Calculus II

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Class
MATH 2414
Differentiation and integration of transcendental functions; parametric equations and polar coordinates; techniques of integration; sequences and series; improper integrals. The Maple computer algebra system will be used throughout the course.

Competencies

  1. To demonstrate competency in applications of definite integrals, the student should be able to:
    1. Find the area between two curves.
    2. Find the volume of a solid of revolution by the Disk Method.
    3. Find the volume of a solid of revolution by the Shell Method.
    4. Find the arc length of a function over an interval.
    5. Solve applications involving work.
    6. Find moments, center of mass, and centroids.
    7. Calculate fluid pressure and fluid force (optional).
  2. To demonstrate competency in integration techniques, the student should be able to:
    1. Use basic integration rules.
    2. Perform integration by parts.
    3. Perform trigonometric integration.
    4. Use trigonometric substitutions.
    5. Use partial fractions.
    6. Integrate using tables and a computer algebra system.
    7. Use l’Hopital’s Rule.
    8. Evaluate improper integrals.
  3. To demonstrate competency in infinite series, the student should be able to:
    1. Determine the limit of a sequence.
    2. Use the definition of an infinite series.
    3. Determine whether a geometric series converges or diverges.
    4. Use the Integral Test to determine whether a series converges or diverges.
    5. Determine whether a p-series converges or diverges.
    6. Use the Comparison Test to determine whether a series converges or diverges.
    7. Use the Alternating Series Test to determine whether a series converges.
    8. Use the Ratio Test and the Root Test to determine whether a series converges or diverges.
    9. Find Taylor Polynomials.
    10. Determine the interval of convergence of a power series.
    11. Represent a function by a power series.
    12. Apply Taylor series.
  4. To demonstrate competency in conics, parametric equations, and polar coordinates, the student should be able to:
    1. Sketch plane curves.
    2. Find parametric equations.
    3. Analyze parametric equations using calculus.
    4. Convert rectangular equations to polar form.
    5. Convert polar equations to rectangular form.
    6. Graph polar equations.
    7. Find tangents, area, and arc length using polar coordinates.
  5. To demonstrate competency in vectors, the student should be able to:
    1. Understand the three-dimensional coordinate system.
    2. Perform vector addition and scalar multiplication, and interpret the results geometrically.
    3. Use vectors to solve problems involving force and velocity.
    4. Perform and apply the vector dot product.
    5. Perform and apply the vector cross product.
    6. Find parametric equations of a line in space.
    7. Find an equation of a plane in space.

Campus Resources for Students

Weatherford:
The Academic Support Center is a free public tutoring service provided by the college, offered in LART- LL Room 2, 817-598-6278

Video tapes

Computer assisted instruction

Instructor’s office hours

Course Learning Objectives

Upon successful completion of this course, students will:

  1. Use the concepts of definite integrals to solve problems involving area, volume, work, and other physical applications.
  2. Use substitution, integration by parts, trigonometric substitution, partial fractions, and tables of anti-derivatives to evaluate definite and indefinite integrals.
  3. Define an improper integral.
  4. Apply the concepts of limits, convergence, and divergence to evaluate some classes of improper integrals.
  5. Determine convergence or divergence of sequences and series.
  6. Use Taylor or MacLaurin series to represent functions.
  7. Use Taylor or MacLaurin series to integrate functions not integrable by conventional methods.
  8. Use the concept of polar coordinates to find areas, lengths of curves, and representations of conic sections.
Required Textbooks
Calculus, Larson, Hostetler, and Edwards, Brooks/Cole, 10th ed., 2014.

Required Supplies

Scientific calculator, paper, pencil, and notebook.
ISBN-10
978-1-285-05709-5
Evaluation Standards

These course objectives and student learning outcomes will be assessed through the administration of a minimum of 3 in-class exams (65%), quizzes/homework (10%), and a comprehensive, departmental final exam (25%).

Grading Standards

A - Student’s work is exceptional and consistently above average.
B - Student’s work is above average. Required assignments were completed in a timely manner and have met at least the minimum required standards.
C - Student’s work is acceptable. Majority of assignments meet the minimum required standards.
D - Student’s work fails to meet the minimum requirements for a grade of "C." Overall performance was sub-standard in comparison to normal expectations for this class.
F - Student’s work is clearly unacceptable. Student either did not attempt the work or failed to meet any of the minimum required standards.

To enroll in the next higher mathematics course that has a prerequisite, a student must earn a grade of C or better. A student could take the Compass test to also indicate competency for placement in a higher mathematics course.

Required Institutional Core Learning Outcomes

Communication (COM), Critical Thinking (CT), Empirical & Quantitative Reasoning (EQR)

Disabilities

ADA Statement:

Any student with a documented disability (e.g. learning, psychiatric, vision, hearing, etc.) may contact the Office on the Weatherford College Weatherford Campus to request reasonable accommodations. Phone: 817-598-6350 Office Location: Office Number 118 in the Student Services Building, upper floor. Physical Address: Weatherford College 225 College Park Drive Weatherford, TX.

Academic Integrity
Academic Integrity is fundamental to the educational mission of Weatherford College, and the College expects its students to maintain high standards of personal and scholarly conduct. Academic dishonesty of any kind will not be tolerated. Academic dishonesty includes, but is not limited to, cheating on an examination or other academic work, plagiarism, collusion, and the abuse of resource materials including unauthorized use of Generative AI. Departments may adopt discipline specific guidelines on Generative AI usage approved by the instructional dean. Any student who is demonstrated to have engaged in any of these activities will be subject to immediate disciplinary action in accordance with institutional procedures.
Hope Statement
Any student who faces challenges securing basic resources such as food, clothing, or housing and believes this may affect their performance in their course of study is urged to contact the Director of Student Resources, Dr. Deborah Cregger, for support at (817) 598-6444. Her office is on the first floor of Student Services. If the student prefers, they may contact their instructor, who can reach out on their behalf. Weatherford College also provides the Coyote Pantry. The Pantry maintains boxed and canned foods for students in need. The location of the Coyote Pantry is two blocks west of the Weatherford campus at the Baptist Student Ministry (118 E. Park Ave., Weatherford). Pantry hours are Mon-Thurs. 8:30 am-4:30 pm and Fri. 8.30 am-12:00 pm (817-599-6586).
Grading Key

100-90 = A
89-80 = B
79-70 = C
69-60 = D
59-below = F

Revised
Fall 2021
Last Modified
Friday, September 10, 2021, 3:32 PM