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.

Complex Numbers 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, 26183 downloads) View online
ARW Exercise 1.2 Download PDF (1.27 MiB, 18685 downloads) View online
ARW Exercise 1.3 Download PDF (1.64 MiB, 5175 downloads) View online
ARW Exercise 1.4 Download PDF (653.33 KiB, 11662 downloads) View online
ARW Exercise 1.5 Download PDF (690.22 KiB, 12927 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, 20588 downloads) View online
ARW Exercise 2.2 Download PDF (602.28 KiB, 2944 downloads) View online
ARW Exercise 2.3 Download PDF (657.81 KiB, 2061 downloads) View online
Notes by Shariq Mehtab Syed:
ARW Exercise 2.1 Download PDF (774.94 KiB, 30029 downloads) View online
ARW Exercise 2.2 Download PDF (977.55 KiB, 1997 downloads) View online
ARW Exercise 2.3 Download PDF (410.76 KiB, 22414 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, 27327 downloads) View online
ARW Exercise 3.1 Download PDF (630.02 KiB, 51423 downloads) View online
ARW Exercise 3.2 Download PDF (781.02 KiB, 56715 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, 24304 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, 4039 downloads) View online
ARW Exercise 5.2 Download PDF (395.67 KiB, 12194 downloads) View online

:: Advertisement ::


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, 44681 downloads) View online
ARW Exercise 6.2 Download PDF (1.23 MiB, 6226 downloads) View online
ARW Exercise 6.3 Download PDF (861.66 KiB, 44167 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, 3389 downloads) View online
ARW Solutions of Exercise 7.1 Download PDF (363.36 KiB, 14137 downloads) View online
ARW Articles of Exercise 7.2 Download PDF (131.18 KiB, 6121 downloads) View online
ARW Solutions of Exercise 7.2 Download PDF (111.31 KiB, 7013 downloads) View online
ARW Articles of Exercise 7.3 Download PDF (157.9 KiB, 6291 downloads) View online
ARW Solutions of Exercise 7.3 Download PDF (519.81 KiB, 17522 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, 10386 downloads) View online
ARW Exercise 8.2 Download PDF (1.09 MiB, 37085 downloads) View online
ARW Exercise 8.3 Download PDF (658.47 KiB, 28771 downloads) View online
ARW Exercise 8.4 Download PDF (854.59 KiB, 27707 downloads) View online
ARW Exercise 8.5 Download PDF (1.46 MiB, 7399 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, 18198 downloads) View online
ARW Exercise 9.2 Download PDF) (457.81 KiB, 589 downloads) View online
ARW Exercise 9.2 by Umer Asghar Download PDF) (476.62 KiB, 15726 downloads) View online
ARW Exercise 9.3 Download PDF) (992.56 KiB, 1098 downloads) View online
ARW Exercise 9.4 Download PDF) (450.02 KiB, 26028 downloads) View online
ARW Exercise 9.5 Download PDF) (1 MiB, 1972 downloads) View online
ARW Exercise 9.6 Download PDF) (508.84 KiB, 1618 downloads) View online
ARW Exercise 9.7 Download PDF) (789.57 KiB, 56463 downloads) View online
ARW Exercise 9.8 Download PDF) (952.79 KiB, 938 downloads) View online
ARW Exercise 9.9 Download PDF) (975.02 KiB, 22779 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, 8493 downloads) View online
ARW Exercise 10.2 Download PDF (1.48 MiB, 182 downloads) View online
ARW Exercise 10.3 Download PDF (3.9 MiB, 1119 downloads) View online
ARW Exercise 10.4 Download PDF (608.67 KiB, 2255 downloads) View online
ARW Exercise 10.5 Download PDF (1.02 MiB, 10575 downloads) View online
ARW Exercise 10.6 Download PDF (749.21 KiB, 34031 downloads) View online
ARW Exercise 10.7 Download PDF (1.54 MiB, 26752 downloads) View online

The Laplace Transformation 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 $F=\mathcal{L}(f)$.

Here is the list of other contents given in this chapter.

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

View online or download

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

We will try our best to find new notes which are clear. If someone else has these notes, they can send us — 2017/05/05 07:25 by Admin

Dear, Can you send me /Uploaded the chapter 11 Excerise.. . Book Mathematicial Method Chapter 11 — 2017/05/24 12:07 by Sami Ullah Zakir

Notes of chapter 11 are available here: http://www.mathcity.org/bsc/notes_of_mathematical_method/ch11_the_laplace_transform 2017/05/24 12:07 by Admin

Advertisement: