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- Elementary Linear Algebra by Muhammad Usman Hamid @notes
- ======Elementary Linear Algebra by Muhammad Usman Hamid====== {{ :notes:elementary-linear-algebra-m-usman-hamid.jpg?nolink|Elementary Linear Algebra by Muhammad Usman Hamid}} Linear Algebra is the study of vectors and linear transformations. The
- FSc Part 1 (KPK Boards) @fsc
- ex numbers. * know the solution of simultaneous linear equations with complex co-efficients. * write the polynomial $P(z)$ as product of linear factors. * solve quadratic equations in complex... atrix and rank of a matrix. * solve a system of linear equations of both homogeneous and non-homogeneous... this unit the students will be able to * know linear, quadratic and square root functions. * define
- Notes of Algebra @notes
- ell></col><col lg="4"><well> [[::Notes:elementary-linear-algebra-m-usman-hamid|{{::notes:elementary-linear-algebra-m-usman-hamid.jpg?350}}]] <caption> **[[::Notes:elementary-linear-algebra-m-usman-hamid]]** </caption> Linear Algebra is the study of vectors and linear transformations. B
- Operation Research by Sir Haidar Ali @notes
- ==Summary & contents==== <grid> <col sm="6"> * Linear programming * Linear function * Objective function * Optimal solution * General linear programming problem * Graphical solution of linear programming problem * Corner point * Infeasible
- Topology: Handwritten Notes @notes
- osed unit ball; Convex set * Vector space * Linear combination; Spanning set; Linearly independent ... ormal sets (definition); Parsevel's equality * Linear Operator; The Kernel or Null space of a linear operator; Continuous linear operator * Bounded linear operator * Norm of a bounded lienar operator
- Algebra II by Syed Sheraz Asghar @notes
- Subspace * Sum of Subspaces * Direct Sum * Linear Transformation or Homomorphism * Kernel of T or Kernel of Linear Transformation * Quotient Space * Linear Combination * Linearly Dependent * Linear Span * Basis * Dimension * Maximal L.I Set * Minima
- Functional Analysis by M Usman Hamid and Zeeshan Ahmad @notes
- atics and its applications. The impetus came from linear algebra, linear ordinary and partial differential equations, calculus of variations, approximation theory and, in particular, linear integral equations, whose theory had the greatest... and convergence, completion, **Normed Spaces:** linear spaces, normed spaces, difference between a metri
- Question 2, Exercise 1.3 @fsc-part1-kpk:sol:unit01
- on 2(i)===== Factorize the polynomial $P(z)$ into linear factors. $$P\left( z \right)={{z}^{3}}+6z+20$$ ==... n 2(ii)===== Factorize the polynomial $P(z)$ into linear factors. $$P(z)=3z^2+7.$$ ====Solution==== \begi... Factorize the polynomial $P\left( z \right)$ into linear factors. $$P\left( z \right)={{z}^{2}}+4$$ ====S... n 2(iv)===== Factorize the polynomial $P(z)$ into linear factors. $$P(z)={{z}^{3}}-2{{z}^{2}}+z-2.$$ ====S
- Question 2, Exercise 1.3 @math-11-kpk:sol:unit01
- on 2(i)===== Factorize the polynomial $P(z)$ into linear factors. $$P\left( z \right)={{z}^{3}}+6z+20$$ ==... n 2(ii)===== Factorize the polynomial $P(z)$ into linear factors. $$P(z)=3z^2+7.$$ ====Solution==== \begi... Factorize the polynomial $P\left( z \right)$ into linear factors. $$P\left( z \right)={{z}^{2}}+4$$ ====S... n 2(iv)===== Factorize the polynomial $P(z)$ into linear factors. $$P(z)={{z}^{3}}-2{{z}^{2}}+z-2.$$ ====S
- Khuram Ali Khan
- erator Jensen's Inequality, Electronic Journal of Linear Algebra, Vol. 31, (2016) pp. 125-133, (March, 201... 2014. - RUQAYYA HAFEEZ, Global Behaviour of Non Linear Difference Equations; Department of Mathematics, ... - ISHRAT FATIMA, Jessen's Inequality for Isotonic Linear Functionals via Time Scales, Department of Mathem
- MTH103: Exploring Quantitative Skills @atiq
- ges will be discussed. Students will also explore linear models, including rectangular coordinates, functi... tions, absolute value function, inverse function, linear functions, polynomial functions, rational functio... related to functions. === Algebraic Models: === Linear equations, quadratic equations and their applicat
- Definitions: FSc Part 1 (Mathematics): PTB @fsc-part1-ptb
- Non Abelian group under Binary operation. * **Linear function:** The function $\{(x,y)|y=mx+c\}$ is called a linear function. Geometrical representation of linear function is a straight line. * **Quadratic function:**
- Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib @fsc-part1-ptb
- use addition of real numbers is commutative. ====Linear Function==== A linear function is a function of the form \( f(x) = mx + c \), where \( m \) and \( c \) a... xample:==== The function \( f(x) = 2x + 3 \) is a linear function because its graph is a straight line wit
- Notes for Numerical Methods by M Usman Hamid @notes
- uction * Error analysis * Solution of the non-linear equations * Bisection methods * False positio... wton Raphson extended formula * The solution of linear system of equations * Gauss elimination method ... * Diagonally dominant system * Ill condition linear system * Jacobi’s method * Gauss seidel itera
- Partial Differential Equations by M Usman Hamid @notes
- ition Principle, Exercises * FIRST-ORDER QUASI-LINEAR EQUATIONS AND METHOD OF CHARACTERISTICS * Cla... General Solutions, Canonical Forms of First-Order Linear Equations, Method of Separation of Variables, Exe... consequences. * CLASSIFICATION OF SECOND-ORDER LINEAR EQUATIONS * Second-Order Equations in Two Ind