Engineering mathematics - I

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Technical Publications, 2008 - 860 pages
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Differential Calculus
Curve tracing, Curvature of Cartesian curves, Curvature of parametric and polar curves.
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.
Partial Derivatives
Function of two or more variables, Partial differentiation, Homogeneous functions and Euler's theorem, Composite functions, Total derivatives, Derivative of implicit function, Change of variables, Jacobianes.
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.
Solid Geometry
Sphere, Cylinder, Cone, Standard conicoids (Ellipsoid, Paraboloid and Hyperboloid).Multiple Integral
Double and triple integration, Change of order of integration, Change of variable, Application of double integration to find areas. Application of double and triple integration to find volumes, Beta and Gamma functions.
Infinite Series
Convergence and divergence of series, Tests 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.
Complex Numbers
De-Moivre's theorem and applications, Exponential and 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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Table of Contents
Chapter 1 Differential Calculus 11 to 176
Chapter 3 Applications of Partial Differentiation 3 1 to 3
Chapter2 Partial Derivatives 21 to 278
Chapter 5 Multiple integral and Integral Calculus 51 to 5220
Chapter 3 Applications of Partial Differentiation 31 to 374
Chapter 4 Solid Geometry 41 to 4126
Chapter 5 Multiple Integral and Integral Calculus 51to5220
Chapter 7 Complex Numbers 71 to 7 156
University Question Papers P1toP26

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