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Do you want to learn how to work with quantities that have both magnitude and direction? Do you want to understand the concepts of scalars, vectors, tensors, components, projections, products, and equations of vectors? Do you want to master the skills of performing algebraic, geometric, differential, and integral operations on vectors using different methods and tools? If you answered yes to any of these questions, then this course is for you! This course covers the fundamentals of vectors and their applications in mathematics and mechanics. You will learn how to: - Define and classify scalars, vectors, and tensors and their properties - Represent vectors by directed line segments, unit vectors, direction cosines, and coordinates - Perform vector addition, subtraction, and multiplication by a scalar using the triangle and parallelogram laws - Apply vector algebra to various geometrical problems involving mid-points, parallelism, and collinearity - Find the position vector of a point and use it to locate the point in space - Resolve vectors into components in two and three dimensions and use them to simplify vector operations - Divide a line in a given ratio internally or externally using vectors - Project a vector on another vector or a plane and use it to find the angle or distance between them - Find the centroid of a set of points or a polygon using vectors - Find the scalar and vector products of two vectors and use them to calculate the area, volume, and orthogonality of geometrical figures - Find the scalar and vector triple products of three vectors and use them to determine the coplanarity and linear dependence of vectors - Solve vector equations with unknown vectors or scalars using various techniques - Find the vector equation of a line or a plane and use it to describe the direction, intersection, angle, and distance of lines and planes - Find the parametric and non-parametric equations of circles, parabolas, ellipses, and hyperbolas using vectors - Differentiate and integrate vector-valued functions and use the rules of vector differentiation and integration - Apply vector differentiation and integration to find the derivatives, arc length, and curvature of parametric curves - Find the tangential, normal, and binormal vectors and the osculating, normal, and rectifying planes of a parametric curve using the Frenet-Serret formulas - Apply vectors to various problems in mechanics, such as forces, equilibrium, work, energy, momentum, displacement, velocity, acceleration, and motion in different coordinate systems and frames of reference This course is suitable for anyone who wants to learn or review the basics of vectors and their applications. It is especially useful for students and professionals in engineering, physics, geometry, calculus, and other related fields. By the end of this course, you will have a firm understanding of vectors and their operations. You will also be able to apply the knowledge and skills you learned to real-world problems and challenges that involve vectors. 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.

Vector products and vector equations (standard and parametric) equations of geometries.

Differentiation and integration of vectors and their applications to mechanics and differential geometry.