Engineering Mathematics-I (BAS103) AKTU syllabus – unit-wise topics
The complete Engineering Mathematics-I syllabus for AKTU, unit by unit. Next to each topic you can see how often it has appeared in past papers, so you know where the marks are.
Unit 1: Matrices
- Elementary Transformations – asked 3 times
- Inverse of a Matrix – asked 1 times
- Rank of a Matrix – asked 7 times
- Solution of Systems of Linear Equations – asked 7 times
- Characteristic Equation
- Cayley-Hamilton Theorem and Its Applications – asked 4 times
- Linear Dependence and Independence of Vectors – asked 2 times
- Eigenvalues and Eigenvectors – asked 11 times
- Complex Matrices: Hermitian, Skew-Hermitian and Unitary – asked 2 times
- Applications of Matrices to Engineering Problems
Unit 2: Differential Calculus-I
- Successive Differentiation (nth-Order Derivatives) – asked 12 times
- Leibnitz Theorem
- Curve Tracing – asked 6 times
- Partial Derivatives – asked 2 times
- Euler's Theorem for Homogeneous Functions – asked 10 times
- Total Derivative – asked 2 times
- Change of Variables – asked 2 times
- Rolle's, Lagrange's and Cauchy's Mean Value Theorems – asked 7 times
- Envelopes of Families of Curves – asked 2 times
- Continuity and Differentiability – asked 1 times
Unit 3: Differential Calculus-II
- Taylor's and Maclaurin's Expansions for Functions of One and Two Variables – asked 5 times
- Maxima and Minima of Functions of Several Variables – asked 3 times
- Lagrange's Method of Multipliers – asked 8 times
- Jacobians – asked 12 times
- Approximation of Errors – asked 4 times
Unit 4: Multiple Integration
- Double Integrals – asked 10 times
- Triple Integrals – asked 7 times
- Change of Order of Integration – asked 7 times
- Change of Variables – asked 5 times
- Beta and Gamma Functions and Their Properties – asked 4 times
- Dirichlet's Integral and Its Applications to Area and Volume – asked 3 times
- Liouville's Extensions of Dirichlet's Integral – asked 1 times
Unit 5: Vector Calculus
- Gradient, Curl, Divergence and Their Physical Interpretations – asked 15 times
- Directional Derivatives – asked 6 times
- Line Integrals
- Surface Integrals
- Volume Integrals
- Gauss' Divergence Theorem (Without Proof) and Applications – asked 6 times
- Green's Theorem (Without Proof) and Applications – asked 3 times
- Stokes' Theorem (Without Proof) and Applications – asked 5 times
- Laplacian and Radial Scalar Fields – asked 2 times