Course11110709860 lectures
Mathematical Methods and its Applications
Prof. S. K. Gupta and Prof. P. N. Agrawal · IIT Roorkee
About
This course is a basic course offered to UG student of Engineering/Science background. It contains ODE,PDE, Laplace transforms, Z-transforms, Fourier series and Fourier transforms. It plays an important role for solving various engineering sciences problems.Therefore, it has tremendous applications in diverse fields in engineering sciences.
INTENDED AUDIENCE : UG students of technical universities/colleges.
Lectures
Week 1
- Introduction to linear differential equations
- Linear dependence, independence and Wronskian of functions, Existence and Uniqueness theorem
- Solution of second order homogeneous linear differential equations with constant coefficient-
- Solution of second order homogeneous linear differential equations with constant coefficient-II
- Methods of Undetermined coefficients
Week 2
- Methods for finding particular integrals for second order linear differential equations with constant coefficients I
- Methods for finding particular integrals for second order linear differential equations with constant coefficients II
- Methods for finding particular integrals for second order linear differential equations with constant coefficients III
- Cauchy-Euler equation
- Methods of reduction for second order-linear differential equations
Week 3
- Methods of variation of parameters
- Solution of second order differential equations by changing dependent variables
- Solution of second order differential equations by changing independent variable
- Solution of higher-order homogeneous linear differential equations with constant coefficients
- Methods for finding particular integral for higher-order linear differential equations with constant coefficient s
Week 4
- Formulation of partial differential equations
- Solution of Lagrange's equation I
- Solution of Lagranage's equations II
- Solution of first order non-linear equation I
- Solution of first order non-linear equation II
Week 5
- Solution of first order non linear equation III
- Solution of first order non linear equation IV
- Introduction to Laplace transforms
- Laplace transforms of some standard functions
- Existence theorem for Laplace transforms
Week 6
- Properties of Laplace transforms-I
- Properties of Laplace transforms-II
- Properties of Laplace transforms-III
- Properties of Laplace transforms-IV
- Convolution Theorem for Laplace Transforms-I
Week 7
- Convolution Theorem for Laplace Transforms-II
- Initial and Final Value Theorems for Laplace Transforms
- Laplace Transforms of Periodic Functions
- Laplace Transforms of Unit Step Function
- Laplace Transforms of Dirac delta Functions
Week 8
- Applications of Laplace Transforms-I
- Applications of Laplace Transforms-II
- Applications of Laplace Transforms-III
- Z- transform and inverse Z- transform of elemetary functions
- Properties of Z-transforms-I
Week 9
- Properties of Z - transformatons - II
- Initial and final theorems for Z- transforms
- Convolution theorem for Z-transforms
- Convergence of Z- transform
- Application of Z-transforms-I
Week 10
- Applications of Z- transform- II
- Fourier Series and its Convergence-I
- Fourier Series and its Convergence-II
- Fourier Series of Even and Odd functions
- Fourier half-range series
Week 11
- Parseval’s Identity
- Complex form of Fourier series
- Fourier integrals
- Fourier sine and cosine integrals
- Fourier transforms
Week 12
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Roorkee
- Department
- Mathematics
- Taught by
- Prof. S. K. Gupta, Prof. P. N. Agrawal
- Level
- Undergraduate
- Language
- English
- Subjects
- Mathematics
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
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