Do you want to learn how to work with numbers that go beyond the real line? Do you want to understand the concepts of imaginary unit, conjugate, modulus, argument, and polar and exponential forms of complex numbers? Do you want to master the skills of performing algebraic and geometric operations on complex numbers using different methods and tools? If you answered yes to any of these questions, then this course is for you! In this course, you will learn how to: - Define and classify complex numbers and their real and imaginary parts - Perform addition, subtraction, multiplication, and division of complex numbers using the standard form a + bi - Find the conjugate, modulus, and argument of a complex number and use them to compare and simplify complex numbers - Represent complex numbers on the Argand plane and visualize their geometric properties and transformations - Convert complex numbers from rectangular to polar and exponential forms and vice versa - Use De-Moivre's theorem and Euler's formula to find the powers and roots of complex numbers in polar and exponential forms - Use complex numbers to define and manipulate trigonometric and hyperbolic functions and their inverses - Use complex numbers to define and manipulate logarithmic functions and their properties - Use complex numbers to graph and solve equations of circles, lines, and other curves on the complex plane This course is suitable for anyone who wants to learn or review the basics of complex numbers and their applications. It is especially useful for students and professionals in engineering, physics, computer science, cryptography, and other related fields. By the end of this course, you will have a solid understanding of complex numbers and their operations. You will also be able to apply the knowledge and skills you gain to real-world problems and challenges that involve complex numbers. Once enrolled, you have access to dynamic video lessons, interactive quizzes, and live chat support for an immersive learning experience. You engage with clear video explanations, test your understanding with instant-feedback quizzes and interact with our expert instructor and peers in the chat room. Join a supportive learning community to exchange ideas, ask questions, and collaborate with peers as you master the material, by enrolling right away.

This course introduces multi-variable real-valued functions and thoroughly addresses their limits, continuity, partial and total derivatives, applications and related concepts. You will learn how to: - Define and classify real-valued functions of several variables and their properties, such as domain, range, graphs, level curves and surfaces - Find the limit of a function of several variables as the independent variables approach certain values, and use the formal and informal definitions of limits - Find the continuity of a function of several variables at a point or on a set, and use the graphical, formal, and informal definitions of continuity - Find the partial derivative of a function of several variables with respect to one of the independent variables, and use the formal definition and various rules of partial differentiation - Find the higher-order partial derivatives of a function of several variables by applying the partial differentiation rules repeatedly, and use the notation and terminology for higher partial derivatives - Find the partial derivative of a function of several variables that is composed of other functions, and use the chain rule to differentiate composite functions - Find the partial derivative of a function of several variables that is homogeneous, and use the Euler's theorem to simplify the calculation - Find the total differential and derivative of a function of several variables, and use them to approximate the change in the function value - Find the partial derivative of a function of several variables that is defined implicitly by an equation - Find the Jacobian determinant of a function of several variables, and use it to obtain derivatives of implicit functions - Find the Taylor series expansion of a function of several variables, and use it to approximate the function value and its derivatives - Find the equation of the tangent plane and the normal line to a surface defined by a function of two variables, and use them to analyze the local behaviour of the surface - Find the extreme values of a function of several variables, and use the partial derivatives and the second derivative test to determine the nature of the extrema - Find the extreme values of a function of several variables subject to some constraint, and use the partial derivatives and the method of Lagrange multipliers to solve the constrained optimization problem This course is suitable for anyone who wants to learn or review the advanced topics of calculus and its applications. It is especially useful for students and professionals in analysis, differential equations, optimization, physics, engineering, and other related fields. By the end of this course, you will have a solid understanding of derivatives of functions of several variables. You will also be able to apply the knowledge and skills you gain to real-world problems and challenges that involve functions of several variables and their derivatives. Once enrolled, you have access to dynamic video lessons, interactive quizzes, and live chat support for an immersive learning experience. You engage with clear video explanations, test your understanding with instant-feedback quizzes and interact with our expert instructor and peers in the chat room. Join a supportive learning community to exchange ideas, ask questions, and collaborate with peers as you master the material, by enrolling right away.

Integral transforms (Laplace, Fourier, Mellin, Hankel and other transforms ), their inverses and applications to the solutions of ordinary differential equations.