En este curso se estudian los conceptos básicos sobre las Ecuaciones Diferenciales Ordinarias (EDO) Se muestran los principales métodos de solución para ecuaciones diferenciales de primer y segundo orden y sus aplicaciones. Se trata la transformada de laplace y la solución mediante el uso de series de potencias.
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Los cursos de Cálculo Diferencial y Cálculo Integral tradicionalmente se ofrecen separados y respetando ese orden. El primero estudia la derivada, y el segundo, la integral, siendo este momento en el que aparece el Teorema Fundamental del Cálculo (TFC) para establecer la relación entre ambos conceptos. En el presente curso vamos a hacer una diferencia: introduciremos la derivada y la integral como conceptos relacionados desde un principio.
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Calculus through Data & Modeling: Differentiation Rules continues the study of differentiable calculus by developing new rules for finding derivatives without having to use the limit definition directly. These differentiation rules will enable the calculation of rates of change with relative ease the derivatives of polynomials, rational functions, algebraic functions, exponential and logarithmic functions, and trigonometric and inverse trigonometric functions.
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After completing this course, students will learn how to successfully apply functions to model different data and real world occurrences. This course reviews the concept of a function and then provide multiple examples of common and uncommon types of functions used in a variety of disciplines. Formulas, domains, ranges, graphs, intercepts, and fundamental behavior are all analyzed using both algebraic and analytic techniques. From this core set of functions, new functions are created by arithmetic operations and function composition.
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In this introductory course on Ordinary Differential Equations, we first provide basic terminologies on the theory of differential equations and then proceed to methods of solving various types of ordinary differential equations. We handle first order differential equations and then second order linear differential equations. We also discuss some related concrete mathematical modeling problems, which can be handled by the methods introduced in this course.
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This course is about differential equations and covers material that all engineers should know. Both basic theory and applications are taught. In the first five weeks we will learn about ordinary differential equations, and in the final week, partial differential equations. The course is composed of 56 short lecture videos, with a few simple problems to solve following each lecture. And after each substantial topic, there is a short practice quiz. Solutions to the problems and practice quizzes can be found in instructor-provided lecture notes. There are a total of six weeks in the course, and at the end of each week there is an assessed quiz.
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Mathematical thinking is crucial in all areas of computer science: algorithms, bioinformatics, computer graphics, data science, machine learning, etc. In this course, we will learn the most important tools used in discrete mathematics: induction, recursion, logic, invariants, examples, optimality. We will use these tools to answer typical programming questions like: How can we be certain a solution exists? Am I sure my program computes the optimal answer? Do each of these objects meet the given requirements?
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En este segundo curso de acceso gratuito* del programa especializado Educación Matemática para profesores de primaria, conocerás las cuestiones particulares sobre el aprendizaje de las matemáticas y las dificultades y los errores más frecuentes que tienen que enfrentar los estudiantes al aprenderlas. El curso tiene una duración aproximada de seis semanas, con una dedicación promedio de 4 horas semanales. Todas las evaluaciones tienen retroalimentación y podrás descargar la mayoría de los recursos del curso.
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This course covers the fundamental concepts and topics of quantum mechanics which include basic concepts, 1D potential problems, time evolution of quantum states, and essential linear algebra. It provides undergraduate level foundational knowledge and build on them more advanced topics.
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This course helps to build the foundational material to use mathematics as a tool to model, understand, and interpret the world around us. This is done through studying functions, their properties, and applications to data analysis. Concepts of precalculus provide the set of tools for the beginning student to begin their scientific career, preparing them for future science and calculus courses. This course is designed for all students, not just those interested in further mathematics courses.
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En este curso de acceso gratuito*, conocerás algunos temas de las matemáticas escolares con la profundidad necesaria para que puedas ayudar a tus estudiantes a aprenderlas. En este curso, podrás conocer las matemáticas desde cuatro perspectivas: su historia, los conceptos y procedimientos que las caracterizan, las distintas formas en que se hacen presentes (p. ej., tablas, gráficas o expresiones simbólicas), y los fenómenos y situaciones que les dan sentido.
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Are you interested in Data Science but lack the math background for it? Has math always been a tough subject that you tend to avoid? This course will teach you the most fundamental Linear Algebra that you will need for a career in Data Science without a ton of unnecessary proofs and concepts that you may never use. Consider this an expressway to Data Science with approachable methods and friendly concepts that will guide you to truly understanding the most important ideas in Linear Algebra.
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En este tercer curso de acceso gratuito* del programa especializado Educación Matemática para profesores de primaria, conocerás los conceptos y técnicas para planificar e implementar tus clases. El curso tiene una duración aproximada de seis semanas, con una dedicación promedio de 4 horas semanales. Todas las evaluaciones tienen retroalimentación y podrás descargar la mayoría de los recursos del curso.