B.E. I Sem (All Branches)

I SEMESTER

102. ENGINEERING MATHEMATICS - I

Units & Contents of the Subject

I. Differential Calculus

  •  Asymptotes (Cartesian Coordinates Only)

  •  Curvature

  •  Concavity, Convexity and Point of Inflexion (Cartesian Coordinates Only)

  •  Curve Tracing (Cartesian and Standard Polar Curves – Cardioids, Lemniscates of

  •  Bernoulli, Limacon, Equiangular Spiral)

II. Differential Calculus

  •  Partial Differentiation, Euler’s Theorem on Homogeneous Functions

  •  Approximate Calculations

  •  Maxima & Minima of Two and More Independent Variables

  •  Lagrange’s Method of Multipliers

III. Integral Calculus

  •  Applications in Finding the Length of Simple Curves

  •  Surface and Volumes of Solids of Revolution

  •  Double Integral, Areas & Volumes by Double Integration

  •  Change of Order of Integration

  •  Beta Function and Gamma Function (Simple Properties)

IV. Differential Equations

  • Differential Equations of First Order and First Degree – Variable Separable,

  • Homogeneous Forms, Reducible to Homogeneous Form, Linear Form, Exact Form,

  • Reducible to Exact Form

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  • Linear Differential Equations of Higher Order with Constant Coefficients Only

V. Differential Equations

  • Second Order Ordinary Differential Equations with Variables Coefficients

  • Homogeneous and Exact Forms

  • Change of Dependent Variable

  • Change of Independent Variable, Normal Forms

  • Method of Variation of Parameter