ENGINEERING MATHEMATICS – 1

Unit-I

Differential Calculus:

Determination of nth derivative of standard functions. Leibnitz’s theorem (without proof) and Problems. Polar curves and angle between Polar curves. Pedal equations of polar curves.

Unit-II

Partial differentiation:

Partial Derivatives, Euler’s Theorem. Total differentiation. Differentiation of Composite and implicit functions. Jacobians and their properties. Errors and approximations.

Unit-III

Integral Calculus:

Reduction formulae for the integration of sinnx, cosnx, tannx, cotnx, secnx, cosecnx, and sinmxcosnx and evaluation of these integrals with standard limits – Problems. Tracing of standard curves in Cartesian form, Parametric form and Polar form.

Unit-IV

Applications of Integral Calculus:

Derivative of arc length. Applications to find area and length of given curves. Volumes and surface areas of solids of revolution. Differentiation under integral sign (Integrals with constant limits)

Unit-V

Differential Equations:

Solution of first order and first degree differential equations: variables separable, homogeneous, exact, linear and equations reducible to above types. Illustrative examples from Engineering Field. Orthogonal trajectories of Cartesian and polar curves.

Unit-V|

Infinite Series:

Convergence, divergence and oscillation of an infinite series, comparison test, p-series, D’Alembert’s ratio test, Raabe’s test, Cauchy’s root test, Cauchy’s integral test (all tests without proof) for series of positive terms. Alternating series, Absolute and Conditional convergence. Leibnitz’s test (without proof) and Problems.

Unit-VII

Analytical Geometry in three dimensions:

Direction cosines and direction ratios. Planes, Straight lines, Angle between planes / straight lines, Coplanar lines. Shortest distance between two skew lines.

Unit-VIII

Vector Calculus:

Vector differentiation. Velocity, Acceleration of a particle moving on a space curve. Vector point function. Gradient, Divergence, Curl, Laplacian. Solenoidal and Irrotational vectors - Problems.

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VTU - BE - Syallabus - ENGINEERING MATHEMATICS – I

ENGINEERING MATHEMATICS – 1

Unit-I

Unit-II

Unit-III

Unit-IV

Unit-V

Unit-V|

Unit-VII

Unit-VIII

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