Download Notes of Mathematical Method by SM Yousuf
Notes of the Mathematical Method written by by S.M. Yusuf, A. Majeed and M. Amin and published by Ilmi Kitab Khana, Lahore.
List of chapters
Chapter 04: System of Linear Equations
The difficulty level of this chapter is low. Most of the questions involve calculations. This chapter is wide range of applications in Linear Algebra and Operations Research. In many universities teachers include this chapter in the syllabus of Linear Algebra and Operations Research for BS students of mathematics and other subjects.
- Preliminaries
- Equivalent equations
- Gaussian elimination method
- Gauss-Jordan elimination method
- Consistency criterion
- Network flow problems
Exercise 4Chapter 05: Determinants
- Determinant of a square matrix
- Axiomatic definition of a determinant
- Determinant as sum of products of elements
- Determinant of the transpose
- An algorithm to evaluate Det A
- Determinants and inverse of matrices
Chapter 10: Higher Order Linear Differential Equations
- Higher order linear differential equations
- Exact equations
Chapter 11: The Laplace Transform
Let 
be a real valued piecewise continuous function defined on  "[0,\infty)")
. The Laplace transform of , denoted by  "\mathcal{L}(f)")
, is the function 
defined by=\int_0^{\infty}%20e^{-st}%20f(t)%20dt, "F(s)=\int_0^{\infty} e^{-st} f(t) dt,")
provided the above improper integral converges. We have  "F=\mathcal{L}(f)")
. Laplace transformation has lot of applications in engineering and applied mathematics.
Here is the list of contents given in this chapter.
- The Laplace transform
- Properties of the Laplace transform
- Inverse Laplace transform
- Convolution
- Solution of initial value problem
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