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BAS103AKTU · Sem 1

Engineering Mathematics-I

AKTU B.Tech first year scheme (BAS series, from session 2022-23) · 100 marks: 70 end-sem theory (3 hours) + 30 sessional (20 class tests + 10 teacher assessment). End-sem paper: Section A 7 x 2 = 14 (all compulsory), Section B any 3 of 5 x 7 = 21, Section C 5 questions with one part to attempt from each x 7 = 35 (one question per unit). L-T-P 3-1-0, 4 credits.

Official syllabus

Revised 0 of 109 high-repeat questions

One-Night Pass Pack

Write |A - λI| = 0 as λ^3 - S1 λ^2 + S2 λ - |A| = 0 (S1 = trace, S2 = sum of principal 2x2 minors). Compute A^2 and A^3, then show A^3 - S1 A^2 + S2 A - |A| I = O. Multiply by A^-1: A^-1 = (A^2 - S1 A + S2 I) / |A|. For A^-2, A^-3 multiply again by A^-1.
Full-marks tip: State the theorem in one line first. Show A^2 and A^3 fully; most marks are lost to arithmetic slips there. Check your A^-1 by verifying A x A^-1 = I in a line at the end.

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Unit-wise syllabus

U1Matrices

Weightage: Not officially published (Section C has one question per unit; Sections A and B are spread across units)

Elementary transformations, inverse and rank of a matrixSolution of system of linear equations (consistency)Characteristic equation and Cayley-Hamilton theorem with applicationsLinear dependence and independence of vectorsEigenvalues and eigenvectorsComplex matrices: Hermitian, skew-Hermitian and unitaryEngineering applications

U2Differential Calculus-I

Weightage: Not officially published (Section C has one question per unit; Sections A and B are spread across units)

Successive differentiation (nth order derivatives)Leibnitz theorem and its applicationsCurve tracing (Cartesian and polar)Partial derivativesEuler's theorem for homogeneous functionsTotal derivative and change of variables

U3Differential Calculus-II

Weightage: Not officially published (Section C has one question per unit; Sections A and B are spread across units)

Taylor's and Maclaurin's theorems for one and two variablesMaxima and minima of functions of several variablesLagrange's method of multipliersJacobiansApproximation of errors

U4Multiple Integration

Weightage: Not officially published (Section C has one question per unit; Sections A and B are spread across units)

Double and triple integralsChange of order of integrationChange of variablesBeta and Gamma functions and their propertiesDirichlet's integral and applications to area and volumeLiouville's extension of Dirichlet's integral

U5Vector Calculus

Weightage: Not officially published (Section C has one question per unit; Sections A and B are spread across units)

Gradient, divergence and curl with physical meaningDirectional derivativeLine, surface and volume integralsGauss divergence theorem, Green's theorem and Stokes' theorem (without proof) with applications

Curated video lectures

Free lectures from well-known educators, matched to units. Videos load only when you tap “Watch here”, to save data.

Full BAS103 course, all 5 units

Tending to Infinity · Playlist · 34 videos · Hinglish

Unit 1 Matrices (rank, Cayley-Hamilton, eigenvalues) for BAS103

Fearless Innocent Math · Playlist · 12 videos · Hinglish · Unit 1

Partial differentiation, Euler's theorem, Jacobians, maxima and minima

Dr. Gajendra Purohit · Playlist · 17 videos · Hinglish · Unit 3

Integral calculus: double integrals and applications

Dr. Gajendra Purohit · Playlist · 20 videos · Hinglish · Unit 4

Vector calculus: gradient, divergence, curl, Gauss, Green and Stokes

Dr. Gajendra Purohit · Playlist · 12 videos · Hinglish · Unit 5

Exam Guide Radar

Standard textbook

B. V. Ramana, Higher Engineering Mathematics (McGraw-Hill); also B. S. Grewal, Higher Engineering Mathematics (Khanna Publishers) and R. K. Jain & S. R. K. Iyengar, Advanced Engineering Mathematics (Narosa), as listed in the syllabus

Exam guide students buy

Quantum Series: Engineering Mathematics-I (Quantum Publications), AKTU first year

Unit-wise short and long answers with solved AKTU papers. Buy the edition that matches your scheme code (BCS/BAS, not the old KCS/KAS).

Local market tip

Buy the Quantum edition printed for BAS103 (2023 or later) from shops near your college or Aminabad in Lucknow; avoid older KAS103T editions, which carry the 100-mark paper pattern and a different unit 2.