General Course Information for MTH223: Calculus IV

Course: MTH223 - Calculus IV
Textbook: For the correct edition of the textbook assigned to a specific class, go to:

Course Prerequisite(s):
Course Description:

A study of functions of several variables: extrema and Lagrange Multipliers, with application to today's optimization-problems in engineering, business, and ecology. Vector algebra and space geometry; Kepler's Laws with application to satellite orbital velocity problems and the rendezvous phenomenon, iterated integrals and applications, the Jacobian transformation will be studied. A graphing calculator is required.

Course Learning Outcomes:
  • Understanding that a sequence is a function on the integers into R1. The notion of a limit of a sequence. Pattern recognition for sequences, monotonic sequences, and convergence of monotone and bounded sequences. The Fibonacci sequence.
  • Partial sums of a series as a sequence. Convergent and divergent series, geometric, harmonic; and the Nth-Term Test as a necessary condition for convergence of a series. The integral and p-series as a
  • The integral and p-series as a sequence. Deriving the p-series test, the ration and root tests, direct comparison tests. The alternating series test will be derived by the student.
  • Taylor polynomials and approximations to sufficiently smooth functions. Be able to derive the Taylor polynomials of sufficient accuracy as to approximate within a proscribed degree of accuracy.
  • Power series definitions, development and radius of convergence. Differentiation and integration of power series (converging uniformly on a contact set). Understand Ramanujan's contribution to series approximation of p.
  • Classification of ordinary and partial differential equations. Recognize a solution (general and singular, as well as a particular solution). Be able to find particular solutions matching pre-stipulated initial value conditions. Recognize ode applicable to the separation of variable methodology. Be able to perform that separability technique, and demonstrate sufficient skills in integration techniques so as to develop confidence and self-sufficiency in its approach.
  • Recognize and select an appropriate methodology to solve homogeneous ode of the first order. Exponential growth and decay applications. Exactness of first-order equations; test and solution techniques.
  • Generating integrating factors for the 2nd-order equation, if they exist. Recognizing and solving the Bernoulli nonlinear differential equation. Be able to solve generalized, and idealized, differential equations emerging from mechanical and electrical engineering applications.
  • Recognize and solve 2nd-order homogeneous linear equations. Know the concept of linear independence of functions over a subset of R1. Know the definition and conceptual considerations regarding basis of a solution space; know that all elements of that solution space can be written as linear combinations of that basis.
  • Recognize and solve 2nd-order homogeneous, linear, ordinary differential equations with forcing function. Know the methodology of undetermined coefficients. Be able to form a Wronskian from the basis functions for the corresponding homogenous equations and be able to apply it to the variation of parameters technique.
  • Demonstrate proficiency in graphing-calculator usage by investigation of Euler's technique for numerical approximation of simple initial-value problems. Recognize and perform the enhanced Euler's technique, and be able to compare rates of convergence. Be familiar with Milne's method, Runge-Kutta. Understand predictor-corrector techniques of numerical solutions of non-linear initial-value problems of ordinary differential equations.

Students with Disabilities:
Students seeking special accommodations due to a disability must submit an application with supporting documentation, as explained under this subject heading in the General Catalog. Instructors are required to provide such accommodations if they receive written notification from the University.

Writing Across the Curriculum:
Students are expected to demonstrate writing skills in describing, analyzing and evaluating ideas and experiences. Written reports and research papers must follow specific standards regarding citations of an author's work within the text and references at the end of the paper. Students are encouraged to use the services of the University's Writing Center when preparing materials.

The following website provides information on APA, MLA, and other writing and citation styles that may be required for term papers and the like:

National University Library:
National University Library supports academic rigor and student academic success by providing access to scholarly books and journals both electronically and in hard copy. Print materials may be accessed at the Library in San Diego or through document delivery for online and regional students. Librarians are available to provide training, reference assistance, and mentoring at the San Diego Library and virtually for online or regional students. Please take advantage of Library resources:


Contact the Library:

  • (858) 541-7900 (direct line)
  • 1-866-NU ACCESS x7900 (toll free)

Use the Library Training Tools (on the Library Homepage) for additional help

  • Recorded class presentations
  • Tutorials & Guides (APA/MLA, Peer-Review, and more)

Plagiarism is the presentation of someone else's ideas or work as one's own. Students must give credit for any information that is not either the result of original research or common knowledge. If a student borrows ideas or information from another author, he/she must acknowledge the author in the body of the text and on the reference page. Students found plagiarizing are subject to the penalties outlined in the Policies and Procedures section of the University Catalog, which may include a failing grade for the work in question or for the entire course. The following is one of many websites that provide helpful information concerning plagiarism for both students and faculty:

Ethical behavior in the classroom is required of every student. The course will identify ethical policies and practices relevant to course topics.

Students are expected to be competent in using current technology appropriate for this discipline. Such technology may include word processing, spreadsheet, and presentation software. Use of the internet and e-mail may also be required.

Learning to work with and value diversity is essential in every class. Students are expected to exhibit an appreciation for multinational and gender diversity in the classroom.

As a diverse community of learners, students must strive to work together in a setting of civility, tolerance, and respect for each other and for the instructor. Rules of classroom behavior (which apply to online as well as onsite courses) include but are not limited to the following:

  • Conflicting opinions among members of a class are to be respected and responded to in a professional manner.
  • Side conversations or other distracting behaviors are not to be engaged in during lectures, class discussions or presentations
  • There are to be no offensive comments, language, or gestures