This course on Multivariable Calculus aims to teach students the fundamentals of vectors, vector operations, dot products, and equations of lines in three dimensions. By the end of the course, students will be able to calculate vector lengths, perform vector operations, find the angle between vectors, and determine equations of lines in 3D space. The teaching method involves theoretical explanations followed by practical examples to reinforce learning. This course is intended for learners interested in advancing their understanding of calculus beyond the single-variable level.
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
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