Engineering Math 1 engineering mathematics introduction

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Derivatives and their Applications(14 hours) • Introduction • Higher order derivatives • Mean value theorem • Rolle’s Theorem • Lagrange’s Mean Value Theorem • Cauchy’s Mean Value Theorem • Power series of Single Valued Function • Taylor’s Series • Maclaurin’s Series • Indeterminate forms: L’Hospital Rule • Asymptotes to Cartesian and Polar Curves • Pedal equations to Cartesian and Polar Curves: Curvature and Radius of Curvature • Integration and its Applications(11 hours) • Introduction • Definite Integrals and their properties • Improper Integrals • Differentiation under Integral Sign • Reduction formula: Beta Gama functions • Application of Integrals for finding areas, arc length, surface and solid of revolution in the plane for Cartesian and Polar curves • Plane Analytic Geometry(8 hours) • Transformation of Coordinates: Translation and rotation • Ellipse and Hyperbola: Standard forms. Tangent, and Normal • General equation of conics in Cartesian and Polar forms • Ordinary Differential Equations and their Applications (12 hours) • First order and first degree Differential equations • Homogenous Differential equations • Linear differential equations • Equations reducible to linear Differential equations: Bernoulli’s equation • First order and Higher degree differential equation: Clairaut’s equation • Second order and First degree linear differential equations with constant coefficients • Second order and First degree linear differential equations with variable coefficients: Cauchy’s equations • Applications in Engineering 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