Course

Unit 1

Ordinary Differential Equations: First Order Differential Equations – Basic concepts, Exact ODEs, and Integrating factors, Linear differential equations of the first order.

Unit 2

Second Order Differential Equations – linear homogeneous ODE of second order with constantcoefficients. Euler-Cauchy Equations. Solution of second-order linear non-homogeneous ODE by the method of Undetermined Coefficients and by the method of Variation of Parameters.

Unit 3

Laplace Transform: Laplace Transforms, Inverse Transforms, Linearity, s-shifting, Transforms of Derivatives and Integrals, Unit Step Function, t-shifting, partial fractions, solution of initial value problems and system of Differential Equations.

Unit 4

Fourier Series and Fourier Transform: Fourier series, Half range Expansions, Fourier Integrals, Fourier Sine, and Cosine Integrals. Fourier Transforms, Sine and Cosine Transforms, Properties.

Unit 5

Partial Differential Equations: Basic Concepts, Modeling, Vibrating String, Wave Equation, Separation of Variables, solution by Fourier Series. Heat Equation, Solution by Fourier Series.

CO1: Analyze linear and nonlinear differential equations and solve ordinary differential equations of first order.

CO2: Apply various techniques to solve second-order linear homogeneous and nonhomogeneous, differential equations

CO3: Explore Laplace Transforms, properties of Laplace Transform, inverse Laplace Transform, and some of its applications to solve differential equations.

CO4: Apply and solve problems on Fourier series, Fourier integrals, and Fourier Transforms.

CO5: Employ partial differential equations to solve Heat and Wave equations using Fourier series.

TEXTBOOK:

1. Advanced Engineering Mathematics, Erwin Kreyszig, Wiley India, Tenth Edition, 2015.

REFERENCE BOOKS:

1. George Turrell, Mathematics for Chemistry and Physics, Academic Press, 2002.

2. Robert G. Mortimer, Mathematics for Physical Chemistry, 3rd Edition, Elsevier, 200