Vector Algebra, Vector Calculus, and Differential Equations

Many scientific, engineering, and data disciplines rely heavily on understanding how quantities change and interact in multi-dimensional space. This course provides a clear, structured path to mastering the core mathematical principles of vectors and differential equations. You will transition from basic algebraic concepts to analyzing complex vector fields and solving differential equations used to model real-world physical systems. What you'll learn: - Understand foundational vector operations, including dot products, cross products, and projections. - Apply vector differentiation and integration to analyze curves, surfaces, and multi-dimensional spaces. - Solve first-order and higher-order ordinary differential equations using systematic, step-by-step methods. - Explore key vector calculus theorems, including Green's, Stokes's, and the Divergence theorem. - Discover modern applications of vector mathematics in computer graphics, physics engines, and machine learning gradients. The course begins with fundamental definitions of vectors and coordinate systems before advancing to vector fields, calculus operators, and differential equation modeling. You will reinforce your learning through clear written explanations, step-by-step derivations, and practical text-based exercises. Designed for students, aspiring engineers, and self-taught technical professionals, this course requires only a basic background in algebra and basic single-variable calculus. Start building your mathematical foundation today.