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bsc:notes_of_mathematical_method

# Notes of Mathematical Method

Notes of the Mathematical Method written by by S.M. Yusuf, A. Majeed and M. Amin and published by Ilmi Kitab Khana, Lahore.

We always try our best to add new solutions of more chapters as we are able to manage. If you have notes which you thing are worth to share with other then please contact us from here or email at Admin@MathCity.org.

## 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

## Chapter 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 06: Vector Spaces

• Subspaces
• Linear combinations and spanning sets
• Linear dependence and basis
• Row and column spaces
• Rand-Alternative method
• Linear transformations
• Matrix of linear transformation

## Chapter 10: Higher Order Linear Differential Equations

• Higher order linear differential equations
• Exact equations

## Chapter 11: The Laplace Transform

Let $f$ be a real valued piecewise continuous function defined on $[0,\infty)$. The Laplace transform of $f$, denoted by $\mathcal{L}(f)$, is the function $F$ defined by $F(s)=\int_0^{\infty} e^{-st} f(t) dt,$ provided the above improper integral converges. We have $F=\mathcal{L}(f)$. Laplace transformation has lot of applications in engineering and applied mathematics.

The following topics are discussed in this chapter.

• The Laplace transform
• Properties of the Laplace transform
• Inverse Laplace transform
• Convolution
• Solution of initial value problem