Course

Differentiation: Derivatives. Applications of Derivative: Mean Value theory Concavity and Curve Sketching Maxima and Minima.Differential Equations of First Order: Formation of Differential Equations. Solutions of Differential Equations (Variable Separable, Homogeneous Equations and Equations reducible to Homogeneous Form, Linear and Equations reducible to Linear Form, Exact Differential Equations and Equations reducible to Exact form). Differential Equations not of the first degree (solvable for p, solvable for y, solvable for x, Clairauts Equation). Applications.Differential Equations of Higher Order: Homogeneous Linear Differential Equations with Constant Coefficient and Euler- Cauchy Differential Equations, Basis of Solutions and Wronskian. Non- Homogeneous Equations – Method of Undetermined Coefficients and Method of Variation of Parameters.

Course Outcomes:CO1: To understand the basic concept of derivatives and its applications in Physics.CO2: Define first-order ordinary differential equations and demonstrate ability to use techniques to solve them and apply these solutions in engineering contexts.CO3: Solving the higher order ODE using method of undetermined coefficient and other methods.

TEXT BOOKS1.Advanced Engineering Mathematics, Erwin Kreyszig, John Wiley and Sons, 10th edition, 2023.2.Vector Calculus with Applications to Physics, Shaw James Byrnie 2009.3.Advanced Engineering Mathematics by Dennis G. Zill and Michael R.Cullen, second edition, CBS Publishers, 2012.