Merging man & maths https://www.mathcity.org/ Thu, 04 Jun 2026 16:32:54 +0000 FeedCreator 1.8 https://www.mathcity.org/_media/logo.svg https://www.mathcity.org/ https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch03_general_theorem_intermediate_forms Chapter 03: General Theorem, Intermediate Forms [BSc Calculus 3rd Chapter] What is in the this chapter? * Rolle's theorem * Geometrical interpretation of Rolle's theorem * The mean value theorems * Another form of mean value theorem * Increasing and decreasing functions$\frac{0}{0}$$\frac{\infty}{\infty}$$0\times \infty$$\infty \times 0$$\infty-\infty$$0^\infty, 1^\infty, \infty^0$ anonymous@undisclosed.example.com (Anonymous) Fri, 21 Apr 2023 13:46:07 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch11_the_laplace_transform Chapter 11: The Laplace Transform Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin. This book is published by Ilmi Kitab Khana, Lahore - PAKISTAN. Solutions of Chapter 11: The Laplace Transform are given here in pdf form. $f$$[0,\infty)$$f$$\mathcal{L}(f)$$F$$ provided the above improper integral converges. We have $ anonymous@undisclosed.example.com (Anonymous) Sun, 29 May 2022 17:43:26 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch01_real_numbers_limits_and_continuity Chapter 01: Real Numbers, Limits and Continuity [Chapter 01 of Calculus with Analytic Geometry] Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. The notes of this chapter is written by Prof. $\mathbb{R}$$\mathbb{R}$$\mathbb{R}$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:28 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch02_derivatives Chapter 02: The Derivative [Chapter 02: The Derivative BSc Calculus] Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Here are few online resource, which are very helpful to find derivative. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:28 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch07_plane_curves_ii Chapter 07: Plane Curves II Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. [Asymptote] Contents and summary * Asymptotes: A straight line $l$ is called an asymptote for a curve $C$$l$$C$$l$$l$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:32 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch08_analytic_geometry_of_three_dimensions Chapter 08: Analytic Geometry of Three Dimensions Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Contents & Summary * Distance between two points$\mathbb{R}^3$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:33 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch01_complex_numbers Chapter 01: Complex Numbers [Chapter 01 Complex Numbers Methods] Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. 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.$z_1=(x_1,y_1)$$z_2=(x_2,y_2)$$z_1+z_2= (x_1+x_2, y_1+y_2)$$z_1 z_2 = (x_1 x_2 - y_1 y_2, x_1 y_2+y_1 x_2)$$\mathbb{R}^2$$\mathbb{C}$ anonymous@undisclosed.example.com (Anonymous) Mon, 11 Dec 2023 12:59:57 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch02_groups Chapter 02: Groups [Chapter 02: Groups] Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Contents and summary * Definition (axioms of group) * Definition ( commutative group ) * anonymous@undisclosed.example.com (Anonymous) Mon, 11 Dec 2023 13:00:23 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch10_higher_order_linear_differential_equations Chapter 10: Higher Order Linear Differential Equations Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Contents and summary * Higher order linear differential equations anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:51 +0000 https://www.mathcity.org/bsc/notes_of_metric_spaces Notes of Metric Spaces These notes are related to Section IV of B Course of Mathematics, paper B. We are very thankful to Mr. Tahir Aziz for sending these notes. Name Notes of Metric Space Author Prof. Shahzad Ahmad Khan Send by Tahir Aziz anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:51 +0000 https://www.mathcity.org/bsc/notes_of_vector_analysis Notes of Vector Analysis [Vector Ananlysis] Notes of the vector analysis are given on this page. These notes are helpful for BSc or equivalent classes. These notes are written by Amir Taimur Mohmand of University of Peshawar. The books of these notes is not known. If you know about the book, please inform us.$f$$P$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:54 +0000 https://www.mathcity.org/bsc/notes-fouries-series Notes of Fourier Series These notes are provided by Mr. Muhammad Ashfaq. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org Name Notes of Fluid Mechanics Author Qayyum Ullah Khan anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:46 +0000 https://www.mathcity.org/bsc/notes-of-metric-spaces-umer-asghar Notes of Metric Spaces by Umer Asghar These notes are related to Section IV of B Course of Mathematics, paper B. We are very thankful to Mr. Umer Asghar for sending these notes. Name Notes of Metric Space Author Mr. Umer Asghar Pages 19 pages anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:48 +0000 https://www.mathcity.org/bsc/notes-of-number-theory-by-umer-asghar Notes of Number Theory by Umer Asghar These notes are very helpful to prepare one of the sections paper of mathematics for BSc. Author: Umer Asghar Type: Composed Format: PDF (1.14 mB) Pages: 24 Contents and Summary * Divisibility anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:48 +0000 https://www.mathcity.org/bsc/number-theory-by-prof-asghar-ali Number Theory by Prof. Asghar Ali [Number Theory by M Asghar Ali] We are very thankful to Prof. Asghar Ali for send these notes. These notes are very helpful to prepare BSc or ADS mathematics portion of Number Theory. Number theory is a subject in which students learn different concepts created on the set of integers. For example, the concept of divisibilty exists in the set of integer. Let a and b be any two integers suhc that $a\neq 0$ anonymous@undisclosed.example.com (Anonymous) Mon, 21 Mar 2022 19:38:31 +0000 https://www.mathcity.org/bsc/number-theory-by-prof-m-tanveer Number Theory by Prof. M. Tanveer [Number Theory by Prof. M. Tanveer] These notes are very helpful to prepare one of the sections of mathematics for BSc. Also these notes can be used for other classes. Author: Prof. M. Tanveer Type: Handwritten Format: PDF (972 kB) Pages: $a,b, \in \mathbb{Z}$$a \neq 0$$a$$b$$c\in \mathbb{Z}$$b=ac$$a,b, \in \mathbb{Z}$$c \in \mathbb{Z}$$a$$b$$c | a$$c | b$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:54 +0000 https://www.mathcity.org/bsc/vector_analysis_by_hameed_ullah Vector Analysis by Hameed Ullah: Notes [right triangle in semi circle] Note of vector analysis by Hammed Ullah. These notes are send by Umer Asghar, we are very thankful to him for providing these notes. These notes are for helpful for undergraduate level (BSc or BS). Name Notes of vector analysis anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:41:13 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch04_techniques_of_integration Chapter 04: Techniques of Integration These notes are written by Mr. Aqeel Nawaz. We are very thankful to him for providing these notes. * Anti-derivative * Table of integrals * Integration by substitution * Integration by parts * Column (or tabular) integration anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:29 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch04_techniques_of_integration_farooq Chapter 04: Techniques of Integration These notes are written by Prof. Muhammad Farooq. We are very thankful to him for providing these notes. * Anti-derivative * Table of integrals * Integration by substitution * Integration by parts * Column (or tabular) integration anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:30 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch05_the_definite_integral Chapter 05: The Definite Integral These notes are written by Mr. Abrar Mustafa. We are very thankful to him for providing these notes. * The definite integral as limit of a sum * Evaluation of limit of a sum * Evaluation of definite integral anonymous@undisclosed.example.com (Anonymous) Tue, 05 Dec 2023 03:01:56 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch06_plane_curves_i Chapter 06: Plane Curves I Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. [Conic section] Contents and summary * Conic sections * The parabola * The ellipse anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:31 +0000 https://www.mathcity.org/bsc/notes_of_calculus_with_analytic_geometry/ch09_functions_of_several_variables Chapter 09: Functions of Several Variables * Homogeneous Functions * Differentials * Change of variables, the chain rule * Implicit functions * Directional derivative * Tangent planes and normal lines * Extrema of functions of two variables anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:33 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch03_matrices Chapter 03: Matrices Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. 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. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:44 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch04_system_of_linear_equations Chapter 04: System of Linear Equations Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. 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 … anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:45 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch05_determinants 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 anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:47 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch06_vector_spaces Chapter 06: Vector Spaces Notes of Chapter 06 Vector Spaces of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Contents and summary * Subspaces * Linear combinations and spanning sets anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:47 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch07_inner_product_spaces Chapter 07: Inner Product Spaces Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. 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. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:48 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch08_infinite_series Chapter 08: Infinite Series Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. 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. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:49 +0000 https://www.mathcity.org/bsc/notes_of_mathematical_method/ch09_first_order_differential_equations Chapter 09: First Order Differential Equations Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Contents and summary * D.E and their classification * Formation of differential equation anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:50 +0000 https://www.mathcity.org/bsc/notes_of_mechanics/introduction_to_mechanics Introduction to Mechanics [Introduction to Mechanics by Q.K Ghori] Notes of Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. There are thirteen chapters in this book. We don't have all the notes of this book but the notes which we have are listed below. Please choose your require chapter to see the notes. anonymous@undisclosed.example.com (Anonymous) Sat, 13 Jan 2024 10:50:44 +0000 https://www.mathcity.org/bsc/notes_of_mechanics/introduction_to_mechanics/ch02-composition-of-forces Chapter 02: Composition of Forces Notes of Chapter 02: Composition of Forces: Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. Notes of this chapter is send by Mr. Tahir Aziz. We are very thankful for his such effort.$(\lambda,\mu)$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:05 +0000 https://www.mathcity.org/bsc/notes_of_mechanics/introduction_to_mechanics/ch04-centres-of-mass-and-gravity Chapter 04: Centres of Mass and Gravity Notes of Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. These notes are written by Prof. Muhammad Tanveer. Following are the main topics of this chapter. * Linear Moment anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:04 +0000 https://www.mathcity.org/bsc/notes_of_mechanics/introduction_to_mechanics/ch05-friction Chapter 05: Friction Notes of Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. These notes are written by Prof. Muhammad Tanveer. Following are the main topics of this chapter. * Friction * Laws of friction anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:06 +0000 https://www.mathcity.org/bsc/notes_of_mechanics/introduction_to_mechanics/ch06-virtual-work Chapter 06: Virtual Work Notes of Chapter 06: Virtual Work: Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. Notes of this chapter is provide by *Prof. M. Tanveer*. We are very thankful to him for such a kind effort. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:07 +0000 https://www.mathcity.org/bsc/notes_of_mechanics/introduction_to_mechanics/ch07-kinematics Chapter 07: Kinematics Notes of Chapter 07: Kinematics: Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. Notes of this chapter is send by Mr. Tahir Aziz and Mr. Umair Sabi Ullah. We are very thankful to them for such a kind effort. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:09 +0000 https://www.mathcity.org/bsc/notes_of_mechanics/introduction_to_mechanics/ch08-rectilinear-motion Chapter 08: Rectilinear Motion Notes of Chapter 08: Rectilinear Motion: Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. Thanks to Mr. Tahir Aziz and Atiq ur Rehman for sending these notes. * Motion with constant acceleration anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:09 +0000 https://www.mathcity.org/bsc/notes_of_mechanics/introduction_to_mechanics/ch10-motion-of-a-projectile Chapter 10: Motion of a Projectile Notes of Chapter 10: Motion of a Projectile: Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. These notes are written by Prof. Shariq Mehtab Syed * Trajectory of a Projectile anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:09 +0000 https://www.mathcity.org/bsc/notes_of_mechanics/introduction_to_mechanics/ch12-orbital-motion Chapter 12: Orbital Motion Notes of Chapter 12: Orbital Motion: Introduction to Mechanics by Q. K. Ghori published by West Pak Publishing Company (Pvt) Ltd. * Motion under the Central * Elliptic Orbit under a central Force * Polar form of the Orbit anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:09 +0000 https://www.mathcity.org/bsc/paper_pattern/punjab_university/b.sc._paper_pattern_for_general_mathematics Paper Pattern for General Mathematics Paper pattern for General Mathematics chapter-wise for University of the Punjab, Lahore is given on this page. This pattern is extracted from syllabus and old papers, so use at your own risk. This pattern is made by Prof. Muhammad Farooq. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:17 +0000 https://www.mathcity.org/bsc/paper_pattern/punjab_university/b.sc._paper_pattern_for_general_mathematics_split_program Syllabus & Paper Pattern for General Mathematics (Split Program) There was one examination after two years for BA/BSc Program from University of Punjab (PU), Lahore but from this year (2016), PU has made changes in its examination policies for the said program. The BA/BSc Program has been split into two parts. Syllabus is break into two part year wise. After the each year of the program candidate has to appeared in examination instead of appearing after two year. In this regards syllabus of Gen… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:21 +0000 https://www.mathcity.org/bsc/paper_pattern/punjab_university/b.sc._paper_pattern_for_mathematics_a_course Paper Pattern for A-Course of Mathematics Paper pattern for A-Course of Mathematics, chapter-wise for University of the Punjab, Lahore is given on this page. This pattern is extracted from syllabus and old papers, so use at your own risk. * Download PDF ~ BSC_maths_paper_pattern_farooq.pdf bsc punjab_university paper_pattern syllabus anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:23 +0000 https://www.mathcity.org/bsc/paper_pattern/punjab_university/b.sc._paper_pattern_for_mathematics_b_course Paper Pattern for B-Course of Mathematics Paper pattern for B-Course of Mathematics chapter-wise for University of the Punjab, Lahore is given on this page. This pattern is extracted from syllabus and old papers, so use at your own risk. This pattern is made by Prof. Muhammad Farooq. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:29 +0000 https://www.mathcity.org/bsc/paper_pattern/sargodha_university/a-course_of_mathematics A-Course of Mathematics (Paper A & B) This subject is consists of two papers of 100 marks each. One is called “Paper A” and other is called “Paper B”. This page is updated on February 15, 2015. This syllabus is for 1st Annual 2015 and onward organized by University of Sargodha, Sargodha. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:55:54 +0000