Dr A.P.J. Abdul Kalam Technical University, UP (AKTU), Computer Engineering Semester 2, Mathematics-II Syllabus

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Unit - 1 Ordinary Differential Equation of Higher Order

1.1 Linear differential equation of nth order with constant coefficients

1.2 Simultaneous linear differential equations

1.3 Second order linear differential equations with variable coefficients

1.4 Solution by changing independent variable

1.5 Reduction of order Normal form

1.6 Method of variation of parameters

1.7 CauchyEuler equation

1.8 Series solutions Frobenius Method

Unit - 2 Multivariable Calculus-II

2.1 Improper integrals

2.2 Beta Gama function and their properties

2.3 Dirichlet’s integral and its applications

2.4 Application of definite integrals to evaluate surface areas and volume of revolutions

Unit - 3 Sequences and Series

3.1 Definition of Sequence and series with examples

3.2 Convergence of sequence and series

3.3 Tests for convergence of series

3.4 Ratio test D’ Alembert’s test Raabe’s test

3.5 Fourier series Half range Fourier sine and cosine series

Unit - 4 Complex Variable – Differentiation

4.1 Functions of complex variable Limit Continuity and differentiability

4.2 Analytic functions

4.3 Cauchy Riemann equations Cartesian and Polar form

4.4 Harmonic function

4.5 Method to find Analytic functions

4.6 Conformal mapping

4.7 Mobius transformation and their properties

Unit - 5 Complex Variable –Integration

5.1 Complex integrals Contour integrals

5.2 Cauchy Goursat theorem

5.3 Cauchy integral formula

5.4 Taylor’s series Laurent’s series Liouvilles’s theorem

5.5 Singularities Classification of Singularities zeros of analytic functions

5.6 Residues Methods of finding residues Cauchy Residue theorem

5.7 Evaluation of real integrals of the type and

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Other Subjects of Semester-2
Physics
Chemistry
Soft skills-ii
Basic electrical engineering
Programming for problem solving
Emerging technology for engineering
Emerging domain in electronics engineering
Fundamentals of mechanical engineering & mechatronics
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