Do you want to learn how to manipulate and analyze scalar and vector fields using advanced calculus techniques? Do you want to understand the concepts and methods of scalar and vector products, gradient, divergence, curl, and Laplacian operators? Do you want to apply the principles of vector analysis to solve problems in physics, engineering, and other disciplines? If you answered yes to any of these questions, then this course is for you! In this course, you will learn the fundamentals of calculus of scalar and vector fields, which is the branch of mathematics that deals with functions and operators that map points in space to scalars or vectors. You will learn how to use different notations and conventions to express scalar and vector fields, such as Einstein's summation, Kronecker delta, and Levi-Civita symbols. You will learn how to perform scalar and vector products of vectors, which are useful for measuring angles, areas, and volumes. You will learn how to compute and interpret the gradient of a scalar field, which measures the rate and direction of change of a scalar function. You will learn how to compute and interpret the divergence and curl of a vector field, which measure the sources and vortices of a vector field. You will also learn how to use the Laplacian operator, which combines the divergence and the gradient, and is useful for studying heat conduction, electrostatics, and fluid dynamics. This course will equip you with the skills and knowledge to solve various problems involving scalar and vector fields. You will be able to apply the concepts and methods of calculus of scalar and vector fields to fields such as physics, engineering, chemistry, biology, and more. You will also be able to appreciate the power of vector analysis theorems, such as Gauss', Green's, and Stokes' theorems, which relate the integrals of scalar and vector fields over different domains. By the end of this course, you will be able to: - Define and explain the meaning of scalars, vectors, and tensors - Identify and use different notations and conventions for scalar and vector fields - Perform scalar and vector products of vectors and calculate angles, areas, and volumes - Compute and interpret the gradient of a scalar field and its properties - Compute and interpret the divergence and curl of a vector field and their properties - Compute and interpret the Laplacian of a scalar or a vector field and its applications - Use different coordinate systems and bases to express scalar and vector fields and operators - Compute and interpret the gradient, divergence, curl, and Laplacian in orthogonal curvilinear coordinates - Recognize and use some special curvilinear coordinates, such as cylindrical and spherical coordinates - Apply the vector analysis theorems, such as Gauss', Green's, and Stokes' theorems, to relate the integrals of scalar and vector fields over different domains Created for students, engineers, scientists, and anyone passionate about learning the calculus of scalar and vector fields, this course assumes a basic background in calculus, linear algebra, and vector algebra. With engaging video lessons, interactive quizzes, practice problems, and supportive peer interactions, you'll embark on a journey of discovery and mastery like never before. Seize the opportunity to advance your mathematical skills and unlock new problem-solving possibilities with an enrolment right away!