Part A (Maths I): differential calculus, Leibnitz and Taylor, partial differentiation, Jacobians, matrices and eigenvalues, beta/gamma functions, multiple integrals, vector calculus. Part B (Maths II): differential equations, Laplace transforms, Fourier series and complex analysis. Worked examples throughout.
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AKTU end-semester examination, March 2023. Course code AS101 / EAS103 / KAS103 / TAS104.
AKTU end-semester examination, 2015. Course code AS101 / EAS103 / KAS103 / TAS104.
AKTU end-semester examination, 2014. Course code AS101 / EAS103 / KAS103 / TAS104.
AKTU end-semester examination, 2013. Course code AS101 / EAS103 / KAS103 / TAS104.
AKTU end-semester examination, 2012. Course code AS101 / EAS103 / KAS103 / TAS104.
AKTU end-semester examination, 2022. Course code KAS103.
AKTU end-semester examination, 2021. Course code KAS103.
AKTU end-semester examination, 2020. Course code KAS103.
AKTU end-semester examination, 2019. Course code KAS103.
Official AKTU syllabus, unit-wise, from the 2020-21 AICTE model curriculum (KAS / KCS / KEE / KEC / KME). Source: https://aktu.ac.in/pdf/syllabus/syllabus2021/B.Tech.%20Ist%20Year%20Common%20AICTE%20Model%20Curriculum%202020-21%2025082021.pdf
Matrices: Types of Matrices: Symmetric, Skew-symmetric and Orthogonal Matrices; Complex Matrices, Inverse and Rank of matrix using elementary transformations, Rank-Nullity theorem; System of linear equations, Characteristic equation, Cayley-Hamilton Theorem and its application, Eigen values and eigenvectors; Diagonalisation of a Matrix
Differential Calculus- I: Introduction to limits, continuity and differentiability, Rolle’s Theorem, Lagrange’s Mean value theorem and th Cauchy mean value theorem, Successive Differentiation (n order derivatives), Leibnitz theorem and its application, Envelope of family of one and two parameter, Curve tracing: Cartesian and Polar co-ordinates
Differential Calculus-II: Partial derivatives, Total derivative, Euler’s Theorem for homogeneous functions, Taylor and Maclaurin’s theorems for a function of two variables, Maxima and Minima of functions of several variables, Lagrange Method of Multipliers, Jacobians, Approximation of errors
Multivariable Calculus-I: Multiple integration: Double integral, Triple integral, Change of order of integration, Change of variables, Application: Areas and volumes, Center of mass and center of gravity (Constant and variable densities)
Vector Calculus: Vector identities (without proof), Vector differentiation: Gradient, Curl and Divergence and their Physical interpretation, Directional derivatives. Vector Integration: Line integral, Surface integral, Volume integral, Gauss’s Divergence theorem, Green’s theorem and Stoke’s theorem (without proof) and their applications