RTU 1st Year 1st Sem B.Tech. Syllabus Engineering Mathematics.

102 ENGINEERING MATHEMATICS-I

Unit 1

Differential Calculus:Asymptotes(Cartesian Coordinates Only), Curvature(Cartesian Coordinates
Only), Concavity, Convexity and Point of Inflexion (Cartesian Coordinates Only), Curve Tracing
(Cartesian and Standard Polar Curves-Cardioids, Lemniscates of Bernoulli, Limacon,
Equiangular Spiral).

Unit 2

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.

Unit 3

Integral Calculus: Surface and Volumes of Solids of Revolution, Double Integral, Double
Integral by changing into polar form , Areas & Volumes by Double Integration ,Change of Order
of Integration, Beta Function and Gamma Function (Simple Properties).

Unit 4

Differential Equations: Differential Equations of First Order and First Degree - Linear Form,
Reducible to Linear form, Exact Form, Reducible to Exact Form, Linear Differential Equations
of Higher Order with Constant Coefficients Only.

Unit 5

Differential Equations: Second Order Ordinary Differential Equations with Variables
Coefficients, Homogeneous and Exact Forms, Change of Dependent Variable, Change of
Independent Variable, Method of Variation of Parameters.