A discussion of differentiation and integration concepts of the natural logarithm, exponential and inverse trigonometric functions and applications to volumes of revolution, work and arc length. Covers improper integrals and highlights ideas and contributions of Natpier, Huygens and Pascal. Graphing calculator is required.
- Show ability to formulate the functional representations of incremental components of area, volume, surface-area, work, fluid pressure, and be proficient in carrying these through to the integrand of the appropriate definite integral. The student will be successful in retrieving the antiderivative, and evaluating it, during the computation of such integrals.
- Interpret the concept of a definite integral geometrically, numerically, and analytically (e.g., limit of Riemann sums)
- Demonstrate capability to produce an inverse functions, when they exist. Show evidence of solid grasp of the differentiation and integration formulas and rules associated with inverse functions.
- Derive antiderivatives by knowledgeable appeal to the more sophisticated methods of integration by parts, recursion, trigonometric substitution, and partial fractions. The student will demonstrate ability to set up numerical approximations to definite integrals for which closed-form solutions may be impractical to attain. The student will be able to recognize such circumstances.
- Provide evidence of recognition and understanding of behavior of infinite sequences and series. Demonstrate techniques for testing their absolute or conditional convergence, if any. The student will recognize the appropriate logarithmic or trigonometric function to which the power series converges. Similarly, for each such function, the student will be able to generate associated partial sequences of the Maclaurin and Taylor series.
- Compute with conic sections properties presented in algebraic, polar, and other parametric form. Lengths of arc, surface areas, and an understanding of applications to specific problems will be demonstrated.
Why Choose National University?
We’re proud to be a veteran-founded, San Diego-based nonprofit. Since 1971, our mission has been to provide accessible, achievable higher education to adult learners. Today, we educate students from across the U.S. and around the globe, with over 180,000 alumni worldwide.
Focus on one subject at a time — one month at a time — and finish your degree faster.
75+ Degree Programs
Choose from associate, bachelor’s, and master’s degrees, plus credentials and certificates.
On Campus or Online
Study when and where it’s convenient for you with evening, weekend, and 100% online classes.
Apply or transfer any time. Classes start monthly, and applications are accepted year round.
20+ Campus Locations
Attend class onsite at one of over 20 campus locations across California or in Nevada.
As a Yellow Ribbon school, we offer tuition discounts to servicemembers and dependents.
College of Letters and Sciences
“Our faculty are established scholars and creators in their own fields. They are dedicated to making your entry into their disciplines a successful one, preparing you for your career as well as graduate study.”College of Letters and Sciences