There are also a few videos for brushing up on the unit circle. Limits form the foundation on which Calculus is built. We discuss the concept of a limit, and different ways to evaluate limits. Derivatives measure the rate of change in a function over an interval.
The difference in Calculus is that now we are finding the slope of a curve that changes depending on x, instead of just a straight line. There are more practical uses of derivatives than you can imagine in fields such as physics, engineering, biology, chemistry, and others. This unit is primarily concerned with explaining where derivatives come from and the actual process of how to take a derivative. Now that we know the rules for how to take a derivative, we turn our attention to the various uses of derivatives.
This unit assumes you are already proficient with the derivative rules, and we primarily focus on bigger picture concepts in regards to derivatives.
Calculus: An Integrated Approach to Functions and Their Rates of Change: volume 2
The ultimate goal of integration is to find the area under a curve over a given interval. Interestingly, this is somehow linked to the concept of the derivative from the last unit. We explain these connections as well as how to compute the area under a curve. We should already be familiar with exponential and logarithmic functions from a previous algebra course. In this unit we begin by reviewing some basic properties of exponentials and logarithms, and finish with how to take derivatives and integrals dealing with exponential and logarithmic functions.
In this unit we look at some advanced uses of applications. Here we assume the student is already proficient with the integration rules and we focus primarily on the big picture concepts of different ways integrals can be used. Here we examine a few additional advanced families of functions and look at a few derivative and integral rules concerning these functions.
A differential equation in its simplest form is any equation that contains a derivative. Many real life and environmental situations are modeled by a differential equation because they examine how things change over time. It's fast, it's easy and fewer course materials help minimise costs for your students.
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congdong.bancongxanh.com/20315.php In this section: About this product Features Table of contents Preface PDF Courses About this product Description A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. Features A careful, intuitive presentation of key calculus and precalculus ideas, stressing the connections between precalculus and calculus, and tying these ideas into real-world situations. Accessible and interesting to anxious, underprepared calculus students. Unique, innovative approach that targets a key problem in calculus.
Penetrating, well constructed examples that get to the heart of the discussion. Creative exercises and problems. Use of technology is assumed, but no specific technology is required. Topics presented analytically and graphically, numerically and verbally Rule of Four. Full coverage of single variable calculus 2 semesters. Table of contents I. Functions Are Lurking Everywhere.