Course Text General Calculus II Students may select any one of these texts aligned to this course: Larson, R., Hostetler, R. P., and Edwards, B. Calculus Early Transcendental Functions, 3rd edition. Houghton Mifflin Company, 2003. ISBN: 9780618223077 Larson, R., Hostetler, R. P., and Edwards, B. Calculus, 8th edition, Brooks Cole, 2005. ISBN: 9780618502981 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 [find and buy the text: Straighterline.com/textbooks] Course Description This course is designed to acquaint students to calculus principles such as derivatives, integrals, limits, approximation, applications and modeling, and sequences and 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, the Application of and Infinite Sequences and Series. Course Objectives 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 Course Prerequisites General Calculus II continues where General Calculus I (MAT250 by StraighterLine) leaves off. It picks up immediately with Unit 5: Antiderivatives and Definite. StraighterLine suggests, though does not require, that students take General Calculus I or its equivalent before enrolling in General Calculus II. Important Terms In this course, different terms are used to designate tasks:
Homework: 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. 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: Lesson 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 Review Final Exam (Unit 5-7) 300 Total 1000 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 Lesson 43: Antiderivatives of Exponentials Lesson 44: Antiderivatives of Logarithms Use simple substitutions to find antiderivatives. Find antiderivatives of trigonometric integrals. Find antiderivatives for exponential Find antiderivatives for logarithmic
Unit 6: Applications of Lesson 45: Antiderivatives of Inverse Trigonometric Functions Lesson 46: Integration by Part Lesson 47: Integration by Partial Fractions Lesson 48: Trigonometric Substitutions Lesson 49: The Definite Integral Lesson 50: Fundamental Theorem of Calculus Lesson 51: Improper Lesson 52: Net Change and Displacement Use inverse trigonometric functions to evaluate integrals. Define the integration by parts formula. Use integration by parts to evaluate integrals. Review partial fraction decomposition of rational Use partial fractions to integrate rational Use right triangle trigonometry to create substitutions for integrals. Recognize and integrate functions using trigonometric substitutions. Define a Riemann sum. Define a definite integral. Find the area between two curves on the coordinate plane. Explore techniques for approximating definite integrals. Investigate properties of the definite integral. Define the Fundamental Theorem of Calculus. Explore integral defined Find the average value of a function on an interval. Define the Mean Value Theorem for Integration. Explore definite integrals with infinite limits. Explore definite integrals with discontinuous Define convergence of an integral. 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
Unit 7: Infinite Sequences and Lesson 54:Separable Differential Equations Lesson 55: Numerical Solutions to Differential Equations cross sections. Find volumes of solids by cross sections. Solve differential equations by the method of separation of variables. Solve problems involving exponential Apply differential equations to bounded growth and decay problems. 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 Lesson 59: Integration of Vector-Valued Functions Lesson 60: Parametric Use integrals to find the length of an arc on a graph. Use integrals to find the surface area of solids of revolution. Find antiderivatives of vectorvalued Apply vector-valued function to position / velocity problems. Apply vector-valued functions to projectile motion problems. Find the area of a region bounded by a parametric curve. Find the arc length along a parametric curve. Lesson 61: Polar Find the area bounded by a polar curve. Find the arc length along a polar curve. Lesson 62: Other Applications of Definite Use integrals to identify the center of mass of an object. Use integrals to determine probabilities of events. Lesson 63: Sequences Define a sequence and proper notation.
Series 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 Define convergent and divergent Apply tests for divergence. Lesson 65: Estimating Sums Lesson 66: Other Tests for Convergence Define and apply the integral test for convergence of a Define and apply the comparison test for convergence of a Define and apply the limit comparison test for convergence of a Estimate the sum of finite and infinite Define and apply the ratio test for convergence of a Define absolute convergence of a series and use applicable tests. Define an alternating Estimate the sum of an alternating Lesson 67: Objectives Define a power series representation of a function. Find the radius and interval of convergence for a power Differentiate and integrate power Lesson 68: Taylor and Maclaurin series Review Review Review Define Taylor and Maclaurin Use Taylor series to solve application problems.