General Calculus II

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Online Calculus 2 Course Overview

This course is designed to acquaint students to calculus principles such as derivatives, integrals, limits, approximation, applications and modeling, and sequences and series. During this course students will gain experience in the use of calculus methods and learn how calculus methods may be applied to practical applications.  Topics include Antiderivatives and Definite Integrals, the Application of Integrals and Infinite Sequences and Series.

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Calculus 2 Course Text

  • Larson, R., Hostetler, R. P., and Edwards, B.  Calculus, 8th edition, Brooks Cole, 2005.  ISBN: 9780618502981
  • Larson, R., Hostetler, R. P., and Edwards, B. Calculus – Early Transcendental Functions, 3rd edition. Houghton Mifflin Company, 2003. ISBN: 9780618223077
  • Stewart, J.  Calculus: Concepts & Contexts, 3rd Edition.  Cengage Learning, 2004.  ISBN: 9780534409869
  • Varberg, D., Purcell, E., and Rigdon, S.  Calculus, 9th Edition.  Prentice Hall, 2006.  ISBN 9780131429246 [buy a text]
Do I have to buy the textbook?
As in many college courses, purchasing the book is ultimately up to you. The StraighterLine courses use reading assignments and practice work from the textbook as supplements, but you will not be required to turn in anything from the book. StraighterLine recommends that you purchase the appropriate text so you are equipped with as many resources as possible (please note that e-books are generally less expensive but may have slight differences in page numbers and resources compared to a hard copy text).

Online Calculus 2 Course Objectives

After completing this online Calculus II course, students will be able to:After completing this course, students will be able to:
  • Be able to work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal
  • Understand the connections among these representations
  • Understand the meaning of the derivative in terms of a rate of change and local linear approximation
  • Be able to use derivatives to solve a variety of problems
  • Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change
  • Be able to use integrals to solve a variety of problems
  • Understand the relationship between the derivative and the definite integral as expressed in both parts of the fundamental theorem of calculus

Calculus 2 Course Prerequisites

General Calculus II continues where General Calculus I (MAT250) leaves off.  It picks up immediately with Unit 5: Antiderivatives and Definite Integrals.  StraighterLine suggests, though does not require, that students take General Calculus I or its equivalent before enrolling in General Calculus II.

Important Online Course Terms

In this online General Calculus course, different terms are used to designate tasks:

  • Practice Exercise: A non-graded assignment to assist you in practicing the skills discussed in a topic.
  • Suggested Assignments: Practice questions from the textbooks which will help you master key concepts.
  • Exam: A graded online test.

Calculus 2 Course Evaluation Criteria

StraighterLine does not apply letter grades. Students earn a score as a percentage of 100%. A passing percentage is 70% or higher.

If you have chosen a Partner College to award credit for this course, your final grade will be based upon that college's grading scale. Only passing scores will be considered by Partner Colleges for an award of credit.

There are a total of 1000 points in the course:

Topic Assessment Points Available
51 Graded Exam - Unit 5 150
62
 Graded Exam - Unit 6
 150
62
 Midterm Exam (Unit 5-6) 250
68
 Graded Exam - Unit 7 150
68
 Final Exam (Unit 5-7) 300
Total   1000

At the end of the course, each student will receive the number of points earned. The student's final letter grade is determined by the corresponding institution's grading scale.

Online Calculus 2 Course Topics and Objectives

UNIT lESSON tOPIC
Unit 5: Functions and Graphs Lesson 40: Differential Equations and Slope Fields
  • Solve simple differential equations and initial value problems.
  • Generate a slope field for a differential equation.

Lesson 41: Antiderivatives
  • Define the antiderivative and the indefinite integral.
  • Explore basic antiderivative rules.
  • Investigate rules for trigonometric antiderivatives.

Lesson 42: The Chain Rule for Antiderivatives
  • Use simple substitutions to find antiderivatives.
  • Find antiderivatives of trigonometric integrals.

Lesson 43: Antiderivatives of Exponentials
  • Find antiderivatives for exponential functions.

Lesson 44: Antiderivatives of Logarithms
  • Find antiderivatives for logarithmic functions.

Lesson 45: Antiderivatives of Inverse Trigonometric Functions
  • Use inverse trigonometric functions to evaluate integrals.

Lesson 46: Integration by Part
  • Define the integration by parts formula.
  • Use integration by parts to evaluate integrals.

Lesson 47: Integration by Partial Fractio
  • Review partial fraction decomposition of rational functions.
  • Use partial fractions to integrate rational functions.

Lesson 48: Trigonometric Substitutions
  • Use right triangle trigonometry to create substitutions for integrals.
  • Recognize and integrate functions using trigonometric substitutions.

Lesson 49: The Definite Integral
  • Define a Riemann sum.
  • Define a definite integral.
  • Find the area between two curves on the coordinate plane.
  • Explore techniques for approximating definite integrals.

Lesson 50: Fundamental Theorem of Calculus
  • Investigate properties of the definite integral.
  • Define the Fundamental Theorem of Calculus.
  • Explore integral defined functions.
  • Find the average value of a function on an interval.
  • Define the Mean Value Theorem for Integration.
  Lesson 51: Improper Integrals
  • Explore definite integrals with infinite limits.
  • Explore definite integrals with discontinuous functions.
  • Define convergence of an integral.
Unit 6: Applications of Integrals Lesson 52: Net Change and Displacement
  • Define the net change theorem.
  • Compare and contrast the relationship between an object’s displacement and total distance traveled.

Lesson 53: Volume
  • Find the volume of a solid created by rotating a region of the plane around an axis.
  • Use the disc / washer method for finding volumes by rotations.
  • Use the cylindrical shells method for finding volumes by rotations.
  • Define solids created with common cross sections.
  • Find volumes of solids by cross sections.
  Lesson 54: Separable Differential Equations
  • Solve differential equations by the method of separation of variables.
  • Solve problems involving exponential functions.
  • Apply differential equations to bounded growth and decay problems.

 
  Lesson 55: Numerical Solutions to Differential Equations
  • Use slope fields to find approximations to differential equations.
  • Define and use Euler’s method for approximating differential equations.

 
  Lesson 56: Logistic Growth
  • Model logistic growth with a differential equation.
  • Apply logistic models to real-world problems.
  Lesson 57: Work
  • Define work done on an object.
  • Set up and solve problems involving work with integrals.
  • Explore work done on a fluid.
  Lesson 58: Arc Length and Surface of Revolution
  • Use integrals to find the length of an arc on a graph.
  • Use integrals to find the surface area of solids of revolution.

Lesson 59: Integration of Vector-Valued Functions
  • Find antiderivatives of vector-valued functions.
  • Apply vector-valued function to position / velocity problems.
  • Apply vector-valued functions to projectile motion problems.
  Lesson 60: Parametric Integrals
  • Find the area of a region bounded by a parametric curve.
  • Find the arc length along a parametric curve.
  Lesson 61: Polar Integrals
  • Find the area bounded by a polar curve.
  • Find the arc length along a polar curve.

Lesson 62: Other Applications of Definite Integrals
  • Use integrals to identify the center of mass of an object.
  • Use integrals to determine probabilities of events.
Unit 7 Infinite Sequences and Series Lesson 63: Sequences
  • Define a sequence and proper notation.
  • Evaluate the limit of a sequence.
  • Find the nth term of a sequence.
  • Define monotonic and bounded sequences.
  Lesson 64: Series
  • Define a series and proper notation.
  • Define and apply geometric series.
  • Define convergent and divergent series.
  • Apply tests for divergence.
  Lesson 65: Estimating Sums
  • Define and apply the integral test for convergence of a series.
  • Define and apply the comparison test for convergence of a series.
  • Define and apply the limit comparison test for convergence of a series.
  • Estimate the sum of finite and infinite series.
  Lesson 66: Other Tests for Convergence
  • Define and apply the ratio test for convergence of a series.
  • Define absolute convergence of a series and use applicable tests.
  • Define an alternating series.
  • Estimate the sum of an alternating series.
  Lesson 67: Objectives
  • Define a power series representation of a function.
  • Find the radius and interval of convergence for a power series.
  • Differentiate and integrate power series.
  Lesson 68: Taylor and Maclaurin series
  • Define Taylor and Maclaurin series.
  • Use Taylor series to solve application problems.
 Review Review
  • Review

Online Advanced Calculus Tutoring Included

General Calculus II includes 10 hours of free tutoring help— live, one-on-one, on-demand instructional support from SMARTHINKING.

TRANSFERABLE COLLEGE CREDITS: 3

This program provides you with 6-months of course access.

 

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