Calculus: Sequences and Series

Course Number:

MTH 253Z

Transcript Title:

Calculus: Sequences and Series

Created:

Aug 15, 2022

Updated:

May 31, 2025

Total Credits:

4

Lecture Hours:

30

Lecture / Lab Hours:

20

Lab Hours:

0

Satisfies Cultural Literacy requirement:

No

Satisfies General Education requirement:

Yes

Grading Options

A-F, P/NP, Audit

Default Grading Options

A-F

Repeats available for credit:

0

Alignment with Institutional Learning Outcomes

Major

1. Communicate effectively using appropriate reading, writing, listening, and speaking skills. (Communication)

Major

2. Creatively solve problems by using relevant methods of research, personal reflection, reasoning, and evaluation of information. (Critical thinking and Problem-Solving)

Major

3. Extract, interpret, evaluate, communicate, and apply quantitative information and methods to solve problems, evaluate claims, and support decisions in their academic, professional and private lives. (Quantitative Literacy)

Not Addressed

4. Use an understanding of cultural differences to constructively address issues that arise in the workplace and community. (Cultural Awareness)

Not Addressed

5. Recognize the consequences of human activity upon our social and natural world. (Community and Environmental Responsibility)

To establish an intentional learning environment, Institutional Learning Outcomes (ILOs) require a clear definition of instructional strategies, evidence of recurrent instruction, and employment of several assessment modes.

Major Designation

1. The outcome is addressed recurrently in the curriculum, regularly enough to establish a thorough understanding.
2. Students can demonstrate and are assessed on a thorough understanding of the outcome.
   • The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

Minor Designation

1. The outcome is addressed adequately in the curriculum, establishing fundamental understanding.
2. Students can demonstrate and are assessed on a fundamental understanding of the outcome.
   • The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

Suggested Outcome Assessment Strategies

The determination of assessment strategies is generally left to the discretion of the instructor. Here are some strategies that you might consider when designing your course: writings (journals, self-reflections, pre writing exercises, essays), quizzes, tests, midterm and final exams, group projects, presentations (in person, videos, etc), self-assessments, experimentations, lab reports, peer critiques, responses (to texts, podcasts, videos, films, etc), student generated questions, Escape Room, interviews, and/or portfolios.

Course Activities and Design

The determination of teaching strategies used in the delivery of outcomes is generally left to the discretion of the instructor. Here are some strategies that you might consider when designing your course: lecture, small group/forum discussion, flipped classroom, dyads, oral presentation, role play, simulation scenarios, group projects, service learning projects, hands-on lab, peer review/workshops, cooperative learning (jigsaw, fishbowl), inquiry based instruction, differentiated instruction (learning centers), graphic organizers, etc.

The grade will include at least one project.

Course Content

Outcome #1: Recognize and define sequences in a variety of forms and describe their properties, including the concepts of convergence and divergence, boundedness, and monotonicity.

• Sequences

  • Bounded Sequences

  • Monotone Sequences

• Convergence of Sequences

• Divergence of Sequences

• Related Theorems

Outcome #2: Recognize and define series in terms of a sequence of partial sums and describe their properties, including convergence and divergence.

• Definition of Infinite Series

  • Sequences of Partial Sums

• Convergence & Divergence

Outcome #3: Recognize series as harmonic, geometric, telescoping, alternating, or p-series, and demonstrate whether they are absolutely convergent, conditionally convergent, or divergent, and find their sum if applicable.

• Specific Types of Series and Their Convergence Conditions

  • Harmonic Series

  • Geometric Series

  • Telescoping Series

  • Alternating Series

  • P-Series

Outcome #4: Choose and apply the divergence, integral, comparison, limit comparison, alternating series, and ratio tests to determine the convergence or divergence of a series.

• Testing for Convergence of Infinite Series

  • Divergence Test

  • Integral Test

  • Comparison and Limit Comparison Tests

  • Alternating Series Test

  • Ration Test

Outcome #5: Determine the radius and interval of convergence of power series, and use Taylor series to represent, differentiate, and integrate functions.

• Power Series

  • Radius and Interval of Convergence

  • Differentiation and Integration of Power Series

  • Series Representation of Functions, Part 1

• Taylor & Maclaurin Series

  • Series Representation of Functions, Part 2

Outcome #6: Use techniques and properties of Taylor polynomials to approximate functions and analyze error.

• Taylor Polynomials

  • Taylor’s Inequality

• Applications

• Error Analysis

Suggested Texts and Materials

Calculus, Vol. 2, Openstax, Strang, Herman
This is an open textbook available at: https://openstax.org/details/books/calculus-volume-2

Department Notes

Answers to all application problems will be given in complete sentences with correct units. The grade will include at least one project.