Home → Course Related Materials → Single-Variable Calculus II
 
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.
You must be logged in to perform this action.

Single-Variable Calculus II

View Resource
Read the Fine Print
Subject:
Mathematics and Statistics
Institution Name:
The Saylor Foundation
Collection:
Saylor Foundation
Grade Level:
Post-secondary
Abstract:

This course is the second installment of Single-Variable Calculus. The student will explore the mathematical applications of integration before delving into the second major topic of this course: series. The course will conclude with an introduction to differential equations. Upon successful completion of this course, students will be able to: Define and describe the indefinite integral; Compute elementary definite and indefinite integrals; Explain the relationship between the area problem and the indefinite integral; Use the midpoint, trapezoidal, and Simpson's rule to approximate the area under a curve; State the fundamental theorem of calculus; Use change of variables to compute more complicated integrals; Integrate transcendental, logarithmic, hyperbolic, and trigonometric functions; Find the area between two curves; Find the volumes of solids using ideas from geometry; Find the volumes of solids of revolution using disks, washers, and shells; Find the surface area of a solid of revolution; Compute the average value of a function; Use integrals to compute displacement, total distance traveled, moments, centers of mass, and work; Use integration by parts to compute definite integrals; Use trigonometric substitution to compute definite and indefinite integrals; Use the natural logarithm in substitutions to compute integrals; Integrate rational functions using the method of partial fractions; Compute improper integrals of both types; Graph and differentiate parametric equations; Convert between Cartesian and polar coordinates; Graph and differentiate equations in polar coordinates; Write and interpret a parameterization for a curve; Find the length of a curve described in Cartesian coordinates, described in polar coordinates, or described by a parameterization; Compute areas under curves described by polar coordinates; Define convergence and limits in the context of sequences and series; Find the limits of sequences and series; Discuss the convergence of the geometric and binomial series; Show the convergence of positive series using the comparison, integral, limit comparison, ratio, and root tests; Show the divergence of a positive series using the divergence test; Show the convergence of alternating series; Define absolute and conditional convergence; Show the absolute convergence of a series using the comparison, integral, limit comparison, ratio, and root tests; Manipulate power series algebraically; Differentiate and integrate power series; Compute Taylor and MacLaurin series; Recognize a first order differential equation; Recognize an initial value problem; Solve a first order ODE/IVP using separation of variables; Draw a slope field given an ODE; Use Euler's method to approximate solutions to basic ODE; Apply basic solution techniques for linear, first order ODE to problems involving exponential growth and decay, logistic growth, radioactive decay, compound interest, epidemiology, and Newton's Law of Cooling. (Mathematics 102; See also: Chemistry 004, Computer Science 104, Mechanical Engineering 002)

Languages:
English
Material Type:
Activities and Labs, Assessments, Full Course, Homework and Assignments, Lecture Notes, Readings, Syllabi, Video Lectures
Media Format:
Audio, Graphics/Photos, Text/HTML, Downloadable docs, Video, Interactive
Conditions of Use:
Creative Commons Attribution-Noncommercial 3.0
You are welcome to share, remix, and adapt this course under the terms of the Creative Commons Attribution 3.0 Unported License; however, many linked materials within this course are copyright of their respective authors/owners and may not be openly-licensed. Please respect the copyright and terms of use associated with each resource.
Copyright Holder:
The Saylor Foundation

Comments

Add Comment

Send link to this page

The e-mail address to send this link to.
A comment about this link.
Save
Log in or Register
▼

Rate and Review

Evaluate Resource What is this?

Common Core Standards

Align Resource
Not Yet Aligned

    Add new alignment tag:

    Share

    Tags

    Keywords, descriptive words, interested groups & more