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Definitions: FSc Part 1 (Mathematics): PTB @fsc-part1-ptb
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function, because it is defined by second degree equation in * **Unary Operation:** A mathematical p... er 04: Quadratic equations ===== * **Quadratic Equation:** An equation of second degree polynomial in a certain variable is called Quadratic Equation. \\ e.g. $x^2-4=0$, $5x^2-7x=0$\\ Equation of typ
Differential Geometry (Notes) by Ms. Kaushef Salamat @notes
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* 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
Mathematics CUI: LaTeX Resources
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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
Mathematics 10 (Science Group) @matric
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* {{:matric:quadratic-equations.pdf|Quadratic Equation by Ali Hassan Tahir}} ====== MCQs: Complete Book... t students will learn how to * define quadratic equation * solve a quadratic equation in one variable by factorization * solve a quadratic equation in one variable by completing square. * derive
Special Functions by Dr. Muhey-U-Din @notes
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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
Partial Differential Equations by Muzammil Tanveer @notes
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nd Eigen function * Solution of Non-Homogeneous Equation * Solution of Homogeneous Equation * Laplace Equation * Polar form of Laplace Equation * Canonical form/ Normal form / Standard form * General Transform
Fluid Dynamics I by Muhammad Usman Hamid @notes
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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 for control volume with rectilinear acceleration, momentum e
Fluid Mechanics II by Dr Rao Muzamal Hussain @notes
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* 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 Equation for steady flow * Navi
Numerical Analysis II @notes
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ummary & contents==== * Operator * Difference Equation * Homogeneous Linear Difference Equation * Non-Homogeneous Linear Difference Equation * Non-Homogeneous Difference Equation * Formation of Difference Equation * Numerical Integration *
Question 5, Exercise 1.3 @math-11-kpk:sol:unit01
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=====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... ===Question 5(iii)===== Find the solutions of the equation ${{z}^{2}}-2z+i=0$\\ ====Solution==== Given: $$
Question 6, Exercise 1.3 @math-11-kpk:sol:unit01
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=====Question 6(i)===== Find the solutions of the equation ${{z}^{4}}+{{z}^{2}}+1=0$. ====Solution==== $$z... ====Question 6(ii)===== Find the solutions of the equation ${{z}^{3}}=-8$. ====Solution==== Given: $$z^3=-8... ===Question 6(iii)===== Find the solutions of the equation ${{\left( z-1 \right)}^{3}}=-1$.\\ ====Solution==... {3}i}{2}.\end{align} Hence solutions of the given equation are $0$, $\dfrac{3}{2}\pm \dfrac{\sqrt{3}i}{2}$.
Definitions: FSc Part1 KPK @fsc-part1-kpk
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* **Trigonometry equation:** The equation, containing at least one trigonometry function are called Trigonometry equation. \\ e.g. $sin x=\frac{2}{7}$, $cos x-tan x=0$. ... or e-circle. * **Trigonometric function:** The equation, containing at least one trigonometric function,
Definitions: FSc Part1 KPK @math-11-kpk
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* **Trigonometry equation:** The equation, containing at least one trigonometry function are called Trigonometry equation. \\ e.g. $sin x=\frac{2}{7}$, $cos x-tan x=0$. ... or e-circle. * **Trigonometric function:** The equation, containing at least one trigonometric function,
MathCraft: PDF to LaTeX file: Sample-01 @mathcraft
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. for $r \leq u$ and $s \leq v$, we have \begin{equation*} E(x, y ; r, s) \leq E(x, y ; u, v) . \tag{1} \end{equation*} \vspace{2mm} In this paper, first we shall giv... then the following inequality is valid: \begin{equation*} \left(\dfrac{f\left(x_{2}\right)}{f\left(x_{1}\... ght)^{1 /\left(y_{2}-y_{1}\right)} . \tag{2} \end{equation*} Applying Lemma 2.1 for $f=\phi$, (let $r, s,
Differential Geometry: Handwritten Notes @notes
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= **Curves with torsion:**\\ Curve, space curve, equation of tangent, normal plane, principal normal curvat... , principal normal or binormal, rectifying plane, equation of binormal, torsion, Serret Frenet formulae, rad... surfaces:**\\ Surface, tangent plane and normal, equation of tangent plane, equaiton of normal, one paramet... ristic of surface, envelopes, edge of regression, equation of edge of regression, developable surfaces, oscu
Differential Geometry by Syed Hassan Waqas @notes
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Chapter 04: Quadratic Equations @fsc:fsc_part_1_solutions
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Question 5, Exercise 1.3 @fsc-part1-kpk:sol:unit01
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Question 6, Exercise 1.3 @fsc-part1-kpk:sol:unit01
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Question 3 & 4, Exercise 1.3 @math-11-kpk:sol:unit01
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Question 1 Exercise 5.3 @math-11-kpk:sol:unit05
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Question 5 Exercise 6.1 @math-11-kpk:sol:unit06
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Multiple Choice Questions (MCQs) @fsc-part1-kpk
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Multiple Choice Questions (MCQs) @math-11-kpk
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Fluid Mechanics by Ali Raza @notes
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Question 1, Exercise 1.3 @fsc-part1-kpk:sol:unit01
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Question 3 & 4, Exercise 1.3 @fsc-part1-kpk:sol:unit01
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Question 1, Exercise 1.3 @math-11-kpk:sol:unit01
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MTH480: Introductory Quantum Mechanics @atiq
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MTH322: Real Analysis II (Spring 2023) @atiq
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MTH480: Introductory Quantum Mechanics @atiq
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MathCraft: PDF/Image to Word: Sample 01 @mathcraft
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MathCraft: PDF to LaTeX file: Sample-02 @mathcraft
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MathCraft: PDF/Image to Word: Sample 02 @mathcraft
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Question 3 & 4, Exercise 3.2 @math-11-kpk:sol:unit03
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Question 1 Exercise 5.1 @math-11-kpk:sol:unit05
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Question 4 & 5 Exercise 5.1 @math-11-kpk:sol:unit05
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Question 9 Exercise 5.1 @math-11-kpk:sol:unit05
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Question 2 & 3 Exercise 5.4 @math-11-kpk:sol:unit05
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Question 5 & 6 Review Exercise @math-11-kpk:sol:unit05
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Question 3 & 4 Exercise 6.1 @math-11-kpk:sol:unit06
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Question 3 and 4 Exercise 6.2 @math-11-kpk:sol:unit06
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Question 7 and 8 Exercise 6.2 @math-11-kpk:sol:unit06
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Question 7 and 8 Exercise 7.3 @math-11-kpk:sol:unit07
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Important Questions: HSSC-I @fsc-part1-ptb
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Algebraic Number Theory Notes by Anwar Khan @notes
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Fuzzy Sets Theory by Umar Saeed Bunarai @notes
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Mechanics by Sir Nouman Siddique @notes
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Number Theory: Handwritten Notes @notes
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Number Theory Notes by Anwar Khan @notes
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Partial Differential Equations by M Usman Hamid @notes
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Unit 1: Complex Numbers (Solutions) @fsc-part1-kpk:sol
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Unit 03: Integration @fsc:fsc_part_2_solutions
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Unit 01: Complex Numbers (Solutions) @math-11-kpk:sol
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Question 2 Exercise 4.3 @math-11-kpk:sol:unit04
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Question 5 & 6 Exercise 4.5 @math-11-kpk:sol:unit04
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Question 6 Exercise 5.1 @math-11-kpk:sol:unit05
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Question 7 & 8 Exercise 5.1 @math-11-kpk:sol:unit05
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Question 4 Exercise 5.4 @math-11-kpk:sol:unit05
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Question 2 Exercise 6.3 @math-11-kpk:sol:unit06
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Question 10 Exercise 7.2 @math-11-kpk:sol:unit07
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Question 11 Exercise 7.3 @math-11-kpk:sol:unit07
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Question 12 Exercise 7.3 @math-11-kpk:sol:unit07
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Question 14 Exercise 7.3 @math-11-kpk:sol:unit07
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