周次: 8 日期: April 15, 2022 节次: 2 In this lecture, we discuss the improper integral of type II, as well as the convergence test for improper integral of type I with non-negative integrands. In the section part, we will talk about the simplest differential equations, the geometric visualization of a differential equation with slope fields, and separable equations. Type II Improper Integrals Definition....
周次: 8 备注: Attendance check 日期: April 13, 2022 节次: 1 In this lecture, we consider integrals when the domain of integration is infinite, or the range of the integrand is infinite. Such cases are not Riemann integrable, therefore, they are called improper integrals. We would like to manage the integrations for these cases, via some limit procedure. Outline Improper Integrals of...
周次: 7 备注: Attendance check 日期: April 8, 2022 节次: 2 In this lecture, we will take a quick glance at the Numerical Integration methods. Numerical integrations are very useful in practice. The methods we are going to learn are Trapezoidal Method and Simpson’s Method. We will learn how to evaluate an integration numerically,...
周次: 7 日期: April 6, 2022 节次: 1 In this lecture, we explore more examples of integration. Trigonometric substitutions and integration by looking up the integration tables are covered. Note that most of these calculations can be done by hands. § 8.5 Three Basic Substitutions The most common substitutions are $x=a\tan\theta$, $a=\sin\theta$, and $x=a\sec\theta$. They can be useful for dealing with the integrals involving...
周次: 6 日期: April 1, 2022 节次: 2 In this lecture, we continue presenting the integration of rational functions. After finishing this part, we are going to discuss some trigonometric integration techniques. Outline § 8.3 Integration of Rational Functions Method of Partial Fractions ( for $f(x)/g(x)$ Proper) Factorize the denominator $g(x)$, obtain all its linear and quadratic factors, as well as their powers. In...
周次: 6 日期: March 30, 2022 节次: 1 In this lecture, we’ll learn a new technique for integration, called Integration by Parts. The second part of the lecture will be devoted to the partial fractions decomposition of rational functions. By using such technique, we are able to integrate all the rational functions! § 8.2 Integration by Parts Integration by parts...