Wentworth Institute of Technology Department Applied Math and Sciences Fall 2010 Math 510 Calculus III Instructor: Department Office: Dwight F. Horan Location: IRALL 216 Location: Second Floor, Ira Allen 206 Phone: (617) 989-4358 Phone: (617) 989-4333 Email: [email protected] Office hours Monday, Tuesday and Thursday, 11:00 to 12:00. Other times are available by appointment. Students should make appointment by contacting the instructor or the Applied Mathematics and Science Department Administrative Assistant. Credit Hours Lecture 4 hours Total 4 credit hours Meeting Times Class Type Day From To Location M,T, 10:00 am 10:50 am IRALL 105 R,F 10:00 am 10:50 am WAT 004 M,F, 12:00 pm 12:50 pm ANXCN 103 Section 03 Lecture Section 05 Lecture T,R 12:00 pm 12:50 pm IRALL 105 2:00 am 2:50 am Section 09 Lecture M,T,R,F IRALL 003 Course Description This course is designed to build on concepts developed in Calculus I and II. Students will be exposed to Calculus concepts relating to engineering design, inspection, and quality assurance. Skills developed in this course will be of value to all majors. Pre-requisite/Co-requisite Students must have successfully completed Calculus II in order to take this course and have received an acceptable grade in Calculus II. Grades of "IC", "W", and "F" do not satisfy prerequisites, nor does taking the prerequisite concurrent with this course. Required Text (also available in online form) Thomas’ Calculus Early Transcendentals Media Upgrade, 11/e, by Weir, Hass, and Giordano Pearson Publishing The College Bookstore: Location: 103 Ward Street Boston MA 02115 Telephone: 617-445-8814 Resources Any scientific calculator may be used but a graphics or programmable calculator would be best. Some exercises will be presented with these operations in mind. Elementary programming may be required. Demonstrations will be done using the Texas Instruments family of calculators. If you do not have a Ti then it is your responsibility to know how to operate your own particular brand of calculator. A virtual Ti family calculator is available on Blackboard. Course Goals After successful completion of this course students will have a working knowledge of three dimensional vector applications, partial derivative applications and multiple integral applications. Course Learning Outcomes: In addition, specific objectives are: MATH 510 CALCULUS III: Learning Objectives I. Vectors and Geometry of Space Understand the three-dimensional coordinate system. Find the distance between points. Find the center and radius of a sphere. Find the component form of a vector. Express a vector as a product of its length and direction. Find the direction of a vector and the midpoint of a line segment. Find the dot product. Find the projection of vectors. Find the angle between vectors. Find the length and direction of the cross product of vectors. Find parametric equations of a line. Find an equation of a plane. Solve three dimension problems involving lines and planes. Identify equations of cylinders. Identify equations of quadric surfaces. II. Vector-Valued Functions and Motion in Space Find a particle’s position, velocity and acceleration vectors. Find the angle between velocity and acceleration vectors. Find parametric equations for the line tangent to a curve. Find a curve’s unit tangent vector. Find arc length. III. Partial Derivatives Find domain and range of functions of several variables. Identify surface and level curves. Find equations for level curves and level surfaces. Find first-order partial derivatives. Find higher order derivatives. Find the gradient of a function. Find the directional derivative of a function. Find the greatest rate of change of a function and its direction. Find equations of tangent planes and normal lines to surfaces. Find local extrema. Classify local extrema. IV. Polar Coordinates Understand the polar coordinate system. Find the slope of a curve. Graph in the polar system. Find the area of regions. V. Multiple Integrals Evaluate an iterated integral. Evaluate the double integral. Evaluate a double integral over a given region. Find the volume beneath a surface. Reverse the order of integration. Evaluate double integrals in polar coordinates. Find the area of a region by double integration. Evaluate a triple integral. Find the volume of a solid using a triple integral. Instructional Methodologies: Lectures, Labs, and demonstrated examples. Attendance Policy Regular Attendance at every class is expected. If a student misses 10% of his/her scheduled class sessions, he/she may be notified in writing by the instructor through the instructor's department office, that continued absenteeism may result in being withdrawn from the course. Students receiving this notice will be required to consult with their instructor and advisor. If a student misses 15% of his/her scheduled classes, he/she may be given a grade of WA in the course by the instructor. This attendance policy will be in force each semester beginning on the published "last day to add a course" date and continue through to the "last day to drop a course" date. Assignments/Submitted Work/Late Work All written work submitted for this course must meet the Standards for English I. Poorly written papers will be returned to you, without a grade, for revision. Students are encouraged to utilize the Writing Center facility for help polishing their papers. Work submitted late will be subject to a reduced grade. Assignments are listed on the course outline and/or assigned by the instructor. Exams There will be three exams and a final. The dates will be announced in class approximately one week in advance. Exams missed can be made up at the discretion of the instructor. This is not to be confused with retests, which are not usually given. Lab/Homework/Project The homework will be online using MyMathLab. There will be lab assignments throughout the course. The lab assignments will be done using MATLAB. The school has a site license for the software so if you want to use your own laptop make sure it's loaded on there. We will often revisit problems done in class using MATLAB. There will also be a project done in MATLAB. Grading and Student Evaluation System Exams and final/project will count for 80% of your grade. Lab and homework assignments will constitute the last 20%. Labs will be marked down 10% per class day after the due date. Wentworth Grading System: Grade Definition Weight Numerical A Student learning and accomplishment 4.00 96-100 A- far exceeds published objectives for the course/test/assignment and student work 3.67 92-95 is distinguished consistently by its high level of competency and/or innovation. B+ Student learning and accomplishment 3.33 88-91 B goes beyond what is expected in the published objectives for the course/test/ assignment and student work is frequently characterized by its special depth of understanding, development, and/or innovative experimentation. 3.00 84-87 B- Student learning and accomplishment 2.67 80-83 C+ meets all published objectives for the 2.33 76-79 C course/test/assignment and student work demonstrates the expected level of understanding, and application of concepts introduced. 2.00 72-75 C- Student learning and accomplishment 1.67 68-71 D+ based on the published objectives for 1.33 64-67 D the course/test/assignment were met with minimum passing achievement. 1.00 60-63 F Student learning and accomplishment based on the published objectives for than 60 the course/test/assignment were not sufficiently addressed nor met 0.00 Less Grading and Student Evaluation System Each exam will count for 20% of your grade. A final exam will be scheduled during finals week. The final exam will have a weight of 20 %. Additional out-of-class assignments will constitute the last 20%. Drop/Add: The drop/add period for day students ends on Friday of the first week of classes. Dropping and/or adding courses is done online. Courses dropped in this period are removed from the student’s record. Courses to be added that require written permission, e.g. closed courses, must be done using a Drop/Add form that is available in the Student Service Center. Non-attendance does not constitute dropping a course. If a student has registered for a course and subsequently withdraws or receives a failing grade in its prerequisite, then the student must drop that course. In some cases, the student will be dropped from that course by the Registrar. However, it is the student’s responsibility to make sure that he or she meets the course prerequisites and to drop a course if the student has not successfully completed the prerequisite. The student must see his or her academic advisor or academic department head for schedule revision and to discuss the impact of the failed or withdrawn course on the student’s degree status. Make-up Policy: Exams missed can be made up at the discretion of the instructor. This is not to be confused with retests, which are not usually given. Academic Support: The Center for Teaching and Learning (CTL) assists all Wentworth students with academic challenges in the areas of math, science, technical courses specific to majors, and writing. The CTL is a supportive and safe learning environment for students looking to improve or maintain their academic standing. In this studentbased learning environment, students can receive individual help with their studies, meet and work in study groups, or go on-line to find resources to assist them in meeting their goals for academic success. It includes tutors in many subjects, online writing assistance and workshops. Make appointments at www.wit.edu/academics/resources/resources or through Lconnect. Academic Honesty Statement: “Students at Wentworth are expected to be honest and forthright in their academic endeavors. Academic dishonesty includes cheating, inventing false information or citations, plagiarism, tampering with computers, destroying other people’s studio property, or academic misconduct” (Academic Catalog). See your catalogue for a full explanation. Student Accountability Statement: Students caught cheating or plagiarizing will receive a zero for that assignment. A second infraction will result the student’s failure of the course. Class Communication If you are going to miss a class, please inform the instructor either by email or voice mail, if possible. You are still responsible for material missed. Disability Services Statment: Any student who thinks s/he may require a disability-related accommodation for this course should contact me privately to discuss your specific needs. Disability Services coordinates reasonable accommodations for students with documented disabilities. They are located in Watson Hall 003 (the Counseling Center) and can be contacted at 617-989-4390 or [email protected] For more information on acceptable documentation and the Disability Services process, visit the Disability Services website at www.wit.edu/disabilityservices Topics Suggested Assignment (if online assignments are unposted) I. Vectors and Geometry of Space Week 1 Sec 9.1 3-D Coordinate Systems Pg. 504 1-51 every other odd Sec 9.2 Vectors Pg. 513 1-29 odd Week 2 Sec 9.3 The Dot Product Pg. 520 1-12, 27-33 Sec 9.4 The Cross Product Pg. 527 1-23 odd Sec 9.5 Lines and Planes in Space Pg. 535 1-69 every other odd Sec 9.6 Cylinders and Quadric Surface Pg. 542 1-43 odd Week 3 II. Vector-Valued Functions and Motion in Space Week 4 Sec 10.1 Vector Functions and Their Derivatives Pg. 553 1-17 odd Sec 10.3 Arc Length in Space Pg. 564 1-9 odd III. Partial Derivatives Week 5 Sec 11.1 Functions of Several Variables Pg. 588 1-43 Sec 11.2 Limits in Higher Dimensions Pg. 597 1-11 Sec 11.3 Partial Derivatives Pg. 607 1-19, 41-46 Sec 11.5 Directional Derivatives and Gradient Vectors Pg. 625 1-12,17,18,27-29 Sec 11.6 Tangent Planes Pg. 632 1-17 Sec 11.7 Extreme Values and Saddle Points Pg. 641 1-29 odd Double and Iterated Integrals over Rectangles Pg. 661 1-19 odd, 23-27 Double Integrals over General Regions Pg. 668 1-6, 11-43 odd Area by Double Integration Pg. 672 1-3 odd Sec 8.2 Graphing in Polar Coordinates Pg. 483 1-31 Sec 8.3 Areas and Lengths in Polar Coordinates Pg. 487 1-25 odd Double Integrals in Polar Form Pg. 677 1-21 Triple Integrals in Rectangular Coordinates Pg. 684 1-19 odd Week 6 Week 7 Week 8 Week 9 IV. Multiple Integrals Week 10 Sec 12.1 Week 11 Sec 12.2 Week 12 Sec 12.3 Week 13 Week 14 Sec 12.4 Week 15 Sec 12.5 *Other topics as time permits Moments and Center of Mass Copyright ©2010 Wentworth Institute of Technology. All Rights Reserved.