This course covers topics such as vectors, dot product, cross product, equations of lines and planes in three dimensions, conic sections, polar coordinates, double and triple integrals, parametric equations, vector functions, arclength, curvature, and motion in 3D space. The course aims to teach students the fundamentals of multivariable calculus and how to apply these concepts to solve problems in three-dimensional space. The teaching method includes lectures and full-length discussions on various topics. This course is intended for students who have a basic understanding of calculus and are looking to expand their knowledge to include multivariable calculus concepts.
Overview
Syllabus
Calc 3 Intro Lecture.
Vectors Continued and Intro to Dot Product.
The Dot Product, Direction Cosines, Projections, and Work | Calculus 3 Lecture.
The Cross Product, Area, Volume, and Torque..
Equations of Lines and Planes in Three Dimensions.
Equations of Lines and Planes in Three Dimensions (Part 2).
Conic Sections, Parabolas, Ellipses, and Hyperbolas (Advanced Lecture).
Quadric Surfaces.
Polar Coordinates.
Multivariable Functions and Their Limits Part 1.
Multivariable Limits Part 2.
Introduction to Double Integrals.
Double Integrals as Iterated Integrals.
Double Integrals Over General Regions: Full Lecture.
Double Integrals in Polar Coordinates: Full Lecture.
Applications of Double Integrals: Full Lecture.
Triple Integrals: Full Lecture.
Triple Integrals in Cylindrical Coordinates: Full Lecture.
Triple Integrals in Spherical Coordinates: Full Lecture.
Parametric Equations and Vector Functions: Full Lecture.
Derivatives and Integrals of Vector Functions: Full Lecture.
Arclength and Curvature Full Lecture.
Motion in 3D Space: Full Lecture.
Motion in Space Continued: Projectile Motion : Full Lecture.
Taught by
Jonathan Walters
