Mathematics 2 syllabus 2nd semester Aktu

Mathematics 2 syllabus 2nd Semester Aktu

Chapter 1: Ordinary Differential Equation of Higher Order 

Linear differential equation of nth order with constant coefficients, Simultaneous linear differential equations, Second-order linear differential equations with variable coefficients, Solution by changing independent variable, Reduction of order, Normal form, Method of variation of parameters, Cauchy-Euler equation, Series solutions (Frobenius Method). 

Chapter 2: Multivariable Calculus-II 

Improper integrals, Beta & Gama function and their properties, Dirichlet’s integral and its applications, Application of definite integrals to evaluate surface areas and volume of revolutions. Module 3: Sequences and Series [08] 
Definition of Sequence and series with examples, Convergence of sequence and series, Tests for convergence of series, (Ratio test, D’ Alembert’s test, Raabe’s test). Fourier series, Half range Fourier sine and cosine series. 

Chapter 4: Complex Variable – Differentiation 

Limit, Continuity and differentiability, Functions of complex variable, Analytic functions, Cauchy- Riemann equations (Cartesian and Polar form), Harmonic function, Method to find Analytic functions, Conformal mapping, Mobius transformation and their properties 

Chapter 5: Complex Variable –Integration 

Complex integrals, Contour integrals, Cauchy- Goursat theorem, Cauchy integral formula, Taylor’s series, Laurent’s series, Liouvilles’s theorem, Singularities, Classification of Singularities, zeros of analytic functions, Residues, Methods of finding residues, Cauchy Residue theorem, Evaluation of real integrals of the type and . 

COURSE OUTCOMES 

1. Understand the concept of differentiation and apply for solving differential equations. 
2. Remember the concept of definite integral and apply for evaluating surface areas and volumes. 
3. Understand the concept of convergence of sequence and series. Also evaluate Fourier series 
4. Illustrate the working methods of complex functions and apply for finding analytic functions. 
5. Apply the complex functions for finding Taylor’s series, Laurent’s series and evaluation of definite integrals.