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# 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.

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## 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 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.

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