MAT266 - Calculus II for Engineers Instructor: XXX Office: XXX SLN : XXX Time/Day: MWF XX-XX Telephone: (480)-965-XXX Hours: XXX Instructor Web Page: XXX E-mail: XXX Text: Essential Calculus, Early Transcendentals, 2nd Edition, by James Stewart (Cengage) Videos: https://math.la.asu.edu/~surgent/video/mat266_exp.html Test reviews: https://math.asu.edu/resources/math-courses/mat266 Tentative Lecture and Test Schedule Week of Section Concepts/Comments 1/13 5.1-5.4 Introduction; Review of the Definite and Indefinite Integral 1/20 5.5, 6.1 MLK, Jr. (Monday, 1/20) Substitution, Integration by Parts 1/27 6.2 Trigonometric Integrals and Substitutions 2/3 6.3, 6.4 Partial Fractions, Integration with Tables & CAS 2/10 6.5, 6.6 Numerical Integration (cont.), Test 1 Review, Improper Integrals 2/17 7.1 Test 1 (Wed. 2/19), Area Between Curves 2/24 7.2, 7.3 Volumes (Slicing, Disks and Washers), Volume (Shells) 3/2 7.4, 7.6 Arc Length, Applications to Physics and Engineering (Work) 3/9 Spring Break (3/9 – 3/15) 3/16 7.6, 8.1, 8.2 Work (cont.), Sequences, Series 3/23 8.4 Test 2 Review, Test 2 (Wed. 3/25), Convergence Tests 3/30 8.4, 8.5 Convergence Tests (cont.), Power Series 4/6 8.6, 8.7 Rep. Functions as Power Series, Taylor & Maclaurin Series 4/13 9.1, 9.2 Parametric Curves, Calculus with Parametric Curves 4/20 9.3 Test 3 Review, Test 3 (Wed.4/22), Polar Curves, Tangents to Polar Curves 4/27 9.4 Areas and Lengths in Polar Coordinates, Final Exam Review 5/5 ALL The Final Exam is Tuesday, 5/5 from 7:10-9:00pm (room t.b.a.) Prerequisite: MAT 265 or MAT 270 (Calculus I) with a grade C or better. Catalog Description Methods of integration, applications of calculus, elements of analytic geometry, improper integrals, Taylor series.Important Dates and Points Allocations Testing Schedule Grade Allocations Min. % for Grades Test Covering through Date Tests* 50% A 90% 1 5.5, 6.1-6.5 2/19 Homework & Quizzes 25% B 80% 2 6.6, 7.1-7.4, 7.6, 8.1-8.2 3/25 Final Exam 25% C 70% 3 8.4-8.7, 9.1, 9.2 4/22 Total 100% D 60% Final Comprehensive, including 9.3, 9.4 5/5 *No test will be dropped E <60% Course Overview The purpose of the course is to gain a working understanding of methods of integration, applications of calculus, elements of analytic geometry, improper integrals and series, to include Taylor Series. All the standard methods of techniques of integration are covered. Applications of calculus include general methods where the goal is for the student to divide a quantity into small pieces, estimate with Riemann sums and recognize the limit as an integral. Taylor Series and Taylor Polynomials are covered. Parametric and polar curves are introduced and methods of calculus are applied to them. Learning Outcomes At the completion of this course, students will be able to: • Evaluate an integral using the substitution method, integration by parts, trig substitution or partial fractions. • Use tables to match the form of a given integral to a form given on the table to evaluate the integral. • Approximate the definite integral using the Midpoint, Trapezoidal or the Simpson’s Rule. • Evaluate an improper integral where either the definite integral is extended to cover the case where the interval is infinite or where f has an infinite discontinuity on [a, b]. • Determine the area of a region enclosed by given curves. • Determine the volume of the solids of revolution obtained by rotating a region about a line using washer, disc or shell method. • Determine the arc length of a curve. • Solve applied problems involving work, including the work to stretch a spring and the work to empty a tank of liquid. • Determine if a sequence converges or diverges and find the limit. • Determine if a series converges or diverges using geometric series or test for divergence. • Find a radius and interval of convergence for a power series. • Perform differentiation and integration on known power series to create new power series. • Find a power series representation and the interval of convergence for a given a function. • Find either a Taylor Series or Maclaurin Series for a given a function. • Convert between Cartesian and parametric form and sketch a curve defined parametrically. • Determine the tangent line at a point on a curve defined parametrically • Find the area below a parametric curve and the arc length along a curve. • Convert between Cartesian and polar form and sketch a curve defined in polar coordinates. • Find the area made by a polar curve.Homework & Quizzes: Homework and quizzes will be collected and graded. Students may work together on homework, but each individual student is required to write-up and turn in their own work. No late homework is accepted. Students will also submit homework online through WeBWorK. (Click on your instructor’s name at http://webwork.asu.edu.) Students are also responsible for reading each section before it is taught in class. Quizzes are given at the discretion of the instructor and frequently reflect material that has recently been discussed in class. Exams: There will be three 50 minute midterm exams given during the semester. All exams will be taken in the classroom on the dates indicated on the given table. Non CAS graphing calculators are allowed on the exams, but graphing calculators that do symbolic algebra are not allowed on the exams (see below). Your calculator may be viewed during exams and it will be taken away if it is a CAS calculator or have its memory cleared if anything suspicious is written therein. The Instructor has the right to regard any suspicious material in your calculator memory as cheating. Any student who accesses a phone or any internet-capable/camera device during an exam for any reason automatically receives a score of zero on the exam. All such devices must be turned off and put away and made inaccessible during the exam. Makeup exams are given at the discretion of the instructor and only in the case of verified medical or other emergency, which must be documented. The instructor must be notified before the test is given. Call the instructor or the Math Department Office (480-965-3951) and leave a message or directly notify your instructor. Picture ID requirement for testing: For each exam including the final, you must bring a picture ID. Final Exam: Tuesday, May 5th, 7:10-9:00 pm. Location: to be announced. The