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...
周次: 5 日期: March 25, 2022 节次: 2 In this course, we will discuss the definition of hyperbolic functions. And we shift our attention to several integration techniques. These techniques can help us integrate more functions. A typical technique called “Integration by Parts” will be discussed as well....
周次: 5 日期: March 23, 2022 节次: 1 In this lecture, we define the inverse trigonometric functions, and develop some basic properties. The properties we are focusing on are the differentiation and integration properties. A brief introduction on hyperbolic functions, in particular the hyperbolic cosine and hyperbolic sine functions are given. As the second half, we discuss some integration techniques. Those techniques could help...
周次: 4 备注: Attendance check 日期: March 18, 2022 节次: 2 In this lecture, we continue on the discussion of logarithmic and exponential functions. The simplest differential equation is discussed, there are a lot of real applications even for such simple equations. And the definitions of growth rates are given in terms of the notation “big-oh...
周次: 4 日期: March 16, 2022 节次: 1 In this and next lectures, we will quickly go through the contents in chapter 7. Since a lot of the contents have been taught last semester or have known in high school age. § 7.1 Inverse Functions and Their Derivatives We have learned inverse functions, their domain and range, their graph, etc. In particular, we have...