Dive into advanced calculus concepts through this comprehensive lecture series. Explore vectors, dot products, cross products, and their applications in physics. Master equations of lines and planes in three dimensions, study conic sections and quadric surfaces, and delve into polar coordinates. Grasp multivariable functions and their limits, double and triple integrals in various coordinate systems, and their practical applications. Investigate parametric equations, vector functions, and their derivatives and integrals. Analyze motion in 3D space, including projectile motion, while learning about arclength and curvature. Gain a deep understanding of Calculus 3 topics through detailed explanations and examples.
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
