Stoke's Theorem Explanation of orientation and normal vectors to the surface.

Second Year Math Sindh textbook Jamshoro Solution Exercise 2.2 Question 4-6

Second Year Math Sindh textbook Jamshoro Solution Exercise 2.2 Question 1-3

Second year Mathematics Sindh text book board Jamshoro Exercise 2.1

Second Order Ordinary Differential Equations

Cyclone

Combinatorial Methods, Fundamental Principle of Counting, Permutations and Combinations Sample Space

Introduction to Probability, Sample Space Events and types of events favourable and possible outcome

Conservative Vector Fields, test for conservation, curl of a vector field.

Green's Theorem, connection between line integral along a curve and double integral over the region.

Line integrals in space, Parameterization of curves in space work done by force field along a curve.

Triple integral in cartesian coordinate, Volume bounded by surface applications of triple integrals.

Method of Lagrange Multipliers, Constrained Optimization, one constraint, and multiple constraints.

Double integrals and change of order of integration, integration over the general regions.

Simultaneous Decomposition method for Partial Differential Equations, a novel Decomposition method.

Adomian Decomposition method for the wave equation with homogenous Dirichlet Boundary Conditions.

Adomian Decomposition Method for inhomogenous Heat equation with time-dependent boundary conditions.

Adomian Decomposition Method for Heat equation with time-dependent Dirichlet boundary conditions.

Adomian Decomposition Method for Heat Equation (Partial Differential Equations)

Equation of Tangent Planes and Normal Lines of a surface in Space.

Directional Derivatives and Gradients, Rate of Change in the direction of a vector.

Partial Derivatives ( Derivatives of Multivariable functions)

The existence of the Limit of a multivariable function and Continuity of a multivariable function.

Limits and Continuity of functions of two variables (multivariable functions) multivariable calculus

Quadric (Quadratic) Surfaces and their Traces 3 Dimensional Surfaces multivariable calculus

Traces of Surfaces in 3 Dimensional Coordinate System Multivariable calculus

homogenous first order differential equations odes solved examples important Problems

Equations of Planes in Space, Line of Intersection of Two Planes, Parallel and Perpendicular Planes

Equation of Lines in Space, Parametric and Symmetric representation of a Line in 3 space.

Introduction to multivariable Calculus, multivariable functions.

Power Method and Inverse Power Method for Eigenvalues and Eigenvectors

Fixed Point Iteration Successive Approximation Method, and Convergence Criteria Sufficient Condition

Secant and Newton Raphson method Geometrical Interpretation Solved Problem Numerical Analysis

Newton Raphson Method With Solved Example and Geometrical Interpretation, Open Methods.

False Position Method, Error Analysis of Bisection Comparision of False Position and Bisection.

Numerical Method for Nonlinear Equations Bisection Method (Bracketing method)

Truncation error and Rounding off Error Integral Derivatives and Taylor Series

Errors and Approximations in Numerical Methods

Polynomial Interpolation and curve fitting Applications of Linear Algebra

QR Factorization of a matrix Gram Schmidt Process orthogonalization and orthonormalization

LU Decomposition method for Matrices A = LU | Numerical Methods | Solution of Linear Equation

This lesson is about the Least Square Solutions to Linear Systems QR Factorization method. (Part 2)

Least Squares Solutions to Linear Systems . (Part 1)

Singular Value Decomposition With Explanation and Solved Examples (when singular values are zero)

Eigen Values Eigen Vectors Diagonalization A-invariant Matrices Defective Eigenvalues .

Dimension of subspace theorems Null space row space column space and Rank nullity theorem

change of basis and coordinate systems Transition Matrices solved Problems

Linear Dependent and Independent Sets, Basis, Set of Functions, and Wronskian, spanning sets.

Converting Second order PDE to the system of first-order PDEs. Convection Diffusion Equation.

A new ANSATZ Method for Solving Partial Differential equations an initial value problem

Vector space, subspace, null space, row space, column space, basis, module Part 2.

Vector Space, Subspace , Module , Row space, Column space, Null space. Part 1

Matrix Operations Inverse of a Matrix and Characterization of Invertible Matrix. Elementary Matrix

Systems of PDEs Using Laplace Transform Solved Example.

Systems of Partial Differential Equations Using Laplace Transforms (A very new approach)

Linear and Non Linear Transformations Matrix of a Linear Transformation

Linear Independence, Linear Dependence Spanning sets are explained mathematically and geometrically

Solution of Systems Homogenous and Non Homogenous and Parametric representation

Matrix Equation AX = b. Equivalence of algebraic system and matrix equation.

Vector Equations Linear Combinations and Spanning sets.