This is a book on single variable calculus including most of the important applications of calculus. It also includes proofs of all theorems presented, either in the text itself, or in an appendix. It also contains an introduction to vectors and vector products which is developed further in ...
It is a theorem in each text on vector calculus that every closed vector field defined over a simply connected domain is exact. The function f is called a potential function because we can draw surfaces of constant value of f in space (surfaces defined by the equation f(x, y, z) = C...
Ch 18. Vectors & Vector Calculus Ch 19. Understanding Kinematics Ch 20. Understanding Mechanics Ch 21. VCE Specialist Mathematics...What Is a Karnaugh Map? - Definition & Examples Related Study Materials Browse by Courses Glencoe Algebra 1: Online Textbook Help McDougal Littell Pre-Algebra: Onli...
The derivative of a target function with a vector of input variables similarly is a vector. This vector of derivatives for each input variable is the gradient. Gradient (vector calculus): A vector of derivatives for a function that takes a vector of input variables. You might recall from high...
Some of the necessary topics include Differential and Integral Calculus, Partial Derivatives, Vector-Values Functions, Directional Gradient, Hessian, Jacobian, Laplacian and Lagrangian Distribution. Algorithms and Complex Optimizations: This is important for understanding the computational efficiency and scalabili...
Pixel art vs. vector art One of the primary differences between the two formats is the structure. Raster images are made up of a finite number of pixels. Vector art, on the other hand, is deeply rooted in mathematical equations or geometric shapes; hence, its data is more about lines, ...
What is deepfake AI (deep fake)? How to calculate the inception score The actual formula to calculate inception score requires the use of calculus and is beyond the scope of this definition. For a more complete explanation, however, an abbreviated mathematical expression for inception score can ...
Reciprocal: Reciprocal of a = 1/a Additive Identity Property: a + 0 = 0 + a = a Multiplicative Identity Property: a × 1 = 1 × a = a Additive Inverse: a + (-a) = 0 What is the Definition of Algebra? The definition of Algebra states that Algebra is a branch of mathematics th...
In vector calculus there is an operator called del which is actually the greek letter nabla (∇). This operator looks like an upside down upper-case delta, but it performs a much different operation. The del operator is what is known as a vector operator. It is similar to a vector, ...
As you might have guessed, the scalar (absolute value) magnitude of the velocity vector is thespeedof motion. Incalculusterms, velocity is the first derivative of position with respect to time. You can calculate velocity by using a simple formula that includes rate, distance, and time. ...