# MTH 174-003L_ Calculus with Analytic Geometry II

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```					MTH 174-003L, Calculus with Analytic Geometry II
Spring, 2006
Mike Brunner Text: Calculator:

MW 1900-2120

Room LW 0104

EMail: mfbmath1@hotmail.com Calculus, Early Transcendentals, fifth edition, by Stewart (5e)

A graphing calculator is required (preferably TI-82, TI-83, TI-85, TI-86) and must be brought to class each day, and may not be shared on any test or exam.

Prerequisites: You should have taken, and passed, with a grade of C or better, Math173 at NOVA, or have taken, and passed, with a grade of C or better, a comparable class elsewhere. Attendance: Attendance will be taken each class period and the importance of attending could not possibly be overemphasized!!! Remember, Calculus is HARD! Calculus is SUPPOSED to be hard! Calculus WILL BE hard! But Calculus is NOT IMPOSSIBLE! (except for those who do not attend!) We know this because thousands, in fact millions (perhaps billions) have taken Calculus, and, in fact (except for those who do not attend) most have usually passed Calculus. Homework: While there is no direct penalty for absences (see above) there are, most assuredly, penalties aplenty for not doing homework! For example: an inability to pass in-class, unannounced, quizzes (see below), an inability to understand the next day’s work, and the general malaise associated with heavy guilt and a desire to “take back” a poor decision. The suggested homework problems should be considered as a minimum amount to do in order to begin the process of mastery of Calculus. The experience of millions (perhaps billions) (see above) of previous Calculus students is that the more problems you attempt the more probable is your success in Calculus. Tests/Exam/Quiz’: The attached, tentative, schedule of classes and topics, shows the tentative dates for the major tests. Each test (for those who attend and take the test on the assigned day) will be approximately 100 points and the final test (for those who attended and took the assigned tests on the assigned days) will be approximately 150 points. In addition there may be un-announced quizzes each of which will be worth approximately 20 points, and may consist of problems similar to a previous night’s homework, or, in fact, may be the collection of a previous night’s homework. For each test you will be permitted to have, and use, one 8.5” x 11” paper per chapter, with notes on either, or both sides

Makeup Tests: There are NONE!!! Don’t miss a test!!! If a student is absent on the day of a test then that student will be given a “SPECIAL” test for the next scheduled test. This “SPECIAL” test will consist of the regularly scheduled test and several extra problems which will cover the material from the previously “missed” test. The grade received on this “SPECIAL” test will be the recorded grades for the “missed” test and the regularly scheduled test. If a student is absent from two consecutive tests s/he will be “administratively” dropped from the course. Grading Scale: 90 -100% 80 - 89% 70 - 79% 60 - 69% below 60% A B C D F

TENTATIVE (very tentative) SCHEDULE Date: 1/9 Sections: Suggested Problems: Topics:

Inverse Trig Functions 3.6 41-49 odd, 25,27,29 Implicit differentiation 3.9 1-15 odds,21,23(a-d),29a,31,33,42,43,49,53 Hyperbolic Functions 4.4 5.5 No Class 6.1 1-25 odd Area between curves (review? of ) logs/exponents Volume - Disc, Washer Volume - Shell Average Value 1,3,5,9,13,15,17,18,40,45,49,55,57 7-34 every 3rd L’Hopital’s Rule Substitution Rule

1/11

1/16 1/18

1/23 1/25 1/30 2/1 2/6

6.2 6.3 6.5

1-19 odd, 23,27,47,55 3,7,9,15,19,28,37,41,43 1-17 odds

Test 3.6 - 6.5 and Inverse Trig Fns 7.1 7.2 3,7,9,11,13,17,19,21,25,42,53 1,9,13,17,23,40 Integration by parts Trigonometry

2/8 2/13

7.3 7.5 7.6 7.4 7.7 7.8

5,7,9,11,17,23,40 1,7,9,17,23,45,49 1,3,5,11,13 43,45 5-29 every third 1,3,9,13,19,27,33,49,69

Trig Substitution Strategies Tables, Calculators Partial Fractions Trapezoid Rule Improper Integrals

2/15

2/20 2/22 2/27 2/28 3/1 3/6 3/8

No Class (President’s Day) Test Chapter 7 8.1 10.1 No Class No Class 1,3,5,9,10,22,37 3,9,11,15,19,27,29,31,35,39 Spring Break Arc Length Parametrics

TENTATIVE (very tentative) SCHEDULE 3/13 3/15 3/20 3/22 3/27 3/329 4/3 4/5 4/10 4/12 4/17 4/219 4/24 4/26 5/1 10.2 10.3 10.4 10.5 1,3,5,13,17,19,23,27,31,33,35 1,3,7,9,11,15,19 1-35 odds,43,45,57,61,63,65 5,7,9,11,17,21,25,27,35,39,41,45 Tangents, Average Value Arc Length (parametric) Polar Coordinates Areas and Lengths

Test 8.1 and Chapter 10 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 Test 11.1 - 11.7 11.9 11.10 Last Test 1,2,3,5,7,11,13,15,17,25,29 1,2,3,7,11,13,15,17,19,23,25,37,41,45,49,53,57 Power Series Taylor, Maclaurin 1,2,5,7,9,13,15,17,19,21,23,24,39,41,51,53,55,57,65 1,2,11,13,19,21,29,31,37,41,43,45,63 1,2,3,5,7,11,15,21,25,31 1,2,3,5,7,13,17,21,23,33,35 1,3,5,7,,17,19,23,25,27,29 1,3,5,7,17,19,23,25,27,29 all odds 1,2,3,5,7,9,11,13,15,17,19,21,23,29,30 Series Integral Test Comparison Tests Alternating Series Ratio Test Strategies Power Series Sequences

5/3

COLLEGE-WIDE COURSE CONTENT SUMMARY MTH 174 - CALCULUS WITH ANALYTICAL GEOMETRY II (5 CR.) COURSE DESCRIPTION: Continues the study of analytic geometry and the calculus of algebraic and transcendental functions including rectangular, polar, and parametric graphing, indefinite and definite integrals, methods of integration, and power series along with applications. Lecture 5 hours per week. GENERAL COURSE PURPOSE: The above course is primarily for students in mathematics, engineering, sciences, and in other areas requiring strong mathematical backgrounds. The general purpose is to give students a basic understanding of the concepts of integral calculus, power series, and vectors, and to prepare students for multivariable calculus. ENTRY LEVEL COMPETENCIES : Prerequisite is satisfactory completion of MTH 173 - "Calculus with Analytic Geometry I" or equivalent. COURSE OBJECTIVES: As a result of the learning experiences provided in this course, the student should be able to: A. solve problems involving volume, arc length, work and centroids of plane areas B. differentiate and integrate expressions involving transcendental functions C. define conics, vectors, sequence, limit of a sequence, infinite series, convergence and divergence of a series D. solve problems involving conics, rotation and translation of coordinate axes, and polar coordinates E. find areas bounded by curves in polar form F. solve problems involving parametric equations, vectors G. solve problems involving improper integrals and infinite limits of integration H. find series representations of functions and use Taylor's Theorem with Remainder I. differentiate and integrate power series J. solve problems in indeterminate form K. obtain competency in the use of a graphing utility and CAS in the topics below MAJOR TOPICS TO BE INCLUDED: A. Applications of Integrals 1. Volume 2. Arc length B. Transcendental Functions (inverse trigonometric, hyperbolic, and inverse hyperbolic) 1. Definition 2. Properties 3. Differentiation and integration C. Techniques of Integration 1. Substitution 2. Integration by parts 3. Trigonometric substitution 4. Quadratic irrationalities 5. Partial fractions 6. Change of limits D. Conics 1. Definition 2. Rotation and translation transformations 3. Forms and graphs of second degree equations in x and y E. Polar Coordinates 1. Polar coordinate systems 2. Transformation from polar to Cartesian coordinates and vice versa 3. Polar functions 4. Graphing 5. Intersection of curves in polar coordinates 6. Plane areas in polar coordinate

F. Parametric Equations and Vectors 1. Transformations between parametric and Cartesian coordinates 2. Parametric functions 3. Differentiation and integration of parametric functions 4. Length of an arc 5. Vectors in 2 dimensions 6. Dot product G. Indeterminate Forms 1. Definition 2. L'Hopital's Rule 3. Other indeterminate forms H. Improper Integrals 1. Infinite limits of integration 2. Comparison test for convergence 3. Infinite integrands I. Infinite Series 1. Definition of sequence and limit of a sequence 2. Definition of infinite series 3. Convergence tests for positive series 4. Alternating series (conditional and absolute convergence) 5. Power series (definition, radius of convergence, convergence tests, Maclaurin and Taylor series) 6. Taylor's Theorem and forms of the remainder J. Technology

EXTRA TOPICS (optional) A. Surface Area B. Liquid pressure C. Centroids of solids of revolution D. Complex functions

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