Imaginary numbers

שלום! היום נערוך היכרות עם המספר i, הידוע גם בשם היחידה המדומה. מספר זה שונה מכל מה שאתם מכירים. זה מספר מוזר ביותר, מוזר אף יותר מכמה מהמספרים המוזרים האחרים המוכרים לנו במתמטיקה, כמו פַּי או e....

אנחנו מתבקשים לחסר מהמספר המרוכב 2 פחות 3i את המספר המרוכב 6 פחות 18i. הדבר הראשון שנרצה לעשות הוא להפטר מהסגריים האלה. כך שנקבל פשוט אוסף של חלקים ממשיים ומדומים שנוכל לחבר יחד. יש לנו כאן 2 פחות...

[MUSIC] reasoning, computational skills and physical knowledge are all critical components of an engineer's judgement. Building those skills starts with understanding how to model components...

[MUSIC] class. Everything Is The Same: Modeling Engineered Systems. I hope you are looking forward to the class. One of the most fundamental goals in this class is to train you to synthesize different...

[MUSIC]. Hi, my name is Andy Wilson and I'm a graduate student working in Todd Murphey's lab. And I'm Henry Hung, I'm an undergraduate working in Todd Murphey's...

Hi. Here I'm going to show you an example of how to simplify an expression when you have a negative inside of a square root. In the example we have here, we have 5 minus the square root of...

Last time, we learned that vector and matrix representations can make your life easier. Specifically when you implement Euler integration for a complicated system involving many states. But how do we...

- TO MULTIPLY THE GIVEN COMPLEX NUMBERS WE'LL MULTIPLY THESE ALGEBRAICALLY LIKE WE NORMALLY WOULD THEN WE NEED TO MAKE SURE THE PRODUCT IS IN THE FORM OF A COMPLEX NUMBER MEANING IT'S...

[MUSIC] about Newton's laws in Lecture three, but in the absence of mass. Today we are going to look at what happens when the mass at a point is non zero. That is we are going to look at the...

Last time we talked about analogies between physical systems. Today we are going to talk about using physical systems to understand and reason about mathematical expressions. If I give you a matrix of...