Hello B.Tech students,
Mathematics-1 is a fundamental course in the B.Tech curriculum that provides students with a strong mathematical foundation. This course covers a range of topics, including differential and integral calculus, differential equations, and linear algebra. In differential calculus, students learn how to analyze the behavior of functions and their derivatives, while integral calculus teaches them how to calculate areas, volumes, and other quantities using integrals. Differential equations are used to model real-world phenomena, and linear algebra provides a powerful tool for solving systems of linear equations and studying vector spaces. Mathematics-1 lays the groundwork for advanced mathematical concepts that are essential for many fields of engineering, such as control systems, signal processing, and optimization. It also teaches critical problem-solving skills that are applicable in a wide range of professional and academic settings. By studying Mathematics-1, B.Tech students gain a deep understanding of the principles of mathematics and its applications in engineering, which prepares them for success in their future careers.
I am sharing Mathematics-1 question bank with answers and solutions in Q&A format for engineering/BTech first year. This is available as a PDF file for free download below.
List of topics covered in Mathematics-1 question bank with solutions (Q&A) for engineering/BTech first year:
Mathematics-1 is a fundamental course in the B.Tech curriculum that provides students with a strong mathematical foundation. This course covers a range of topics, including differential and integral calculus, differential equations, and linear algebra. In differential calculus, students learn how to analyze the behavior of functions and their derivatives, while integral calculus teaches them how to calculate areas, volumes, and other quantities using integrals. Differential equations are used to model real-world phenomena, and linear algebra provides a powerful tool for solving systems of linear equations and studying vector spaces. Mathematics-1 lays the groundwork for advanced mathematical concepts that are essential for many fields of engineering, such as control systems, signal processing, and optimization. It also teaches critical problem-solving skills that are applicable in a wide range of professional and academic settings. By studying Mathematics-1, B.Tech students gain a deep understanding of the principles of mathematics and its applications in engineering, which prepares them for success in their future careers.
I am sharing Mathematics-1 question bank with answers and solutions in Q&A format for engineering/BTech first year. This is available as a PDF file for free download below.
List of topics covered in Mathematics-1 question bank with solutions (Q&A) for engineering/BTech first year:
- Unit I - 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
- Unit II - Differential Calculus- I: Introduction to limits, continuity and differentiability, Rolle’s Theorem, Lagrange’s Mean value theorem and Cauchy mean value theorem, Successive Differentiation (nth order derivatives), Leibnitz theorem and its application, Envelope of family of one and two parameter, Curve tracing: Cartesian and Polar co-ordinates
- Unit III - 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
- Unit IV - 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)
- Unit V - 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