## Engineering mathematics - IDifferential 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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### Contents

Table of Contents | 1-1 |

Chapter 1 Differential Calculus 11 to 176 | 1-76 |

Chapter 3 Applications of Partial Differentiation 3 1 to 3 | 2-74 |

Chapter2 Partial Derivatives 21 to 278 | 2-78 |

Chapter 5 Multiple integral and Integral Calculus 51 to 5220 | 5-2 |

Chapter 3 Applications of Partial Differentiation 31 to 374 | 5-74 |

Chapter 4 Solid Geometry 41 to 4126 | 126 |

Chapter 5 Multiple Integral and Integral Calculus 51to5220 | 220 |

Chapter 7 Complex Numbers 71 to 7 156 | 7-1 |

University Question Papers P1toP26 | P-26 |

### Common terms and phrases

a n is convergent absolutely convergent an+i asymptotes parallel axis cardioid Cauchy's Root Test centre co-efficient co-ordinates composite function converge or diverge cos0 cos2 cos6 cos8 cosG cosh cosP cylinder D'Alembert's Ratio Test Differentiating w.r.t. dx dx dx dy dz dxdy dy dx dz dz ellipse Equating real equation of sphere Euler's theorem Evaluate Example Find the area Find the equation Find the radius function of degree Given curve highest power homogeneous function isin latus rectum lowest degree term maximum meets x-axis minimum value moment of inertia parabola parallel to x-axis partial derivatives partially w.r.t. perpendicular Prove quadric radius of curvature Ratio Test region required equation right circular sec2 sequence sin0 sin2 sin6 sin8 sinh Solution sphere x2 surface symmetrical tangent plane tanh y-axis