AKTU B.Tech Mathematics Syllabus 2026-27 — which book covers which unit

4 credits · 60 NCrF hours · Basic Science (Mathematics) · Semester 1

• Differential Calculus — limits, continuity & differentiability of functions of two variables, partial derivatives, composite functions, total derivative, Euler’s theorem for homogeneous functions, Taylor’s & Maclaurin’s expansion, Jacobians, maxima & minima
• Multiple Integrals — double & triple integrals, change of order of integration, change of variable, Beta & Gamma functions, Dirichlet’s integral, area & volume
• Matrix Algebra — elementary transformation, inverse by E-transformation, rank by echelon form, Gauss elimination & Gauss–Seidel methods, eigenvalues & eigenvectors, diagonalization
• Vector Spaces — subspaces, spanning set, linear independence, basis & dimension, linear transformations, range & null space, rank–nullity theorem
• Vector Calculus — scalar & vector point functions, gradient, directional derivatives, divergence & curl, solenoidal & irrotational vectors, Stokes’ theorem, Gauss divergence theorem

Engineering Mathematics-I

Covers: Four of the five units — differential calculus (Taylor/Maclaurin, partial differentiation, maxima–minima, Lagrange multipliers), multiple integrals with Beta & Gamma functions, vector spaces (basis, linear transformations, dependence) and the complete matrix-algebra unit (rank, eigenvalues, diagonalization, Cayley–Hamilton).

Engineering Mathematics-II

Covers: The vector-calculus unit in full — gradient, divergence, curl, line/surface/volume integrals with Gauss, Stokes and Green’s theorems.

Engineering Mathematics-III

Covers: The numerical linear-algebra methods this unit names — Gauss elimination, Gauss–Jordan and Gauss–Seidel for systems of linear equations.

3–4 credits · 45–60 NCrF hours (varies by stream) · Basic Science (Mathematics) · Semester 2

• Differential Equations — nth-order linear equations with constant coefficients, Cauchy–Euler equation, variation of parameters, change of independent variable, normal form (CE, ME, TX, CH variants)
• Series Solution & Special Functions — ordinary & singular points, Frobenius method, indicial equation and its root cases (ECE, EE, CH variants)
• Laplace Transform — existence, linearity, shifting theorems, change of scale, transforms of derivatives & integrals, periodic & unit-step functions, inverse transform, partial fractions, convolution, solving ODEs
• Fourier Series & Fourier Transform — Dirichlet’s condition, half-range sine & cosine series, Parseval’s identity, Fourier integral theorem, Fourier & inverse Fourier transform, finite sine/cosine transforms (ECE, EE, CH, TX variants)
• Sequences & Series — monotonic and Cauchy sequences, convergence & divergence, comparison, ratio, Raabe’s and logarithmic tests (CE, ME, ECE, EE variants)
• Complex Variables — analytic functions, Cauchy–Riemann equations, harmonic functions, Milne–Thomson method, complex integrals, Cauchy integral theorem & formula, Taylor & Laurent series, singularities, residues, evaluation of real definite integrals
• Applied Linear Algebra — eigenvalue & singular value decomposition, matrix factorization, LU (Doolittle) and QR decomposition, kernel & range, inner product space, norm (TX, CH variants)

Engineering Mathematics-II

Covers: The differential-equations and complex-variable strands in full — first- and higher-order ODEs, variation of parameters, plus analytic functions, Cauchy–Riemann, Cauchy integral formula, poles, residues and the residue theorem. Its Legendre-polynomial and Bessel-function unit also carries the series-solution / special-functions topics.

Engineering Mathematics-III

Covers: Transform calculus — Laplace transform and its properties, inverse Laplace, convolution theorem, and Fourier transforms.

Engineering Mathematics-I

Covers: The sequences-&-series unit (convergence tests, power series) and the Fourier-series half of the transforms unit, including half-range series and Parseval’s theorem.

Introduction to Discrete Structure & Linear Algebra

Covers: The applied-linear-algebra unit’s decompositions — eigenvalue decomposition, singular value decomposition (SVD) and Cholesky.

4 credits · 60 NCrF hours · Basic Science (Mathematics) · Semester 1

• Calculus — limits, continuity & differentiability for functions of two variables, partial derivatives, composite functions, total derivative, Euler’s theorem, Jacobians, maxima & minima for several variables, Lagrange’s method of multipliers, approximation of errors
• Multiple Integrals — double & triple integrals, change of order, change of variable, Beta & Gamma functions, Dirichlet’s integral, area & volume
• Vector Calculus — gradient of a scalar field, directional derivatives, divergence & curl, solenoidal & irrotational vectors, integration of vectors, Stokes’ theorem, Gauss–Ostrogradsky divergence theorem
• Matrices — complex matrices (Hermitian, skew-Hermitian, unitary), elementary transformation, rank by echelon form, Gauss elimination & Gauss–Seidel, eigenvalues & eigenvectors, similarity transformation, diagonalization
• Introduction to Vector Space — definition of a field, vector spaces & subspaces, linear dependence & independence, basis and dimension

Engineering Mathematics-I

Covers: The calculus, multiple-integral, matrices and vector-space units — partial differentiation with Lagrange multipliers, Beta & Gamma functions, rank/eigenvalues/diagonalization, and vector spaces with basis and linear transformations.

Engineering Mathematics-II

Covers: The vector-calculus unit — gradient, divergence, curl and the Gauss/Stokes/Green integral theorems.

Introduction to Discrete Structure & Linear Algebra

Covers: The linear-algebra strand from the AI/ML angle that this CS variant emphasises — determinant, trace, eigenvalue decomposition and SVD.

4 credits · 60 NCrF hours · Basic Science (Mathematics) · Semester 2

• Differential Equations — nth-order linear equations with constant coefficients, Cauchy–Euler equation, variation of parameters, change of independent variable, normal form
• Complex Analysis — analytic functions, Cauchy–Riemann equations (Cartesian & polar), harmonic functions, Milne–Thomson method, complex integrals, Cauchy integral theorem & formula, Taylor & Laurent series, singularities, residues, Cauchy residue theorem
• Laplace Transform — standard transforms, shifting theorems, change of scale, transforms of derivatives & integrals, periodic & unit-step functions, inverse transform, partial fractions, convolution, application to ODEs
• Fourier Series & Fourier Transform — Dirichlet’s condition, expansion over c to c+2l, change of interval, half-range sine & cosine series, Parseval’s identity, Fourier integral theorem, Fourier & inverse Fourier transform, finite sine/cosine transforms
• Applied Linear Algebra — eigenvalue & singular value decomposition, matrix factorization, LU (Doolittle) & QR decomposition, linear transformation and its matrix representation, kernel & range, inner product space, norm of a vector

Engineering Mathematics-II

Covers: The differential-equations and complex-analysis units in full — higher-order ODEs and variation of parameters, plus analytic functions, Cauchy–Riemann, Cauchy integral formula, poles, residues and the residue theorem.

Engineering Mathematics-III

Covers: Transform calculus — the Laplace transform, inverse Laplace, convolution theorem and Fourier transforms.

Engineering Mathematics-I

Covers: The Fourier-series half of the transforms unit — half-range sine & cosine series and Parseval’s theorem.

Introduction to Discrete Structure & Linear Algebra

Covers: The applied-linear-algebra unit — eigenvalue decomposition, singular value decomposition (SVD) and Cholesky factorization, written for the AI/data-science context this course targets.

4 credits · 60 NCrF hours · Basic Science (Mathematics) · Semester 1

• Statistical Techniques (AG) — measures of central tendency, mean deviation, standard deviation, skewness & Karl Pearson’s coefficient, principle of least squares, curve fitting of straight line and parabola
• Differential Calculus — limits, continuity & differentiability, derivatives of standard/composite/implicit functions, chain rule, logarithmic & parametric differentiation, maxima & minima
• Integral Calculus — integration by substitution, parts and partial fractions, definite integrals, area under simple curves
• Differential Equations — order & degree, separation of variables, homogeneous equations, exact & Bernoulli equations, higher-order linear equations with constant coefficients
• Matrices & Vector Analysis — types of matrices, determinants, minors & cofactors, adjoint & inverse, solution of linear systems; scalar & vector products, gradient, divergence, curl, directional derivatives

Engineering Mathematics-I

Covers: The calculus and matrices strands — differentiation and its applications, definite & multiple integrals, and the matrix unit (rank, determinants, eigenvalues).

Engineering Mathematics-II

Covers: The differential-equations unit (separable, homogeneous, exact, Bernoulli and higher-order linear equations) and the vector-analysis topics — gradient, divergence and curl.

Introduction to Probability & Statistics

Covers: The AG statistical-techniques unit — central tendency, dispersion, skewness, and curve fitting by least squares.

4 credits · 60 NCrF hours · Basic Science (Mathematics) · Semester 2

• Functions of a Complex Variable — limit, continuity & differentiability, analytic functions, Cauchy–Riemann equations, harmonic & conjugate functions, Milne–Thomson method
• Vector Calculus — vector differentiation, the del operator, gradient, normal & directional derivative, divergence & curl, line/surface/volume integrals, Green’s, Stokes’ and Gauss’ divergence theorems
• Matrices — types of matrices, elementary transformations, rank, reduction to normal & triangular form
• Fourier Series & Partial Differential Equations — Fourier series of periodic functions, formation and solution of PDEs
• Applications of PDE — wave, heat and steady-state flow problems

Engineering Mathematics-II

Covers: The complex-variable, vector-calculus and partial-differential-equation units — analytic functions and Cauchy–Riemann, the full vector-integral theorems, and formation/solution of linear and non-linear PDEs.

Engineering Mathematics-I

Covers: The matrices unit and the Fourier-series topics, including half-range series.

4 credits · 3L–1T–0P · Basic Science Course

• Partial Differential Equations — origin, linear & non-linear PDEs of first order, Lagrange’s method, Charpit’s method, higher-order linear PDEs with constant coefficients
• Applications of PDE & Fourier Transform — separation of variables, one-dimensional heat and wave equations, two-dimensional heat (Laplace) equation, complex Fourier transform, Fourier sine & cosine transforms, convolution theorem
• Statistical Techniques — moments, skewness, kurtosis, curve fitting by least squares, correlation & regression, binomial/Poisson/normal distributions, tests of significance, chi-square, t-test and z-test
• Numerical Techniques I — zeroes by bisection, regula-falsi and Newton–Raphson, rate of convergence; interpolation by finite differences, Newton’s forward & backward formulae, Lagrange’s and Newton’s divided differences
• Numerical Techniques II — solution of linear systems, matrix decomposition, Jacobi and Gauss–Seidel; numerical differentiation & integration (trapezoidal, Simpson’s rules); ODEs by Picard’s and fourth-order Runge–Kutta methods

Engineering Mathematics-III

Covers: Both numerical-techniques units almost completely — bisection, Newton–Raphson, regula-falsi, Newton & Lagrange interpolation, numerical differentiation, trapezoidal & Simpson’s rules, Gauss elimination/Jordan/Seidel, and Runge–Kutta — plus the Fourier-transform half of unit II.

Engineering Mathematics-II

Covers: The partial-differential-equations unit — formation, linear and non-linear PDEs, and homogeneous PDEs with constant coefficients.

Probability & Statistics for Data Science

Covers: The statistical-techniques unit — moments, skewness & kurtosis, curve fitting, correlation & regression, the standard distributions, and the significance tests (t, F, chi-square, z).

4 credits · 3L–1T–0P · Basic Science Course

• Partial Differential Equations — first-order linear & non-linear PDEs, Lagrange’s and Charpit’s methods, higher-order PDEs with constant coefficients
• Applications of PDE & Fourier Transform — separation of variables, heat and wave equations, Laplace equation, complex Fourier transform, sine & cosine transforms, convolution theorem
• Statistical Techniques I — measures of central tendency, moments, skewness & kurtosis, curve fitting, least squares, straight line and second-degree parabola, correlation & rank correlation, regression lines
• Statistical Techniques II — probability, discrete & continuous random variables, probability mass & density functions, expectation and variance, binomial, Poisson and normal distributions
• Statistical Techniques III — sampling theory, hypothesis testing, level of significance, confidence limits, t-test, Z-test and chi-square test, statistical quality control, control charts for variables (X̄, R) and attributes (p, np, c)

Probability & Statistics for Data Science

Covers: The three statistical-techniques units — central tendency & dispersion, moments/skewness/kurtosis, curve fitting, correlation (including rank, partial and multiple) and regression, the standard distributions, and the full significance-test set (t, F, chi-square, Z).

Introduction to Probability & Statistics

Covers: A parallel route through the probability half — probability spaces, conditional probability, random variables and densities, Bayes’ rule, sampling and large-sample significance tests.

Engineering Mathematics-II

Covers: The partial-differential-equations unit — formation, linear & non-linear PDEs and higher-order PDEs with constant coefficients.

Engineering Mathematics-III

Covers: The Fourier-transform topics of unit II and the probability distributions (binomial, Poisson, normal, exponential) of unit IV.

4 credits · 3L–1T–0P · Basic Science Course

• Integral Transforms — Fourier integral & transform, complex Fourier transform, inverse transforms, convolution theorem, sine & cosine transforms, application to heat/wave/Laplace equations; Z-transform and its application to difference equations
• Probability Distributions — random variables, probability mass & density functions, binomial, Poisson and normal distributions
• Numerical Techniques — bisection, regula-falsi and Newton–Raphson methods, rate of convergence; interpolation by finite differences, Newton’s forward & backward formulae, Lagrange’s and Newton’s divided differences
• Tests of Hypothesis & ANOVA — level of significance, critical region, Student’s t-test, chi-square test, F-test, one-way and two-way analysis of variance
• Design & Quality Control — principles of experimental design, completely randomized design, randomized block design, Latin square design, statistical quality control, control charts for variables and attributes

Engineering Mathematics-III

Covers: The numerical-techniques unit in full (bisection, Newton–Raphson, regula-falsi, Newton & Lagrange interpolation), the Fourier-transform half of the integral-transforms unit, and the probability distributions.

Probability & Statistics for Data Science

Covers: The probability-distribution unit and the hypothesis tests — t-test, F-test, chi-square and Z-test.

Introduction to Discrete Structure & Linear Algebra

Covers: The analysis-of-variance (ANOVA) topics of the hypothesis-testing unit.