Master Calculus 3 concepts with this free online course covering vectors, multivariable functions, integrals, vector fields, and advanced techniques. Perfect for beginners.
Calculus 3 is an extensive course with a total duration of 75 hours and 24 minutes. Renowned for its depth and clarity, the course has earned an exceptional average rating of 5 out of 5 stars, reflecting its high-quality instruction and comprehensive content.
Belonging to the category of Basic Studies, specifically under Calculus, this course delves into advanced topics fundamental to understanding multidimensional spaces and multivariable calculus. It begins by introducing vectors and their application in a 3-D coordinate system, progressing to operations with vectors such as the dot product and cross product.
Students will learn to navigate 3-D space through lectures focused on lines, planes, and surfaces, including the use of cylindrical and spherical coordinates. This foundational knowledge sets the stage for exploring vector functions, their derivatives, integrals, and various applications like arc length and velocity.
The course offers a detailed examination of multivariable functions, addressing domain, continuity, partial derivatives, and the chain rule. Students will explore advanced concepts such as directional derivatives, gradients, tangent planes, normal lines, and optimization techniques including LaGrange Multipliers.
A significant portion of the course is dedicated to multiple integrals. Students are guided through double and triple integrals, including regions defined by polar, cylindrical, and spherical coordinates. Practical applications such as finding the center of mass and volume are thoroughly covered.
Finally, the course introduces vector fields, including divergence, curl, and the computation of line integrals over both conservative and non-conservative fields. Advanced theorems like Green's Theorem, and Divergence/Stokes' Theorem are also explored, solidifying students' understanding of the complex interplay between calculus and vector analysis.
Calculus 3 stands out for its methodical approach and the depth of topics covered, making it an invaluable resource for anyone seeking to master multivariable calculus.
Video class: Calculus 3 Lecture 11.1: An Introduction to Vectors
2h37m
Video class: Calculus 3 Lecture 11.2: Vectors in 3-D Coordinate System
1h10m
Video class: Calculus 3 Lecture 11.3: Using the Dot Product
2h29m
Video class: Calculus 3 Lecture 11.4: The Cross Product
2h11m
Video class: Calculus 3 Lecture 11.5: Lines and Planes in 3-D
3h21m
Video class: Calculus 3 Lecture 11.6: Cylinders and Surfaces in 3-D
2h32m
Video class: Calculus 3 Lecture 11.7: Using Cylindrical and Spherical Coordinates
1h40m
Video class: Calculus 3 Lecture 12.1: An Introduction To Vector Functions
2h04m
Video class: Calculus 3 Lecture 12.2: Derivatives and Integrals of Vector Functions
2h42m
Video class: Calculus 3 Lecture 12.3: Arc Length/Parameterization, TNB (Frenet-Serret) Intro
2h12m
Video class: Calculus 3 Lecture 12.3/12.5: TNB (Frenet-Serret) Frames, Curvature, Torsion, Encapsulation
2h37m
Video class: Calculus 3 Lecture 12.4: Velocity and Acceleration of Vector Functions
1h02m
Video class: Calculus 3 Lecture 13.1: Intro to Multivariable Functions (Domain, Sketching, Level Curves)
1h49m
Video class: Calculus 3 Lecture 13.2: Limits and Continuity of Multivariable Functions (with Squeeze Th.)
2h14m
Video class: Calculus 3 Lecture 13.3: Partial Derivatives (Derivatives of Multivariable Functions)
2h28m
Video class: Calculus 3 Lecture 13.4: Finding Differentials of Multivariable Functions
1h51m
Video class: Calculus 3 Lecture 13.5: The Chain Rule for Multivariable Functions
2h11m
Video class: Calculus 3 Lecture 13.6: Finding Directional Derivatives and Gradients
2h37m
Video class: Calculus 3 Lecture 13.7: Finding Tangent Planes and Normal Lines to Surfaces
1h41m
Video class: Calculus 3 Lecture 13.8: Finding Extrema of Functions of 2 Variables (Max and Min)
3h38m
75 hours and 24 minutes of online video course
Exercises to train your knowledge
Certificate of course completion
100% free, from content to certificate
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