AM-101-ENGINEERING MATHEMATICS – I |
PART – A |
1. Differential Calculus: Curve tracing, Curvature of Cartesian curves;
Curvature of parametric and polar curves.
2. Integral Calculus: Rectification of standard curves; Areas bounded by
standard curves; Volumes and surfaces of revolution of curves; Centre of
gravity and Moment of inertia of simple bodies by integral calculus and of
composite areas by the principle of moments; Applications of integral
calculus to find centre of pressure, mean and root mean square values.
3. Partial Derivatives: Function of two or more variables; Partial
differentiation; Homogeneous functions and Euler’s theorem; Composite
functions; Total derivative; Derivative of an implicit function; Change of
variable; Jacobians.
4. Applications of partial differentiation : Tangent and normal to a surface;
Taylor’s and Maclaurin’s series for a function of two variables; Errors and
approximations; Maxima and minima of function of several variables;
Lagrange’s method of undetermined multipliers.
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PART-B |
5. Solid Geometry: Sphere, cylinder, cone, standard conicoids (Ellipsoid,
Paraboloid and Hyperboloid).
6. Multiple Integral: Double and triple integration, change of order of
integration, change of variable. Application of double integration to find
areas. Application of double & triple integration to find volumes, Beta and
gamma functions.
7. Infinite Series : Convergence and divergence of series, Test of convergence :
Comparison test, Integral test, Ratio test, Rabee’s test, Logarithmic
test,Cauchy’s root test. Convergence and absolute convergence of alternating
series, Power series and Uniform convergence.
8. Complex Numbers: De-Moivre’s theorem and applications, exponential &
logarithmic complex functions, circular and hyperbolic functions of complex
variables, real and imaginary parts of inverse functions. Summation of
trigonometric series.
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TEXT BOOKS |
1. Jain, R.K. and lyengar, S.R.K., Advanced Engineering Mathematics, Narosa
Publishing House, New Delhi.
2. Grewal, B.S., Higher Engineering Mathematics, Khanna Publishers, New Delhi.
3. Bali, N.P., A Text Book on Engineering Mathematics, Luxmi Publications, New
Delhi.
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REFERENCE BOOKS |
1. Kreyszig, E., Advanced Engineering Mathematics, John Wiley.
2. Ray Wylie, C., Advanced Engineering Mathematics,6th ed., McGraw Hill.
3. Zill D.G., and Cullen, M.R., Advanced Engineering Mathematics, CBS
Publishers.
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