MATH 2411

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  Metropolitan Community College COURSE OUTLINE FORM (Page 1 of 8) Revised 8/28/2012 Course Title: Calculus II Course Prefix & No.: MATH 2411 LEC: 7.5 LAB: 0 Credit Hours: 7.5 COURSE DESCRIPTION: Topics include logarithmic, exponential, inverse trigonometric and hyperbolic functions with their derivatives, and related integrals. The course includes techniques of integration, improper integrals, and infinite series. It discusses polar coordinates and relates them to calculus. COURSE PREREQUISITE (S): Within two years, successful completion of MATH 2410. RATIONALE: This course extends the topics of single variable calculus. It increases the number of functions to which integration and differentiation may be applied. Techniques of integration are covered to increase the students understanding and ability to solve applied problems. Series representations of all the major functions are developed and used to increase the student’s understanding of how series can be used to model functions. Polar coordinates and the applications to calculus are covered and developed to form the framework for calculus III. Applications to business, the sciences and engineering are presented.   REQUIRED TEXTBOOK (S) and/or MATERIALS: Edition: 9 th  Edition  Author: Larson & Edwards Publisher: Cengage Learning Materials: Scientific Calculator required. All Calculators that have a built-in computer algebra system (CAS) will not be permitted during any of the exams or quizzes. Examples of CAS calculators include the TI-89, TI-92, TI-Nspire, HP-40, HP-41, Casio ALGEBRA FX 2.0, Casio ClassPad 300, and Casio ClassPad 330.    Attached course outline written by: Michael Flesch Date: 10/SS Reviewed/Revised by: Calculus Text Committee Date: 10/SS Effective quarter of course outline: 13/FA Date: 7/29/13  Academic Dean: Date Course Objectives, Topical Unit Outlines, and Unit Objectives must be attached to this form.  Metropolitan Community College COURSE OUTLINE FORM (Page 2 of 8) Revised 8/28/2012 TITLE: Calculus II PREFIX/NO: MATH 2411 COURSE OBJECTIVES: Upon completion of MATH 2411 each student will be able to: 1. Differentiate and integrate logarithmic, exponential, trigonometric, inverse trigonometric and hyperbolic functions. 2. Solve application problems using integration to find areas, volumes, arc length, area of surfaces of revolution, work, fluid pressure, and force. Moments, centers of mass, and centroids may also be introduced. 3. Recognize and use various techniques of integration. 4. Evaluate indeterminate forms. 5. Evaluate improper integrals. 6. Determine the convergence or divergence of infinite series. 7. Derive power series for functions using these to help in differentiation, integration, and computation. 8. Graph polar and parametric curves by hand and relate them to rectangular coordinates for area, arc length, and tangent lines. Develop the calculus for polar and parametric forms. TOPICAL UNIT OUTLINE/ UNIT OBJECTIVES:  At the completion of each unit the student will be able to: Unit 1. Inverse Trigonometric and Hyperbolic Functions & Introduction to Differential Equations 1. Graph the hyperbolic and inverse trigonometric functions. 2. Differentiate and integrate hyperbolic and inverse trigonometric functions. 3. Memorize the differentiation and integration rules below:  Metropolitan Community College COURSE OUTLINE FORM (Page 3 of 8) Revised 8/28/2012 4. Use tables to differentiate and integrate inverse trigonometric, hyperbolic, and inverse hyperbolic functions. 5. Use initial conditions t find particular solutions of differential equations. 6. Use slope fields to approximate solutions of differential equations. 7. Solve problems involving Differential equations with Growth and Decay. 8. Use Separation of variables to solve a differential equation. Unit 2. Applications of Integration 1. Find the area between two curves using integration. 2. Find the volume of a solid of revolution using the disk and shell methods. 3. Find the arc length of a smooth curve. 4. Find the area of a surface of revolution. 5. Solve work problems with both a constant and variable force. 6. Find the center of mass of a planar lumina. 7. Use integration to find fluid pressure and force. Unit 3. Techniques of Integration 8. Use integration tables. 9. Perform integration by parts. 10. Integrate trigonometric integrals. 11. Integrate using trigonometric substitution. 12. Integrate by partial fractions. 13. Evaluate improper integrals. 14. Integrate improper integral  Metropolitan Community College COURSE OUTLINE FORM (Page 4 of 8) Revised 8/28/2012 Unit 4. Series 1. Determine convergence or divergence of sequences. 2. Use the following tests to determine the convergence or divergence of an infinite series: integral test, p-series, comparison test, ratio/root tests, geometric series, and divergence test. 3. Represent functions by power series such as Maclaurin or Taylor series. 4. Differentiate and integrate power series, and use power series for computational purposes. Unit 5. Parametric and Polar Curves, Conic Sections 1. Graph in polar coordinates, plotting points and functions by table. 2. Graph the plane/space curve represented by parametric equations using a table and indicate orientation. 3. Convert to and from polar to rectangular coordinates. 4. Compute arc length and tangent lines for parametric curves. 5. Compute arc length, tangent lines, and area for polar curves. 6. Find the slope and concavity of curves described in polar coordinates or parametric form. 7. Develop the conics using their definition as a locus of points meeting a specific definition. 8. Put the equation of a conic in standard form and plot, identify the important points on each graph. The following is a listing of specific sections from Larson ’s  Table of Contents that should be taught. Section Pages and Problems Unit 1 Inverse Trigonometric, Hyperbolic Functions, and Differential Equations Section 5.6 Inverse Trigonometric Functions: Differentiation p. 379 Problems Section 5.7 Inverse Trigonometric Functions: Integration p. 385 Problems Section 5.8 Hyperbolic Functions p. 396 Problems Section 6.1 & 6.2 Slope Fields  –   Euler’s Method may be skipped Differential Equations  –  Growth & Decay p. 409 Problems p. 418 Problems Section 6.3 Separation of Variables for differential equations. p. 429 Problems
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