About Part I: Vector Arithmetic, Lec 1 | MIT Calculus Revisited: Multivariable Calculus

Tangential and Normal Vectors for Space Curves in Multivariable Calculus Vector Arithmetic in Three-Dimensional Space Multivariable Chain Rule for Composite Functions Vector Equation of a Plane and a Line in Three-Dimensional Space Differentiating Integrals with Respect to a Parameter in Multivariable Calculus Fundamental Theorem for Iterated Double Integrals in Multivariable Calculus Matrix Operations in Linear Algebra Inverting Nonlinear Systems of Equations Using the Jacobian Matrix in Multivariable Calculus Optimality conditions for free problems in two or more independent variables Dot Product Operations in Euclidean Space Exact Differentials in Multivariable Calculus The Jacobian Determinant for Change of Variables in Multiple Integration Integral as Accumulated Summation Limit Vector Arithmetic in Multivariable Calculus Velocity and Acceleration Vectors in Polar Coordinates for Multivariable Calculus N-Dimensional Vector Spaces and Nuples in Multivariable Calculus Partial Derivatives Multivariable Analysis Computing the Inverse of a Matrix by Row Reduction in Linear Algebra Cross Product in Three Dimensional Space Calculus of vector functions Local Linear Approximation and Matrix Algebra in Multivariable Calculus Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) Derivatives and Partial Derivatives of Scalar Functions Polar Coordinates and Their Relation to Cartesian Coordinates in Multivariable Calculus