Vector Algebra
A mini-course taken from our Mechanics 1 course
brought to you by StillKinetic.com
taught by Steve Pomroy
In this course, you'll learn what vectors are and how to manipulate them. After vectors are fully defined, we'll consider basic operations like addition and subtraction, and then move into the multiplication of vectors by the dot product and cross product. By the time you've completed the course, you'll have a solid grounding in vector algebra, and you'll be ready to move on to the many applications throughout STEM disciplines.
The focus of the course is on physical vectors in 2- and 3-dimensional space. We won't look a the more general mathematical vectors that might have any number of dimensions (up to infinity!). This gives you a good foundation to work from if you want to continue into more advanced topics on vectors (including both higher dimensions and vector calculus). It also gives you the tools you need to apply vectors to the study of the physical sciences.
LECTURE: Definition and Description of Vectors
LECTURE: Basic Vector Operations
DEMO: Basic Vector Operations
PRACTICE: Basic Vector Operations
QUIZ: Vector Basics
LECTURE: Vector Conversions in 2 Dimensions
DEMO: Conversions in 2-D
PRACTICE: Conversions in 2-D
QUIZ: Vector Conversions in 2-D
LECTURE: Magnitudes and Angles in 3 Dimensions
DEMO: Magnitudes and Angles in 3-D
FREE PREVIEWPRACTICE: Magnitude and Angles in 3-D
QUIZ: Magnitude and Angles in 3-D
LECTURE: The Dot product (AKA - Scalar Product)
DEMO: The Dot Product
PRACTICE: The Dot Product
QUIZ: The Dot Product
LECTURE: The Cross product (AKA - Vector Product)
DEMO: The Cross Product
PRACTICE: The Cross Product
LECTURE: Cross product Mnemonics
DEMO: Cross Product Mnemonics
PRACTICE: Cross product Mnemonics
QUIZ: The Cross product
LECTURE: Triple Products of Vectors
DEMO: Triple Products
PRACTICE: Triple Products
QUIZ: Triple Products
LECTURE: Vector Algebra Summary and Conclusion
FREE PREVIEWFINAL QUIZ: Vector Algebra
Steve Pomroy
Steve Pomroy holds an undergraduate degree in Mechanical Engineering and a Masters Degree in Aerospace Engineering. With over 20 years in aviation and over 6,000 hours of flying time, most of Steve's professional experience is in flight operations. Most recently, he's been operating as a Captain on a Dash-8-Q400 aircraft at a regional airline in Canada.
Steve's teaching background includes three years teaching Mechanical Engineering at an international college in the Middle East, and many years (and thousands of flight hours!) as a flight instructor, both civilian and military. Aside from in-person instruction (both in the classroom and in the airplane), Steve has also worked behind-the-scenes on tutorial video development for PilotEffect.com. Currently, his program and course-development efforts are focused on engineering courses at StillKinetic.com.
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