Catalyst University
Postulates of Quantum Mechanics: Observables & Operators
Postulates of Quantum Mechanics: Observables & Operators
Brian McLogan
Take the derivative using the product rule and chain rule
👉 Learn how to find the derivative of a function using the chain rule. The derivative of a function, y = f(x), is the measure of the rate of change of the function, y, with respect to the variable x. The process of finding the derivative...
Brian McLogan
Find the intervals of concavity from the second derivative graph
👉 Learn how to determine the extrema, the intervals of increasing/decreasing, and the concavity of a function from its graph. The extrema of a function are the points where the graph changes from increasing to decreasing or vice versa. A...
Brian McLogan
Solve a quadratic equation using the quadratic formula when their are imaginary solutions
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a...
Curated Video
Restricting the Domain to Create Functions
This video explains the concept of putting restrictions on the domain of a function in order to make it well-defined. They give examples of functions and demonstrate how to determine the values that cause the function to be undefined. By...
Brian McLogan
Learn how to find relative extrema and justify using first derivative test
👉 Learn how to find the extreme values of a function using the first derivative test. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A method that can be...
Curated Video
Determining Solutions to Equations Using Graphs
In this video, the teacher explains how to use a graph to determine if a coordinate pair is a solution to an equation. They demonstrate this by graphing different equations and showing how to identify the points that satisfy the...
Flipping Physics
Determining the Spring Constant, k, with a Vertically Hanging Mass
Hooke’s law is demonstrated and graphed. Spring constant, displacement from equilibrium position, and restoring force are defined and demonstrated.
Brian McLogan
Solving logarithmic equations by factoring
👉 Learn about solving logarithmic equations. Logarithmic equations are equations involving logarithms. To solve a logarithmic equation, we first use our knowledge of logarithm laws/properties to express the terms in both sides of the...
Brian McLogan
How to find the common difference between terms of a sequence
👉 Learn how to determine if a sequence is arithmetic, geometric, or neither. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of...
Brian McLogan
Evaluate for sine cosine and tangent using reference angles
👉 Learn how to evaluate trigonometric functions of a given angle. Given an angle greater than 2pi in radians, to evaluate the trigonometric functions of the given angle, we first determine the smallest positive coterminal angle of the...
Flipping Physics
Hooke's Law Introduction - Force of a Spring
Hooke’s law is demonstrated and graphed. Spring constant, displacement from equilibrium position, and restoring force are defined and demonstrated.
Why U
Pre-Algebra 29 - Roots and Unit Fraction Exponents
Exponents can not only be integers. They can also be fractions. Using the rules of exponents, we can see why a number raised to the power "one over n" is equivalent to the nth root of that number.
Curated Video
Modeling Rational Functions by Graphing
In this lesson, mathematicians will learn how to model rational functions by graphing. By understanding the relationship between variables in a rational function, students can visually represent the data in tables and graphs. Through...
Brian McLogan
Find the domain with a radical in the numerator and denominator
👉 Learn how to find the domain of rational functions with radicals in both the numerator and the denominator. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a rational function,...
Brian McLogan
Conics section Characteristics of a parabola with vertical axis of symmetry
Learn all about parabolas in conic sections. We will discover the basic definitions such as the vertex, focus, directrix, and axis of symmetry. We will also take a look a basic processes such as graphing, writing the equation and...
Brian McLogan
Solve trigonometric equation using identities and zero product property
👉 Learn how to solve trigonometric equations using the zero product property. The zero product property states that when the product of two quantities is equal to 0, then either of the quantities is zero. When solving factored...
Brian McLogan
Adding two vectors together then graphing the resultant vector
Learn how to add/subtract vectors. Vectors can be added, subtracted and multiplied. To add or subtract two or more vectors, we simply add each of the corresponding components of the vectors.
Brian McLogan
Learn how to find the angle of a vector not in component form
Learn how to determine the magnitude and direction of a vector. The magnitude of a vector is the length of the vector. The magnitude of a vector is obtained by taking the square root of the sum of the squares of the components of the...
Brian McLogan
How to graph a polar point and then convert to rectangular form
How to graph a polar point and then convert to rectangular form
Brian McLogan
Learn how to rotate a figure 180 degrees about the origin ex 2
👉 Learn how to rotate a figure and different points about a fixed point. Most often that point or rotation will be the original but it is important to understand that it does not always have to be at the origin. When rotating it is also...
KnowMo
Understanding Reciprocal and Exponential Graphs
The video discusses reciprocal and exponential graphs and their shapes. The instructor explains the formula for reciprocal graphs and how the denominators affect the curve shape. They also cover the negative reciprocal graph and its...
Seven Dimensions
Ensuring a Respectful Workplace
This video showcases a toxic work environment where issues of interpersonal relationships, racism, and bullying are prevalent. The employees discuss their experiences with a colleague named Carol, who is accused of being racially...