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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.

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

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, 1425 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
ARW Exercise 5.1 Download PDF (1.27 MiB, 4645 downloads) View online
ARW Exercise 5.2 Download PDF (395.67 KiB, 6565 downloads) View online

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, 863 downloads) View online
ARW Exercise 6.2 NEW Download PDF (1.23 MiB, 250 downloads) View online
ARW Exercise 6.3 NEW Download PDF (861.66 KiB, 318 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, 2415 downloads) View online
ARW Exercise 10.2 Download PDF (1.48 MiB, 986 downloads) View online
ARW Exercise 10.3 Download PDF (3.9 MiB, 702 downloads) View online
ARW Exercise 10.4 Download PDF (608.67 KiB, 2308 downloads) View online
ARW Exercise 10.5 Download PDF (1.02 MiB, 2245 downloads) View online
ARW Exercise 10.6 Download PDF (749.21 KiB, 861 downloads) View online
ARW Exercise 10.7 Download PDF (1.54 MiB, 1689 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.

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
ARW Articles of Ex 11.1 Download PDF (486.17 KiB, 448 downloads) View online
ARW Exercise 11.1 Download PDF (492.54 KiB, 6918 downloads) View online
ARW Exercise 11.2 Download PDF (594.78 KiB, 103 downloads) View online
ARW Exercise 11.3 Download PDF (1.03 MiB, 508 downloads) View online


bsc/notes_of_mathematical_method.txt · Last modified: 2016/02/07 13:34 by Administrator