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Calculus is a broad, well-developed subject, so where do we start? With limits! Calculus begins with limits and continuity of functions. In this article, I take the reader on a tour of the Calculus. Through derivatives and integrals, the story continues. Many applications of these concepts are also detailed. Calculus is an exciting journey, so let’s get started.
In Calculus 3, I begin with vector functions of one variable. After that, I cover the calculus of multivariable functions, including limits, continuity, partial differentiation, directional derivatives, extrema, and Lagrange multipliers. After that, a detailed look at multiple integration and then ending with a broad look at vector calculus.
Are you looking to advance in mathematics and maybe even scientific disciplines? Like calculus, linear algebra is crucial to scientists and engineers, playing a pivotal role in many modern advancements. In linear algebra we use both theory and examples to help you learn the power of this valuable tool.
Number Theory has a long and exciting history. To help understand what Number Theory is all about, in this article, we describe a few basic ideas of Number Theory. From divisibility and mathematical induction to Euler’s theorem and solving polynomial congruence equations, Number Theory can be both highly practical and applicable yet also extremely difficult and abstract. Number Theory also provides us with a playground where students can master proof-writing while learning some very exciting applications of the theory. The Law of Quadratic Reciprocity and the much more recent Tonelli-Shanks algorithm are such examples.
Making the transition from calculus to analysis (or from elementary algebra to abstract algebra) can be one of the most challenging transitions for students. In this article, I guide you through this process and explain how to become confident and skilled. You’ll see many articles and videos that will explain and provide insights to help keep you on track and inspired.
In this article, I take the student on a journey where we’ll learn precalculus. I’ll describe each step for you and provide tutorials and videos where you get the necessary understanding. You will understand the process and goals for each chapter, and you’ll gain valuable insights from a seasoned math educator. Precalculus is a gateway to many other subjects. Let’s get started.