Course Descriptions & Syllabi

Course Descriptions & Syllabi

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Areas of Study | | MATH140 syllabus




COURSE NUMBER: MATH140
COURSE TITLE:Calculus & Analytic Geometry III
DIVISION:Sciences
IAI CODE(S): M1 900 MTH 903 EGR 903
SEMESTER CREDIT HOURS:3
CONTACT HOURS:45
STUDENT ENGAGEMENT HOURS:135
DELIVERY MODE:In-Person

COURSE DESCRIPTION:
The third course in calculus and analytic geometry. Topics include vectors in 2 and 3 dimensions, vector operations, lines and planes in space, quadric surfaces, cylindrical and spherical coordinates, partial derivatives, directional derivatives, gradients, double and triple integrals and their applications. Both the understanding of theoretical concepts and the ability to use manipulative techniques are considered of prime importance. A TI-83 or better calculator is recommended.

PREREQUISITES:
Completion of MATH130 (Calculus & Analytic Geometry II, M1 900 EGR 902 MTH 902) with a grade of C or better.

NOTES: This course involves a great deal of work on the student's part and would be nearly impossible for the student to master the content without persistently working the problems. As prerequisite, students are expected to possess the knowledge of calculus I and II. Students are expected to spend an additional 3-4 hours per week outside of class to complete all assignments. To achieve the general education goals and learning outcomes, students will communicate meaningfully in writing while presenting information. Students will translate quantifiable problems into mathematical terms and solve these problems using mathematical operations. Students will construct graphs and charts, interpret them, and draw appropriate conclusions. Course activities include:
  1. Speaking Assignments: students will present research individually or in groups using current technology to support the presentation; students will participate in discussions and debates related to the topics in the lessons.
  2. Case Studies: Complex situations and scenarios will be analyzed in cooperative group settings or as homework assignments.
  3. Lectures: This format will include question and answer sessions to provide interactivity between students and the instructor.
  4. Videos or Invited Speakers: Related topics will provide impetus for discussion. The class web page is updated every week, which provides supplemental information such as announcements, lecture notes, homework assignment, and students' grades.


STUDENT LEARNING OUTCOMES:
Upon completion of this course, students will be able to:
  • Clearly relate interpretation of solutions to standard algebraic and calculus-driven application problems.
  • Achieve strong critical thinking skills in terms of problem solving. Students are expected to be able to determine from any initial question of any of the following that apply:
    1. The meaning and importance of all given information
    2. the primary unknown for which a solution is desired
    3. any secondary unknowns or relationships that may be required
    4. proper understanding of the techniques required to move toward solution
    5. a proper understanding of the meaning of the solution, and
    6. ability to interpret and properly explain the solution
  • Clearly show work or provide clear explanation as how to setup and generate a solution for application problems.
  • Correctly make use of graphing calculators as a supplemental tool and to check work through graphing technique.
  • Use, understand and write all required algebraic symbols and abbreviations.

The course is the third of a three-semester sequence of integrated calculus and analytic geometry. Both the understanding of theoretical concepts and the ability to use manipulative techniques are considered of prime importance. The approach is intuitive. After the student has attained a conceptual understanding, the theorems are advanced and proved. Time is spent in applications of the notions as they arise throughout the course. The course presumes algebraic and trigonometric competency at the 70% level or higher.


TOPICAL OUTLINE:

MATH140 is a 16-week course. The following list is the time spent on each topic. Students who successfully complete the course will demonstrate the following outcomes by properly finishing their regular homework, quizzes, tests, projects, presentations, and a final exam. Students will translate quantifiable problems into mathematical terms and solve these problems using mathematical operations. Students will construct graphs and charts, interpret them, and draw appropriate conclusions. Students will communicate meaningfully in writing while presenting information and provide solutions with the procedure, results, organization, diagrams and other details necessary for another person to review.

The student should be able to understand and apply the following:
  • Find the length of a vector in Three-dimensional space. (week 1-2)
    • Find the unit vector in the direction of a given vector
    • Determine whether a set of vectors is linearly independent or linearly dependent
    • Express a vector as a linear combination of a set of linearly independent vectors
    • Find the angle between two three-dimensional vectors
    • Calculate scalar product of two vectors
    • Calculate vector product of two vectors
    • Calculate scalar triple product of three vectors
    • Differentiate vector functions
    • Integrate vector functions
    • Find the tangential and normal components of a vector function
  • Understand the following concepts relating vectors, curves, and surfaces in space: (week 3-4)
    • Vector equation of a line
    • Parametric equation of a line
    • Symmetric equation of a line
    • Vector equation of a plane
    • Scalar equation of a plane
    • Angle between two planes
    • The arc length of space curves
    • Curvature of Two-dimensional and Three-dimensional curves
    • Planes and traces
    • Cylinders and rulings
    • Surface of revolution
  • Draw the following quadric surfaces and their level curves by using the software in the computer lab: (week 5)
    • Ellipsoid
    • Elliptic paraboloid
    • Elliptical cone
    • Hyperboloid of one sheet
    • Hyperboloid of two sheets
    • Hyperbolic paraboloid
  • Be able to use the following three coordinate systems: (week 6-7)
    • Rectangular coordinates
    • Cylindrical coordinates
    • Spherical coordinates
  • Understand the following concepts related to partial derivatives: (week 8)
    • Definition of partial derivatives
    • Notation for partial derivatives
    • Instantaneous rates of change
    • Geometric interpretation of partial derivatives
    • Planes tangent to surfaces
    • Higher-order partial derivatives
    • Limits and continuity of functions of more than one variable
    • Implicit differentiation on functions of several variables
    • Chain rule to obtain partial derivatives
    • The total differential of a function
  • Understand the following applications of partial and total derivatives: (week 9-10)
    • Finding local extrema
    • Finding global extrema
    • Highest and lowest points of surfaces
    • Maximum-minimum problems
    • Increments and differentials
    • The linear approximation theorem
    • Differentiability of multivariable functions
    • Lagrange multipliers (one constraint)
    • Lagrange multipliers in three dimensions
    • Problems that have two constraints
    • Sufficient conditions for local extrema
  • Determine the existence of an exact differential. (week 11-13)
    • Learn the definition and properties of a double integral
    • Evaluate double integral
    • Apply the double integral concept to the following applications:
      • Density and mass
      • Volume of revolution
      • Surface area of revolution
      • Moments of inertia
    • Evaluate double integrals by polar coordinates
    • Learn the definition and properties of a triple integral
    • Evaluate triple integrals
  • Understand and use the following basic concepts of the field theory: (Week 14-16)
    • The gradient vector field
    • The divergence of a vector field
    • The curl of a vector field
    • Line integral of a function along a curve
    • Line integrals with respect to coordinate variables
    • Line integrals and vector fields
    • Equivalent line integrals
    • The fundamental theorem for line integrals
    • Independence of path
    • Conservative field and potential functions
    • Conservative force and conservation of energy
    • Green's theorem
    • The divergence and flux of a vector field
    • Surface integrals with respect to coordinate elements
    • The flux of a vector field
    • The divergence theorem
    • More general regions and Gauss's law
    • Stokes' Theorem
    • Conservation and irrotational fields

TEXTBOOK / SPECIAL MATERIALS:

Edwards & Penney, Calculus with Analytic Geometry, 7th Edition, Prentice-Hall, 2008.

A TI-83 or better calculator is recommended.

See bookstore website for current book(s) at https://www.dacc.edu/bookstore

EVALUATION:

The student will be evaluated on the degree to which student learning outcomes are achieved. A variety of methods may be used, such as tests, quizzes, class attendance and participation, reading assignments, projects, homework, presentations, and a final exam. Students are expected to completely solve homework problems as each section is assigned. Homework grade will be assigned based on the solution procedure, results, organization, and presentation. Each solution shall be explained with all the detail and diagrams necessary for another person to review. Three major separate sources will contribute to the grade in this course: Four hourly exams are given during the semester, which are composed by solving problems selected from each chapter. These hourly exams (including quizzes and projects) determine 50% of the grade. A comprehensive final exam is given at the end of the semester, which accounts for 30% of the grade. Homework (including presentation) and/or projects using programmable calculators or computers account for 20% of the grade.

Determination of grade based upon all work completed is as follows:
A= 90%-100%
B= 80%-89%
C= 70%-79%
D= 60%-69%
F= < 60%

BIBLIOGRAPHY:
  • Calculus with Analytic Geometry, Sixth Edition, 2003 by Ellis, Robert and Gulick, Denny.
  • An Introduction to Analysis, (2nd Edition) by James R. Kirkwood, (2002, Hardcover), Waveland Press, Inc.
STUDENT CONDUCT CODE:
Membership in the DACC community brings both rights and responsibility. As a student at DACC, you are expected to exhibit conduct compatible with the educational mission of the College. Academic dishonesty, including but not limited to, cheating and plagiarism, is not tolerated. A DACC student is also required to abide by the acceptable use policies of copyright and peer-to-peer file sharing. It is the student’s responsibility to become familiar with and adhere to the Student Code of Conduct as contained in the DACC Student Handbook. The Student Handbook is available in the Information Office in Vermilion Hall and online at: https://www.dacc.edu/student-handbook

DISABILITY SERVICES:
Any student who feels s/he may need an accommodation based on the impact of a disability should contact the Testing & Academic Services Center at 217-443-8708 (TTY 217-443-8701) or stop by Cannon Hall Room 103. Please speak with your instructor privately to discuss your specific accommodation needs in this course.

REVISION:
Spring 2019

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