This is the final unit in the course and can be the most challenging for students, as it if probably the most theoretical. Calculus of parametric equations and curves.Unit 6: Calculus of Polar and Parametric Equations and Differential Equations Direction/slope fields and Euler’s Method.The definition of a differential equation.The following topics are included in the unit: The unit also includes and introduction to differential equations. This unit rounds out calculus of two-dimensional spaces, introducing students to using calculus on less traditional functions such as parametric and polar functions. Integration using tables and calculators.The unit explores all aspects of convergence and divergence of sequences and series, and concludes with writing functions as power series using Taylor and Maclaurin polynomials. Unit 4: More Advanced Techniques of Integration and Arc Length Unit 3: Advanced Techniques of Integration This unit concentrates on more advanced techniques of integration. Unit 2: More Applications of Integrals and Integration by Parts Volumes of solids of revolution using the shell method.Volumes of solids of known cross section.Volumes of solids of revolution using the disk/washer method.This unit does not use advanced techniques of integration, which are learned in Unit 6. Much like differential calculus, students learn integral calculus so they can use techniques to solve real-world problems. Course Content Unit 1: Applications of Integrals The unit on sequences and series focuses primarily on tests for convergence and divergence, power series, expressing functions as power series, and Taylor/Maclaurin series. The differential equations unit is designed to provide students with an introduction to the topic, which will give them an advantage when they take a more thorough differential equations course. Once students have shown competence with both integral and differential calculus, they are prepared for the final two concepts of the course: differential equations and sequences and series. Integral calculus emphasizes techniques of integration and its applications. The course is intended as the second part of a sequence that begins with Calculus I. Calculus II is a comprehensive calculus course that covers advanced applications and techniques of integration, differential equations, and sequences and series.
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