Module 1 Matrix
Elementary transformation – finding inverse and rank using elementary transformation – solution of linear equations using elementary transformations – eigenvalues and eigenvectors – application of Cayley Hamiltion theorem – Diagonalization – Reduction of quadratic form into sum of squares using orthogonal transformation – nature of quadratic form.
Elementary transformation – finding inverse and rank using elementary transformation – solution of linear equations using elementary transformations – eigenvalues and eigenvectors – application of Cayley Hamiltion theorem – Diagonalization – Reduction of quadratic form into sum of squares using orthogonal transformation – nature of quadratic form.
Module 2 Partial Differentiation
Partial differentiation – chair rules – Eulers theorem for homogeneous functions – Taylors series for function of two variables – maxima and minima of function of two variables (proof of results not expected.)
Partial differentiation – chair rules – Eulers theorem for homogeneous functions – Taylors series for function of two variables – maxima and minima of function of two variables (proof of results not expected.)
Modules 3 Multiple Integrals
Double integrals in cartesian and polar co-ordinates – application in finding area and volume using double integrals – change of variables using Jacobian – triple integrals in cartesian, cylindrical and spherical co-ordinates – volume using triple integrals – simple problems.
Double integrals in cartesian and polar co-ordinates – application in finding area and volume using double integrals – change of variables using Jacobian – triple integrals in cartesian, cylindrical and spherical co-ordinates – volume using triple integrals – simple problems.
Module 4 Laplace Transforms
Laplace transforms – Laplace transform of derivatives and integrals – shifting theorem – differentiation and integration of transforms – inverse transforms – application of convolution property – solution of linear differential equations with constant coefficients using Laplace transform – Laplace transform of unit step function, impulse function and periodic function
Laplace transforms – Laplace transform of derivatives and integrals – shifting theorem – differentiation and integration of transforms – inverse transforms – application of convolution property – solution of linear differential equations with constant coefficients using Laplace transform – Laplace transform of unit step function, impulse function and periodic function
Module 5 Fourier Series
Dirichelt conditions – Fourier series with period 2 and 21 – Half range sine and cosine series – simple problems – rms value.
Dirichelt conditions – Fourier series with period 2 and 21 – Half range sine and cosine series – simple problems – rms value.
mgu university syllabus b.tech
References
1. Advanced Engg. Mathematics Erwin Kreyszig
2. Higher Engg. Mathematics Grawal B.S.
3. Engg. Mathematics N.P.Bali
4. Laplace and Fourier Transforms Goyal and Gupta
5. Advanced Mathematics for Engineers E.S.Sokolinokoff
6. Methods of Applied Mathematics F.B.Hilderbrand
2. Higher Engg. Mathematics Grawal B.S.
3. Engg. Mathematics N.P.Bali
4. Laplace and Fourier Transforms Goyal and Gupta
5. Advanced Mathematics for Engineers E.S.Sokolinokoff
6. Methods of Applied Mathematics F.B.Hilderbrand