Unit-1 (16 Lectures, Mark: 20)
Ordinary Differential Equations: First Order Ordinary Differential Equations, Basic Concepts, Separable
Ordinary Differential Equations, Exact Ordinary Differential Equations, Linear Ordinary Differential
Equations. Second Order homogeneous and non-homogeneous Differential Equations.
Series solution of differential equations and special functions: Power series method, Legendre
Polynomials, Frobenius Method, Bessel’s equations and Bessel’s functions of first and second kind. Error
functions and gamma function.
Unit-2 (14 Lectures, Mark: 20)
Matrices: Introduction to Matrices, System of Linear Algebraic Equations, Gaussian Elimination Method,
Gauss -Seidel Method, LU decomposition, Solution of Linear System by LU decomposition. Eigen Values
and Eigen Vectors, Linear Transformation, Properties of Eigen Values and Eigen Vectors, Cayley-Hamilton
Theorem, Diagonalization, Powers of a Matrix. Real and Complex Matrices, Symmetric, Skew Symmetric,
Orthogonal Quadratic Form, Hermitian, Skew Hermitian, Unitary Matrices.
Unit-3 (14 Lectures, Mark: 20)
Sequences and series: Sequences, Limit of a sequence, Convergence, Divergence and Oscillation of a
sequence, Infinite series, Necessary condition for Convergence, Cauchy’s Integral Test, D’Alembert’s Ratio
Test, Cauchy’s nth Root Test, Alternating Series, Leibnitz’s Theorem, Absolute Convergence and Conditional
Convergence, Power Series.
Unit-4 (16 Lectures, Mark: 20)
Complex Variables and Functions: Complex Variable, Complex Function, Continuity, Differentiability,
Analyticity. Cauchy-Riemann (C- R) Equations, Harmonic and Conjugate Harmonic Functions, Exponential
Function, Trigonometric Functions, Hyperbolic Functions. Line Integral in Complex Plane, Cauchy’s Integral
Theorem, Cauchy’s Integral Formula, Derivative of Analytic Functions. Sequences, Series and Power Series,
Taylor’s Series, Laurent Series, Zeroes and Poles. Residue integration method, Residue integration of real
Integrals.
Suggested Books
1. E. Kreyszig, advanced engineering mathematics, Wiley India (2008)
2. Murray Spiegel, Seymour Lipschutz, John Schiller, Outline of Complex Variables, Schaum Outline
Series, Tata McGraw Hill (2007)
3. R. K. Jain, and S.R.K. Iyengar, Advanced Engineering Mathematics, Narosa Publishing House
(2007)
4. C .R. Wylie and L. C. Barrett, Advanced Engineering Mathematics, Tata McGraw-Hill (2004)
5. B. V. Ramana, Higher Engineering Mathematics, Tata McGraw Hill Publishing Company Limited
(2007)
Mathematics Foundation for Electronics Lab (Scilab/MATLAB/ any other Mathematical Simulation
software)
1. Solution of First Order Differential Equations
2. Solution of Second Order homogeneous Differential Equations
3. Solution of Second Order non-homogeneous Differential Equations
4. Convergence of a given series.
5. Divergence of a given series.
6. Solution of linear system of equations using Gauss Elimination method.
7. Solution of linear system of equations using Gauss – Seidel method.
8. Solution of linear system of equations using L-U decomposition method.
Ordinary Differential Equations: First Order Ordinary Differential Equations, Basic Concepts, Separable
Ordinary Differential Equations, Exact Ordinary Differential Equations, Linear Ordinary Differential
Equations. Second Order homogeneous and non-homogeneous Differential Equations.
Series solution of differential equations and special functions: Power series method, Legendre
Polynomials, Frobenius Method, Bessel’s equations and Bessel’s functions of first and second kind. Error
functions and gamma function.
Unit-2 (14 Lectures, Mark: 20)
Matrices: Introduction to Matrices, System of Linear Algebraic Equations, Gaussian Elimination Method,
Gauss -Seidel Method, LU decomposition, Solution of Linear System by LU decomposition. Eigen Values
and Eigen Vectors, Linear Transformation, Properties of Eigen Values and Eigen Vectors, Cayley-Hamilton
Theorem, Diagonalization, Powers of a Matrix. Real and Complex Matrices, Symmetric, Skew Symmetric,
Orthogonal Quadratic Form, Hermitian, Skew Hermitian, Unitary Matrices.
Unit-3 (14 Lectures, Mark: 20)
Sequences and series: Sequences, Limit of a sequence, Convergence, Divergence and Oscillation of a
sequence, Infinite series, Necessary condition for Convergence, Cauchy’s Integral Test, D’Alembert’s Ratio
Test, Cauchy’s nth Root Test, Alternating Series, Leibnitz’s Theorem, Absolute Convergence and Conditional
Convergence, Power Series.
Unit-4 (16 Lectures, Mark: 20)
Complex Variables and Functions: Complex Variable, Complex Function, Continuity, Differentiability,
Analyticity. Cauchy-Riemann (C- R) Equations, Harmonic and Conjugate Harmonic Functions, Exponential
Function, Trigonometric Functions, Hyperbolic Functions. Line Integral in Complex Plane, Cauchy’s Integral
Theorem, Cauchy’s Integral Formula, Derivative of Analytic Functions. Sequences, Series and Power Series,
Taylor’s Series, Laurent Series, Zeroes and Poles. Residue integration method, Residue integration of real
Integrals.
Suggested Books
1. E. Kreyszig, advanced engineering mathematics, Wiley India (2008)
2. Murray Spiegel, Seymour Lipschutz, John Schiller, Outline of Complex Variables, Schaum Outline
Series, Tata McGraw Hill (2007)
3. R. K. Jain, and S.R.K. Iyengar, Advanced Engineering Mathematics, Narosa Publishing House
(2007)
4. C .R. Wylie and L. C. Barrett, Advanced Engineering Mathematics, Tata McGraw-Hill (2004)
5. B. V. Ramana, Higher Engineering Mathematics, Tata McGraw Hill Publishing Company Limited
(2007)
Mathematics Foundation for Electronics Lab (Scilab/MATLAB/ any other Mathematical Simulation
software)
1. Solution of First Order Differential Equations
2. Solution of Second Order homogeneous Differential Equations
3. Solution of Second Order non-homogeneous Differential Equations
4. Convergence of a given series.
5. Divergence of a given series.
6. Solution of linear system of equations using Gauss Elimination method.
7. Solution of linear system of equations using Gauss – Seidel method.
8. Solution of linear system of equations using L-U decomposition method.
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