Sal finds the first and the second derivatives of the vector-valued function h(t)=(-t_-6,4t_+2t+1).
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-bc/bc-derivatives-advanced/bc-diff-param-vec-func/e/second-derivatives--vector-valued-functions-?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-derivatives-advanced/bc-polar-functions-differentiation/v/derivatives-in-polar-coordinates?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-derivatives-advanced/bc-diff-param-vec-func/v/second-derivative-of-parametric-functions?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC
AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test
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https://www.youtube.com/watch?v=-vv63FS__bY
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Introduction to PCR (polymerase chain reaction).
Watch the next lesson: https://www.khanacademy.org/test-prep/mcat/biomolecules/dna-technology/v/dna-libraries-generating-cdna?utm_source=YT&utm_medium=Desc&utm_campaign=mcat
Missed the previous lesson? https://www.khanacademy.org/test-prep/mcat/biomolecules/dna-technology/v/gel-electrophoresis-dna?utm_source=YT&utm_medium=Desc&utm_campaign=mcat
MCAT on Khan Academy: Go ahead and practice some passage-based questions!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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https://www.youtube.com/watch?v=nHi-3jP6Mvc
Note: All Khan Academy content is available for free at (www.khanacademy.org)
And another example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/null_column_space/v/matrix-vector-products?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/matrices_elimination/v/matrices-reduced-row-echelon-form-2?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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https://www.youtube.com/watch?v=JVDrlTdzxiI
Note: All Khan Academy content is available for free at (www.khanacademy.org)
We want you to feel comfortable moving between seconds, minutes, and hours. Let's create some tables where we compare and covert these measurements of time.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/cc-fourth-grade-math/cc-4th-measurement-topic/cc-4th-unit-conversion/e/measurement-units?utm_source=YT&utm_medium=Desc&utm_campaign=4thgrade
Watch the next lesson: https://www.khanacademy.org/math/cc-fourth-grade-math/cc-4th-measurement-topic/cc-4th-unit-conversion/v/feet-to-inches-exercise-example?utm_source=YT&utm_medium=Desc&utm_campaign=4thgrade
Missed the previous lesson? https://www.khanacademy.org/math/cc-fourth-grade-math/cc-4th-measurement-topic/cc-4th-unit-sense/v/unit-sense-exercise-example-2?utm_source=YT&utm_medium=Desc&utm_campaign=4thgrade
Grade 4th on Khan Academy: 4th grade is the time to start really fine-tuning your arithmetic skills. Not only will you be a multi-digit addition and subtraction rockstar, but you'll extend the multiplication and division that you started in 3rd grade to several digits. You'll also discover that you sometimes have something left over (called a "remainder") when you divide. In 3rd grade you learned what a fraction is. Now you'll start adding, subtracting, multiplying, and comparing them. You'll also see how they relate to decimals. On other fronts, you'll learn how to convert between different units (which is super important when comparing the size and speed of robot unicorns in different countries) and continue your journey thinking about various shapes in two dimensions. Some of the foundational concepts of geometry (like lines, rays and angles) also get introduced. As always, we'll round this out with a healthy dose of applied word problems and explorations of number patterns and properties (including the ideas of factors, multiples and prime numbers). The fun must not stop! (Content was selected for this grade level based on a typical curriculum in the United States.)
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https://www.youtube.com/watch?v=-r7JwuSdj5M
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Introduction to complex numbers. Adding, subtracting and multiplying complex numbers.
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https://www.youtube.com/watch?v=kpywdu1afas
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Word problem solving strategies from chapter 3 of ck12.org Algebra I book
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https://www.youtube.com/watch?v=LRKMoqrMbGw
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Understanding the basics of lists in Python
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https://www.youtube.com/watch?v=zEyEC34MY1A
Note: All Khan Academy content is available for free at (www.khanacademy.org)
More free lessons at: http://www.khanacademy.org/video?v=-MYh3s__qlA
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https://www.youtube.com/watch?v=-MYh3s__qlA
Note: All Khan Academy content is available for free at (www.khanacademy.org)
More on curl
Watch the next lesson: https://www.khanacademy.org/math/multivariable-calculus/line_integrals_topic/line_integrals/v/introduction-to-the-line-integral?utm_source=YT&utm_medium=Desc&utm_campaign=MultivariableCalculus
Missed the previous lesson?
https://www.khanacademy.org/math/multivariable-calculus/partial_derivatives_topic/curl/v/curl-2?utm_source=YT&utm_medium=Desc&utm_campaign=MultivariableCalculus
Multivariable Calculus on Khan Academy: Think calculus. Then think algebra II and working with two variables in a single equation. Now generalize and combine these two mathematical concepts, and you begin to see some of what Multivariable calculus entails, only now include multi dimensional thinking. Typical concepts or operations may include: limits and continuity, partial differentiation, multiple integration, scalar functions, and fundamental theorem of calculus in multiple dimensions.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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https://www.youtube.com/watch?v=fYzoiWIBjP8