![]() ![]() This information will be taken from Chapters 1-5 in the textbook. “AP Calculus AB and BC Course and Exam Description, Effective Fall 2019,” The College Board, 2019.Note: We will begin by review what was taught in AP Calculus AB this will be called Calculus AB Review. Calculus - Early Transcendentals, 8th Edition. No matter what path you choose, remember that calculus, and more generally mathematics is all around us, and keep on studying and remember to make your exams all Fiveable! Geometry is the study of structures and objects in different dimensions, and topology is the study of structures and their properties under different transformations. Geometry and topology are the study of shape and are two related fields. Number theory, which deals with the properties of numbers, is also a subset of algebra as well. Abstract algebra then includes more abstract structures, such as groups, rings, and fields. Linear algebra is usually the first algebra class one will take and will involve the study of matrices and vectors, and introduces the topic of a vector space (which includes more than just vectors). This Final Exam - Practice - Review is designed for AP Calculus BC (Part 2). It covers both ordinary differential equations, differential equations with respect to one variable, and partial differential equations, differential equations with respect to multiple variables.Īnalysis is the study of change, especially relating to functions and other curves, and this serves as a theoretical extension to calculus, with real analysis covering real-valued functions and complex analysis covering complex numbers and complex-valued functions.Īlgebra is the study of structure (not to be confused with high school algebra). Calculus 2 Final Review Techniques of Integration Sequences & Series. Infinite sequences Finite geometric series Partial sums Infinite geometric series Basic convergence tests Comparison tests Ratio & alternating series. Multivariable calculus applies the concepts of single-variable into multiple dimensions and also expands the concept of vector calculus, which eventually sums up and generalizes most of the important theorems in calculus, especially the Fundamental Theorem of Calculus.ĭifferential equations is all about finding ways to solve many different types of differential equations, especially those which are highly applicable to other disciplines. After this, there are multiple courses which follow, which include multivariable calculus, differential equations, real and complex analysis, linear and abstract algebra,, and geometry and topology. In this unit, you will learn how to use a variety of tests to determine whether a sequence or series converges or diverges. However, there are some concepts in single-variable calculus that aren’t covered in AP Calculus that are useful for higher math courses such as hyperbolic functions, the epsilon-delta definition of a limit, and trigonometric substitutions. If you want to go into higher STEM courses, then you may consider higher mathematical courses. We can still explore these functions with derivatives and integrals. Some infinite series converge to a finite value. Don't all infinite series grow to infinity It turns out the answer is no. Infinite series are sums of an infinite number of terms. Polar functions, too, differ, using polar coordinates for graphing. Start Course challenge Math AP Calculus BC (2017 edition) Unit 12: Series 2,100 possible mastery points About this unit Series are sums of multiple terms. However, AP Physics C uses calculus freely and is a good challenge if you are interested in physics or want a little bit of a challenge! While were often familiar with functions that output just one variable and are graphed with Cartesian coordinates, there are other possibilities Vector-valued functions, for example, can output multiple variables. To find the fourteenth term, a 14, use the formula with a 1 64 and r 1 2. ![]() AP Chemistry utilizes calculus indirectly with the concepts of reaction rates and rate laws. Find the fourteenth term of a sequence where the first term is 64 and the common ratio is r 1 2. ![]() Many science courses are also deeply rooted in calculus as well. A lot of statistics is based off of calculus, even if the relationship isn’t explicitly stated. They continue simple patterns involving numbers and objects with and without. 10.1Defining Convergent and Divergent Infinite Series. Students describe number sequences resulting from skip counting by 2s, 5s and 10s. Now, the question is, what’s next after AP Calculus BC? If you are mainly interested in the humanities or want to go into research sciences, then AP Statistics is a great option. Unit 10 Infinite Sequences & Series (BC Only) 10.0Unit 10 Overview: Infinite Series and Sequences. Congratulations, you’re done with this unit, and as a result, you’ve also reached the end of AP Calculus BC! Now, you have all the tools you need to ace that AP test this May! ![]()
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