What happens when the characteristic equations has complex roots?!
Watch the next lesson: https://www.khanacademy.org/math/differential-equations/second-order-differential-equations/complex-roots-characteristic-equation/v/complex-roots-of-the-characteristic-equations-2?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations
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https://www.khanacademy.org/math/differential-equations/second-order-differential-equations/linear-homogeneous-2nd-order/v/2nd-order-linear-homogeneous-differential-equations-4?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations
Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations.
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=6xEO4BeawzA
Learn how to plot a simple inequality on a number line.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/applying-math-reasoning-topic/greater-than-less-than/e/inequalities_on_a_number_line?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra
Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/applying-math-reasoning-topic/cross-topic-arithmetic/v/rational-number-word-problem-example-1?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra
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https://www.khanacademy.org/math/pre-algebra/applying-math-reasoning-topic/greater-than-less-than/v/inequalities-in-one-variable-1-exercise?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra
Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!
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https://www.youtube.com/watch?v=dTwZ5N126gw
Note: All Khan Academy content is available for free at (www.khanacademy.org)
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https://www.youtube.com/watch?v=Cm8kRFMxsf0
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Addition of Water (Acid-Catalyzed) Mechanism. Created by Sal Khan.
Watch the next lesson: https://www.khanacademy.org/science/organic-chemistry/alkenes-alkynes/alkene-reactions/v/polymerization-of-alkenes-with-acid?utm_source=YT&utm_medium=Desc&utm_campaign=organicchemistry
Missed the previous lesson? https://www.khanacademy.org/science/organic-chemistry/alkenes-alkynes/alkene-reactions/v/markovnikov-s-rule-and-carbocations?utm_source=YT&utm_medium=Desc&utm_campaign=organicchemistry
Organic Chemistry on Khan Academy: Carbon can form covalent bonds with itself and other elements to create a mind-boggling array of structures. In organic chemistry, we will learn about the reactions chemists use to synthesize crazy carbon based structures, as well as the analytical methods to characterize them. We will also think about how those reactions are occurring on a molecular level with reaction mechanisms. Simply put, organic chemistry is like building with molecular Legos. Let's make some beautiful organic molecules!
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=O_yeKo6-qIg
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)
Learn how to count animals organized in different patterns.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/early-math/cc-early-math-counting-topic/cc-early-math-count-object-topic/e/how-many-objects-2?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath
Watch the next lesson: https://www.khanacademy.org/math/early-math/cc-early-math-counting-topic/cc-early-math-comparing-numbers/v/comparing-groups-through-10-example?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath
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https://www.khanacademy.org/math/early-math/cc-early-math-counting-topic/cc-early-math-count-object-topic/v/how-many-objects-1?utm_source=YT&utm_medium=Desc&utm_campaign=EarlyMath
Early Math on Khan Academy: Math begins with counting. It's the most important skill we learn in our early years and becomes the foundation for all other math concepts. Once we can count, we can add, subtract, and measure the world around us. Shortly thereafter, we can learn about place values, plots, graphs, time, money, and shapes. These early math skills are presented in this subject's tutorials in a straightforward, understandable, and (dare we say it) fun way!
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https://www.youtube.com/watch?v=EUqhLxFccbM
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/e/unit-vector?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/v/linear-algebra-parametric-representations-of-lines?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
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https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/v/linear-algebra-vector-examples?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=9ylUcCOTH8Y
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Introduction to the intuition behind limits
Watch the next lesson: https://www.khanacademy.org/math/precalculus/limit_topic_precalc/limits_precalc/v/2-sided-limit-from-graph?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
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https://www.khanacademy.org/math/precalculus/limit_topic_precalc/limits_precalc/v/introduction-to-limits-hd?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
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https://www.youtube.com/watch?v=W0VWO4asgmk