets and as algebraic systems, properties of lattices, sublattices, direct product and homomorphism, Boolean algebra and Boolean homomorphism
• Graph Theory — types of graphs, matrix representation, graph isomorphism, walks, paths and cycles, Eulerian and Hamiltonian graphs, planar graphs, Euler’s formula, and Dijkstra’s shortest-path algorithm

Discrete Structure

Covers: The complete course, unit for unit — set theory and relations, algebraic structures, logic and normal forms, graph theory, and combinatorics with lattices. The closest single-book match to this syllabus.

Introduction to Discrete Structure & Linear Algebra

Covers: The same discrete core from the AI angle this R2025 course takes — sets, relations, posets and Hasse diagrams, lattices, first-order logic, normal forms, graph paths, cycles and shortest-path problems.

4 credits · 3L–1T–0P · BS — Basic Science (Mathematics) · EEE, Electrical & Computer, Electronics & Instrumentation, Instrumentation & Control

• Laplace Transforms — existence conditions and properties, transforms of standard functions, derivatives and integrals, unit step and Dirac delta functions, transforms of periodic functions, inverse Laplace by partial fractions and the convolution theorem, solution of second-order ODEs
• Z-Transform — Z-transform of standard functions and its properties, inverse Z-transform by standard functions, partial fractions and convolution, and the solution of difference equations
• Fourier Series — Dirichlet’s conditions, general Fourier series and its convergence, odd and even functions, half-range sine and cosine series, root mean square value, Parseval’s identity, application to the one-dimensional wave and heat equations
• Fourier Transform — complex Fourier transform and its properties, and its relation to the other transforms

Engineering Mathematics-III

Covers: The Laplace and Fourier transform units — Laplace transform and its properties, inverse Laplace, convolution theorem and Fourier transforms.

Engineering Mathematics-I

Covers: The Fourier-series unit — general and half-range sine/cosine series, convergence and Parseval’s theorem.

4 credits · 3L–1T–0P · BS — Basic Science (Mathematics) · EEE, Electrical & Computer, Electronics & Instrumentation, Instrumentation & Control

• Matrices — characteristic equation, eigenvalues & eigenvectors of a real matrix and their properties, Cayley–Hamilton theorem and its applications, orthogonal matrices
• Quadratic Forms — orthogonal transformation of a symmetric matrix to diagonal form, nature of quadratic forms, reduction to canonical form by orthogonal transformation
• Advanced Decompositions — matrix norms, Jordan normal form, QR decomposition, singular value decomposition (SVD) and least-squares solutions

Engineering Mathematics-I

Covers: The matrices and quadratic-form core — rank, eigenvalues & eigenvectors, diagonalisation and the Cayley–Hamilton theorem.

Introduction to Discrete Structure & Linear Algebra

Covers: The decomposition unit — eigenvalue decomposition, singular value decomposition (SVD) and Cholesky.

4 credits · 3L–1T–0P · BS — Basic Science (Mathematics) · ECE, Electronics & Computer, VLSI (C11) · Biomedical, Medical Electronics (C12)

• Descriptive and Bivariate Statistics — mean, median, mode, variance and standard deviation, coefficient of variation, covariance and correlation coefficient, linear regression by least squares
• Probability Foundations — axioms, conditional probability and Bayes’ theorem, discrete and continuous random variables, moments and moment generating functions
• Standard Distributions — binomial, Poisson and geometric; uniform, exponential and normal; functions of random variables
• Two-Dimensional Random Variables — joint, marginal and conditional distributions, covariance, correlation and linear regression, transformation of random variables
• Random Processes — stationarity, autocorrelation and the stochastic-process foundations used in signal processing and communication systems

Probability & Statistics for Data Science

Covers: The statistics and probability units — central tendency and dispersion, Bayes’ theorem, moment generating functions, the standard distributions, correlation & regression and the significance tests.

Introduction to Probability & Statistics

Covers: Probability spaces, conditional and bivariate densities, distribution of sums, Bayes’ rule and the two-dimensional random-variable topics.