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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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
ARW Exercise 4 Download PDF) (1 MiB, 4243 downloads) View online

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
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Chapter 06: Vector Spaces

Vetor Space

  • Subspaces
  • Linear combinations and spanning sets
  • Linear dependence and basis
  • Row and column spaces
  • Rand-Alternative method
  • Linear transformations
  • Matrix of linear transformation
ARW Exercise 6.1 NEW Download PDF (3.52 MiB, 5719 downloads) View online
ARW Exercise 6.2 NEW Download PDF (1.23 MiB, 5371 downloads) View online
ARW Exercise 6.3 NEW Download PDF (861.66 KiB, 3698 downloads) View online

Chapter 10: Higher Order Linear Differential Equations

  • Higher order linear differential equations
  • Exact equations
ARW Exercise 10.1 Download PDF (290.29 KiB, 3524 downloads) View online
ARW Exercise 10.2 Download PDF (1.48 MiB, 1210 downloads) View online
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ARW Exercise 10.6 Download PDF (749.21 KiB, 2690 downloads) View online
ARW Exercise 10.7 Download PDF (1.54 MiB, 2296 downloads) View online

Chapter 11: The Laplace Transform

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
ARW Articles of Ex 11.1 Download PDF (486.17 KiB, 3000 downloads) View online
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