Math 1320
Engineering Calculus II
Fall 2013
Lectures - MTWTh 10:45-11:35 LCB 215
Discussion - Th 9:40-10:30 LCB 219 (sec 5) or Th 10:45-11:35 JTB 320 (sec 6)
Instructor - Dr. Tyler Skorczewski
Office - LCB 311
Office hours - MWF 9:30-10:30 and by appointment
Email - tskorc@math.utah.edu
Teaching Assistant - Olakunle Eso
Office - MEB 3305
Office hours - TW 1-2 in WEB 1622 and by appointment
Email - olakunle.eso@utah.edu
Class webpage - www.math.utah.edu/∼tskorc/1320/1320.html
Book - Calculus: Concepts and Contexts 4th Edition, by James Stewart (ISBN-13: 978-0-495-55742-5)
Final Exam - December 20, 10:30 - 12:30
Note : No classes on
Labor Day - September 2
Fall break - October 13-20
Thanksgiving break - November 28-29
Material covered
Math 1320 Students will understand applications of integration, average behavior of a function, differential
equations solutions through integration, exponential growth/decay, sequences and series and convergence
tests, series approximation, power series, Taylor and Maclaurin series, Taylor’s theorem, the three dimensional coordinate system, vectors, dot product, cross product, equations of planes and surfaces, vector
functions and space curves, derivatives and integrals of vector functions, arc length, curvature, velocity
and acceleration of parametrized curves, multivariate functions, multivariate limits, partial derivatives,
tangent planes and linear approximations, multidimensional chain rule, directional derivative, gradient
vector, minimum/maximum and optimization of multivariate functions, Lagrange multipliers. This material is covered by chapters 6-11 in the text.
Prerequisites
Math 1320 students are required to earn a ‘C’ or better in 1310 to enroll, or they can alternatively
be entered by earning a ‘C’ or better in Math 1210 and by being concurrently enrolled in the MATH
1320 “boot camp” that covers the material in 1310 that is missing from the traditional 1210 sequence.
Practically speaking, you are better prepared for this course if you have a solid understanding of differentiation, integration, trigonometry, and if your grades in the prerequisite courses were above the ‘C’ level.
Course Objectives
The goal of Math 1320 is to further master the basic tools for the study of functions, termed the calculus,
and become skilled in it’s use for solving problems in science and engineering. Math 1310 is a prerequisite
for Math 1320, and it is expected that Math 1310 content is sufficiently mastered to be able to move
forward in 1320. These basic tools and problem solving skills are described below.
• Students will be able to utilize methods of integration to compute volumes of objects with circular-shaped
aspects, and compute lengths of curves. These applications introduce a higher-level concept of integration,
involving the summation of small volume segments dV or small length segments ds, which are computed
by performing an appropriate parametrization to a real-number-line integral.
• Students will be skilled in using integration to compute problems important in physics and engineering.
Students will know how to compute of an average value of a function using the mean value theorem for
integrals, the center of mass for objects, and the computation of work as a force integrated over a distance.
Students will also be able to utilize physical laws to formulate differential equations that solve for the motion
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of masses by forces of gravitation, friction, electrostatics, to name a few. Students will also become familiar
with the phenomenon of exponential growth and decay in science and engineering contexts.
• Students will become skilled in computations and applications of infinite sequences and sums. Students
will become familiar with the properties of infinite sums to either converge to a finite value or diverge to an
infinite value, and will learn about methods to determine convergence. Students will be able to represent
functions as series and approximate functions using Taylor’s theorem.
• Students will also learn important tools of calculus in higher dimensions. Students will become familiar
with 2- and 3-dimensional coordinate systems, vectors and vector operations including the dot and cross
product, and equations of lines, planes, and other surfaces. Students will also learn how to represent motion
of objects in 3D using vector functions, how to represent velocity and acceleration using vector projections
into tangential and centripetal coordinates of acceleration, and how to characterize curves in space by
computing arc length and curvature. For functions of 3D surfaces, students will be able to characterize
aspects of surfaces and volumes using partial derivatives and the gradient vector. Partial derivatives will
also be used to describe approximating tangent planes to points on surfaces, and how to compute derivatives
of multi-dimensional function compositions can be performed using a multi-dimensional version of the chain
rule.
• Students will be able to read and understand problem descriptions, then be able to formulate equations
modeling the problem usually by applying geometric or physical principles. Solving a problem often requires
a series of transformations that include utilizing the methods of calculus. Students will be able to select
the appropriate calculus operations to apply to a given problem, execute them accurately, and interpret the
results using numerical and graphical computational aids.
• Students will gain experience with problem solving in groups, be able to communicate effectively about
problem objectives and the use of solving methods with peers, and solve problems in a team fashion.
Students will also learn how to and articulate questions effectively with both the instructor and TA, and
be able to effectively communicate problem solutions through both written and oral deliveries.
Grading
Grading will be based on performance on written homeworks, lab assignments/attendance, quizzes , 2 midterm
exams, and a final exam. The weighting for each is as follows:
Homeworks
10%
Labs
20%
Quizzes
10%
Midterm Exams 35%
Final Exam
25%
Exams
There will be two midterm exams and one final exam for this class. All exam scores will be counted (I will not
drop a lowest score). The final exam is comprehensive and covers the entire course. Make-up exams will only be
given for university excused absences and must be arranged in advance. The exam dates are given below. Plan
accordingly. You will be required to show your student ID during the test.
Midterm 1
Friday October 4
Midterm 2
Friday November 15
Final Exam Friday December 20, 10:30 - 12:30
Quizzes
There will be weekly quizzes given on Fridays during class. These quizzes will cover key concepts and techniques
from the lectures and homework assigned that week. I will use the 10 best quiz scores when determining grades.
(If for some reason we have less than 11 quizzes, I will drop the lowest one.) There will be no make up quizzes.
Homework
Homework will be assigned regularly to reinforce concepts from the lectures. I will drop the lowest score on the
homeworks when calculating grades. Beyond their contributions to your course grades, the real value in carefully
working the homework problems and in doing the projects is that mathematics (like anything) must be practiced
and experienced to really be understood. Collaboration on homeworks is encouraged, but what you turn in must
be your own work. Homework is due at the beginning of class on the due date. No late homework will be
accepted. A good rule to adhere to is: ”If your homework is important enough that you would be upset if it was
not accepted, then it is important enough to turn in on time.”
Lab/Discussion Sections
Every Thursday the teaching assistant (TA) will direct a lab section. Here the TA will hand out problem work-
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sheets and will facilitate student-led group work, as well as answer questions about the weekly material/book
homework. The worksheets will provide guided practice with problems that highlight the use of calculus in
physical and engineering applications. Credit will be given for both lab attendance and completed worksheets.
Students should expect that worksheets will take additional time outside of lab to finish completely. The TA will
be available for additional office hours the the College of Engineering tutoring lab in WEB 1622. Attendence for
the lab section will be taken and is a part of the grade. However, students can attend either lab section.
Office Hours
Please do not hesitate to come to office hours for help with the course. This can mean discussing difficult concepts
from lectures, help with homework problems, exam preparation, etc. We can often go over ideas with a more
conversational format than lectures allow which helps ensure that you understand the concepts giving you trouble.
If you can’t make the posted hours, you can always make an appointment. In addition, there may be some online
chats to help answer questions.
Tutoring Center
The math department offers free drop-in tutoring for math department classes at the 1000 and 2000 level, as
well as the following 3000 level classes: 3070-3080, 3150, 3160. The tutoring center is located in room 155 of the
T. Benny Rushing Mathematics Center (adjacent to the LCB and JWB). The College of Engineering also has a
tutoring lab in WEB 1622.
Students with Disabilities
The American with Disabilities Act requires that reasonable accommodations be provided for students with physical, sensory, cognitive, systemic, learning, and psychiatric disabilities. Any student with a certified disability who
needs to arrange reasonable accommodations must contact University Disability Services (UDS) and me at the
beginning of the semester to discuss any such accommodations for the course.
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