Engineering Mathematics Notes VTU – M1 Notes VTU of Total Modules
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M1 Notes VTU – Engineering Mathematics Notes VTU – VTU M1 Notes
Differential Calculus -1: Determination of nth order derivatives of Standard functions – Problems. Leibnitz‟s theorem (without proof) – problems. Polar Curves – angle between the radius vector and tangent, angle between two curves, Pedal equation for polar curves. Derivative of arc length – Cartesian, Parametric and Polar forms (without proof) – problems. Curvature and Radius of Curvature – Cartesian, Parametric, Polar and Pedal forms(without proof) and problems.
Differential Calculus -2 Taylor‟s and Maclaurin‟s theorems for function of o ne variable(statement only)- problems. Evaluation of Indeterminate forms. Partial derivatives – Definition and simple problems, Euler‟s theorem(without proof) – problems, total derivatives, partial differentiation of composite functions-problems, Jacobians-definition and problems.
Vector Calculus: Derivative of vector valued functions, Velocity, Acceleration and related problems, Scalar and Vector point functions.Definition Gradient, Divergence, Curl- problems . Solenoidal and Irrotational vector fields. Vector identities – div ( F A), curl ( F A),curl (grad F ), div (curl A). 10hrs.
Integral Calculus: Reduction formulae ∫ sinnx dx ∫cosnx dx ∫sinnxcosmxdx,, (m and n are positive integers), evaluation of these integrals with standard limits (0 to л/2) and problems. Differential Equations: Solution of first order and first degree differential equations – Exact, reducible to exact and Bernoulli‟s differential equations. Applications- orthogonal trajectories in Cartesian and polar forms. Simple problems on Newton‟s law of cooling.
Linear Algebra Rank of a matrix by elementary transformations, solution of system of linear equations – Gauss- elimination method, Gauss- Jordan method and Gauss-Seidel method. Rayleigh‟s power method to find the largest Eigen value and the corresponding Eigen vector. Linear transformation, diagonalisation of a square matrix, Quadratic forms, reduction to Canonical form.