Advertisement:


Notes of Mathematical Method

Cover

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

The notes given here are provided by awesome peoples, who dare to help others. Some of the notes are send by the authors of these notes and other are send by people who didn't write but share these notes as Open Educational Resources (OER). We are thankful to Atiq ur Rehman, Muhammad Farooq, Umer Asghar, Muhammad Tahir Aziz and all those who don't send but write these notes.

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.

image

A complex number is an element $(x,y)$ of the set $$ \mathbb{R}^2=\{(x,y): x,y \in \mathbb{R}\} $$ obeying the following rules of addition and multiplication.

For $z_1=(x_1,y_1)$, $z_2=(x_2,y_2)$, we put

  1. $z_1+z_2= (x_1+x_2, y_1+y_2)$
  2. $z_1 z_2 = (x_1 x_2 - y_1 y_2, x_1 y_2+y_1 x_2)$

The set $\mathbb{R}^2$ with operation defined above is denoted by $\mathbb{C}$.

  • Complex numbers
  • Properties of complex numbers
  • The Argand's diagram
  • De Moivre's theorem
  • Roots of the complex numbers
  • Basic elementary functions
  • Logarithmic functions
  • Inverse hyperbolic functions
  • Inverse trigonometric functions
  • Complex power
  • Summation of series
ARW Exercise 1.1 Download PDF (470.64 KiB, 16180 downloads) View online
ARW Exercise 1.2 Download PDF (1.27 MiB, 4285 downloads) View online
ARW Exercise 1.3 Download PDF (1.64 MiB, 34151 downloads) View online
ARW Exercise 1.4 Download PDF (653.33 KiB, 2142 downloads) View online
ARW Exercise 1.5 Download PDF (690.22 KiB, 4854 downloads) View online
image
  • Definition (axioms of group)
  • Definition ( commutative group )
  • Definition (idempotent)
  • Properties of Group
  • Theorem (The Cancellation Law)
  • Theorem (Solution of Linear Equations )
  • Subgroups
  • Definition ( subgroup )
  • Cyclic Groups
  • Definition ( cyclic group )
  • Cosets-Lagrange’s Theorem
  • Permutations
  • Cycles
  • Transpositions
  • Order of a Permutation
  • Rings and Fields
  • Properties of Rings
Notes by Shahzad Ahmed Khan: NEW
ARW Exercise 2.1 Download PDF (606 KiB, 14326 downloads) View online
ARW Exercise 2.2 Download PDF (602.28 KiB, 1894 downloads) View online
ARW Exercise 2.3 Download PDF (657.81 KiB, 11546 downloads) View online
Notes by Shariq Mehtab Syed:
ARW Exercise 2.1 Download PDF (774.94 KiB, 26174 downloads) View online
ARW Exercise 2.2 Download PDF (977.55 KiB, 27906 downloads) View online
ARW Exercise 2.3 Download PDF (410.76 KiB, 19688 downloads) View online
image

The difficulty level of this chapter is very low. Most of the questions involve calculations. This chapter is wide range of applications in Linear Algebra. In many universities teachers include this chapter in the syllabus of Linear Algebra for BS students of mathematics and other subjects.

  • Introduction
  • Algebra of matrices
  • Partitioning of matrices
  • Inverse of a matrix
  • Elementary row operations
  • Elementary column operations
ARW Articles of Ex 3.1 Download PDF (327.93 KiB, 21348 downloads) View online
ARW Exercise 3.1 Download PDF (630.02 KiB, 40924 downloads) View online
ARW Exercise 3.2 Download PDF (781.02 KiB, 44985 downloads) View online
image

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, 6147 downloads) View online
  • 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, 930 downloads) View online
ARW Exercise 5.2 Download PDF (395.67 KiB, 1783 downloads) View online

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 Download PDF (3.52 MiB, 30640 downloads) View online
ARW Exercise 6.2 Download PDF (1.23 MiB, 12601 downloads) View online
ARW Exercise 6.3 Download PDF (861.66 KiB, 36316 downloads) View online
Spaces

Inner product spaces form and important topic of Functional Analysis. These are simply vector space over the field of real or complex numbers and with an inner product defined on them.

  • Definition and examples
  • Orthogonality
  • Orthogonal matrices
  • Eigenvalues and Eigenvectors
  • Similar matrices
  • Symmetric matrices
  • Diagonalization of matrices
ARW Articles of Exercise 7.1 Download PDF (510.1 KiB, 8497 downloads) View online
ARW Solutions of Exercise 7.1 Download PDF (363.36 KiB, 9361 downloads) View online
ARW Articles of Exercise 7.2 Download PDF (131.18 KiB, 3921 downloads) View online
ARW Solutions of Exercise 7.2 Download PDF (111.31 KiB, 4478 downloads) View online
ARW Articles of Exercise 7.3 Download PDF (157.9 KiB, 3969 downloads) View online
ARW Solutions of Exercise 7.3 Download PDF (519.81 KiB, 11118 downloads) View online
Geometric series

Infinite series are of great importance in both pure and applied mathematics. They play a significant role in Physics and engineering. In fact many functions can be represented by infinite series. The theory of infinite series is developed through the use of special kind of function called sequence.

  • Sequences
  • Infinite series
  • The basic comparison test
  • The limit comparison test
  • The integral test
  • The ratio test
  • Cauchy's root test
  • Alternating series
  • Absolute
ARW Exercise 8.1 Download PDF (494.55 KiB, 3012 downloads) View online
ARW Exercise 8.2 Download PDF (1.09 MiB, 26162 downloads) View online
ARW Exercise 8.3 Download PDF (658.47 KiB, 20153 downloads) View online
ARW Exercise 8.4 Download PDF (854.59 KiB, 19437 downloads) View online
ARW Exercise 8.5 Download PDF (1.46 MiB, 22663 downloads) View online

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

image
  • D.E and their classification
  • Formation of differential equation
  • Initial and boundary conditions
  • Separable equations
  • Homogeneous equations
  • D.E. Reducible to homogeneous form
ARW Exercise 9.1 Download PDF) (829.68 KiB, 2124 downloads) View online
ARW Exercise 9.2 Download PDF) (457.81 KiB, 27135 downloads) View online
ARW Exercise 9.2 by Umer Asghar Download PDF) (476.62 KiB, 3436 downloads) View online
ARW Exercise 9.3 Download PDF) (992.56 KiB, 23093 downloads) View online
ARW Exercise 9.4 Download PDF) (450.02 KiB, 12286 downloads) View online
ARW Exercise 9.5 Download PDF) (1 MiB, 31032 downloads) View online
ARW Exercise 9.6 Download PDF) (508.84 KiB, 20 downloads) View online
ARW Exercise 9.7 Download PDF) (789.57 KiB, 41701 downloads) View online
ARW Exercise 9.8 Download PDF) (952.79 KiB, 26368 downloads) View online
ARW Exercise 9.9 Download PDF) (975.02 KiB, 9908 downloads) View online

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

image
  • Higher order linear differential equations
  • Exact equations
ARW Exercise 10.1 Download PDF (290.29 KiB, 26983 downloads) View online
ARW Exercise 10.2 Download PDF (1.48 MiB, 830 downloads) View online
ARW Exercise 10.3 Download PDF (3.9 MiB, 12334 downloads) View online
ARW Exercise 10.4 Download PDF (608.67 KiB, 11080 downloads) View online
ARW Exercise 10.5 Download PDF (1.02 MiB, 12056 downloads) View online
ARW Exercise 10.6 Download PDF (749.21 KiB, 24993 downloads) View online
ARW Exercise 10.7 Download PDF (1.54 MiB, 17032 downloads) View online

Here we are posting different suggestion/feedback provided by our valued visitors. You can also give us feedback via about us page. We will try our best to overcome these deficiencies.

  • Notes of Exercise 10.3 is not cleared — 2017/03/20 06:39 by Talat Mehmood

Advertisement: