In this course, you will experience working and testing yourself and with the facilitator on challenging problems involving: Partial derivatives vs total differentials, Understanding changes vs gradient, directional derivatives, Error functions.

This is an extensive course to take a head start in dynamical systems, a key to science and engineering studies, particularly involving electrical, mechanical and chemical systems. The main ideas discussed are: Dynamical systems. Is it always dx/dt? Eigenvalue solutions. What is the eigenvalue sayi…

This course will equip you with a detailed knowledge and computation skills regarding complex numbers. It will bridge your gaps related to: Is the real world actually complex? What is the dark matter? Misconceptions about real and complex numbers and their graphing, Is it always the argument or the…

• Student: Muhammad Ali Bhutto
• Student: Muhammad Haris
• Student: Abdul Junaid
• Student: Aiman Khan

Calculus of curves and surfaces as functions, Level curves as domains of integration, Parametric curves, Quadric surfaces. Completion criteria  To pass this course, you have to complete all lessons, practice assignments and quizzes. Maximum completion time Two weeks. Fee structure Individual:&…

Derivative of a function, Points to ponder, Implicit differentiation, Maxima and minima.

Systems of linear equations, Matrix form of linear systems, Gaussian elimination, Existence and uniqueness of solutions.