Explore the fundamentals of multivariable calculus in this comprehensive 90-minute tutorial. Begin with an introduction to vectors in two and three dimensions, learning to calculate vector lengths and perform basic vector operations. Delve into vector addition, scalar multiplication, and subtraction before examining the algebraic properties of vectors. Study the dot product and its applications, including finding angles between vectors and identifying orthogonal vectors. Conclude by mastering vector and parametric equations of lines in three-dimensional space, with practical examples on finding line equations and determining intersection points between lines and planes.
Overview
Syllabus
Introduction to Multivariable Calculus (Calc 3).
Length of a Vector in 2 Dimensions (examples).
1.1 Vector Between Two Points and Vector Length (example).
1.1 Vectors with 3 components (3 dimensions).
1.1 Length of a 3-Dimensional Vector.
1.1 Vector Addition.
1.1 Multiplying a Vector by a Scalar.
1.1 Vector Subtraction.
1.2 Algebraic Properties of Vectors.
1.3 Definition of the Dot Product.
1.3 Dot Product - Angle Between Two Vectors.
1.3 Find the Angle Between Two Vectors (example).
1.3 Orthogonal Vectors.
Vector and Parametric Equations of a Line (Line in 3 dimensions).
Finding the Equation of a Line in 3 dimensions (Example).
Finding the Intersection Point of a Line and a Plane.
Taught by
rootmath
