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- Definitions: FSc Part 1 (Mathematics): PTB @fsc-part1-ptb
- function, because it is defined by second degree equation in * **Unary Operation:** A mathematical p... ank of the matrix. ===== Chapter 04: Quadratic equations ===== * **Quadratic Equation:** An equation of second degree polynomial in a certain variable is called Quadratic Equation. \\ e.g. $x^2
- Partial Differential Equations by M Usman Hamid @notes
- ====== Partial Differential Equations by M Usman Hamid ====== The course provides a foundation to solve PDE... s with special emphasis on wave, heat and Laplace equations, formulation and some theory of these equations are also intended. We are really very thankful to Prof. Mu... es on MathCity.org {{ :notes:partial-differential-equations-m-usman-hamid.jpg?nolink|Partial Differential Eq
- Partial Differential Equations by Muzammil Tanveer @notes
- ====== Partial Differential Equations by Muzammil Tanveer ====== {{ :notes:partial-differential-equations-muzammil-tanveer.jpg?nolink|Partial Differential Equations}} These notes are provided and composed by Mr. [... s on MathCity.org ^ Name |Partial Differential Equations or PDEs | ^ Provider |Mr. Muzammil Tanveer |
- Khuram Ali Khan
- **Field of Research:** Difference and functional equations, Real functions, Mathematical inequalities invol... f a competitive system of second-order difference equations, The Scientific World Journal, Vol. 2014 (2014),... ty Analysis of a System of Exponential Difference Equations, Discrete Dynamics in Nature and Society Vol. 20... or quasi-convex functions, Advances in Difference Equations ( Published January 18, 2019) IF 1.51 ([[https:/
- Mathematics 10 (Science Group) @matric
- bahadar-ali-khan.pdf }} * {{:matric:quadratic-equations.pdf|Quadratic Equation by Ali Hassan Tahir}} ====== MCQs: Complete Book ====== These MCQs was sent by [[:... Download PDF ~ 1.5MB}} ====== Unit 01: Quadratic Equations ====== These notes are send by Ms. [[:people:ami... t students will learn how to * define quadratic equation * solve a quadratic equation in one variable by
- Differential Geometry (Notes) by Ms. Kaushef Salamat @notes
- * Tangent * Arc * Chord * Arc length * Equation of tangent * Oscillating plane * Principal normal * Normal plane * Curvature * Equation of osculating plane * Bi-normal vector * Equation of Bi-normal * Torsion * Seret Frenet formulas * Equation of tangent in Cartesian formulas * Equation of
- Chapter 04: Quadratic Equations @fsc:fsc_part_1_solutions
- ====== Chapter 04: Quadratic Equations ====== {{ :fsc:fsc_part_1_solutions:fsc-1-chap-04-ptb.jpg|Chapter 04: Quadratic Equations}} Notes (Solutions) of Chapter 04: Quadratic Equations, Text Book of Algebra and Trigonometry Class XI (Ma... === * Introduction * Solutions of Quadratic Equations * Exercise 4.1 * Solutions of Equations Re
- Mathematics CUI: LaTeX Resources
- er" ==== LaTeX Codes ==== * **To write inline equation** Use a $\$ $ (dollar) sign to write equation or symbols in between statements or sentences, e.g.\\ Let $I$... athbb{R}$ be a function</code> * **To write an equation** Use double dollar $(\$\$)$ to write dedicated equation, e.g.,\\ $$\sin^2 \theta + \cos^2 \theta =1$$ <cod
- FSc Part 1 (KPK Boards) @fsc
- ers. * know the solution of simultaneous linear equations with complex co-efficients. * write the polyno... as product of linear factors. * solve quadratic equations in complex variable with real co-efficients. ==... nd rank of a matrix. * solve a system of linear equations of both homogeneous and non-homogeneous equations. === Download === <callout type="success" icon="fa fa-
- Special Functions by Dr. Muhey-U-Din @notes
- etric function of one variable * Hypergeometric equation * Symmetric property of Hypergeometric Function... symbol * Confluent Hypergeometric Differential Equation * Solution of Confluent Hypergeometric function... f Confluent Hypergeometric function * Hermite’s Equation * Solution of Hermite’s Equation * Recurrence relation of Hermite equation * Generation function of H
- Question 5, Exercise 1.3 @math-11-kpk:sol:unit01
- =====Question 5(i)===== Find the solutions of the equation ${{z}^{2}}+z+3=0$. ====Solution==== Given: $${{z... }}{2}i\end{align} Thus the solutions of the given equation are $-\dfrac{1}{2}\pm\dfrac{\sqrt{11}}{2}i$. =====Question 5(ii)===== Find the solutions of the equation ${{z}^{2}}-1=z$.\\ ====Solution==== Given: $${{z... }}{2}.\end{align} Thus the solutions of the given equations are $\dfrac{1\pm\sqrt{5}}{2}$. =====Question 5(i
- Question 6, Exercise 1.3 @math-11-kpk:sol:unit01
- =====Question 6(i)===== Find the solutions of the equation ${{z}^{4}}+{{z}^{2}}+1=0$. ====Solution==== $$z... c{1\pm \sqrt{3}i}{2}$$ The value of $z$ from both equations, we have $$z=\pm \dfrac{1}{2}\pm \dfrac{\sqrt{3}... ====Question 6(ii)===== Find the solutions of the equation ${{z}^{3}}=-8$. ====Solution==== Given: $$z^3=-8... 1\pm \sqrt{3}i$ are the solutions of the required equations. =====Question 6(iii)===== Find the solutions o
- Notes of Mathematics
- he real analysis. NEW </well> ===== Differential Equations ===== <well> **[[Notes:Partial-Differential-Equations-M-Usman-Hamid]]** \\ Notes of Partial Differential Equations by Muhammad Usman Hamid. These notes provides a ... s with special emphasis on wave, heat and Laplace equations, formulation and some theory of these equations
- Fluid Dynamics I by Muhammad Usman Hamid @notes
- === **Introduction:** Definition of Fluid, basics equations, Methods of analysis, dimensions and units. Fund... n of fluid motions. **Fluid Statics:** The basic equation of fluid static, The standard atmosphere, pressur... a static fluid, fluid in rigid body motion. Basic equation in integral form for a control volume, basic laws... olume formulation, conservation of mass, momentum equation for inertial control volume, momentum equation fo
- Fluid Mechanics II by Dr Rao Muzamal Hussain @notes
- urbulent flow * Stream lines * Differential Equations of stream lines * Vortex motion * Vorticit... * Kelvin’s Minimum Energy Theorem * Laplace Equation * Normal stress * Tangential stress or sheer stress * Generalization equation of motion * Euler equation of motion for in-viscus (real) fluid * Bernoulli Equation * Bernoulli E