MATH 1920 - Calculus II

4 sem hrs cr

This course is a study of differentiation and integration of trigonometric, inverse trigonometric, logarithmic, and exponential functions; integration techniques, including parts, substitution and partial fractions; indeterminate forms; applications of the integral; sequences and infinite series including Taylor expansions. Prerequisite: MATH 1910  

In rare and unusual circumstances, a course prerequisite can be overridden with the permission of the Department Lead for the discipline.

This course may include proctored exams which must be completed on campus or at an instructor approved proctoring center which may require additional costs to the student. Please consult your instructor for additional details.

Transfer (UT) or Non-Transfer Course (UN): UT

By the end of the course, students will be able to…

• teach the skills necessary for the study of Calculus III.
• fulfill, partially, the math requirements for those in a University Parallel major and emphasis in the areas of mathematics, physics, pre-engineering, chemistry, and computer science.
• help the student better see how knowledge acquired in his past studies of algebra and trigonometry can be applied to calculus-based situations.
• review and extend the student’s ability to differentiate and integrate algebraic and transcendental functions.
• apply previously learned methods of integration to finding volumes, arclength, surface area, and centroids. 
• demonstrate the need for additional methods of integration and learn how to apply these methods to various integral forms.
• recognize and evaluate indeterminate forms.
• introduce methods for determining the convergence or divergence of sequences and infinite series.
• use series and approximation methods to represent functions using power series.  

Student Objectives 

Throughout the course, students will have the opportunity to… 

• differentiate and integrate simple algebraic and trigonometric functions as a review of Calculus I topics.

• use the laws of logarithms to simplify certain expressions, solve for x in logarithmic equations, and graph logarithmic functions (optional). 

• take the derivative of variations of logarithmic functions.

• perform integrations of functions which have logarithmic solutions. Integrals will be both definite and indefinite. 

• define and explore the idea of inverse functions (optional).

• learn the relationship between exponential and logarithmic functions, graph exponential functions, and solve for x in exponential equations (optional).

• differentiate and integrate variations of exponential functions.

• graph, differentiate, and integrate exponential functions with bases other than e (optional).

• define, graph, and solve problems involving the inverse trigonometric functions (optional). 

• differentiate and integrate problems involving inverse trigonometric functions.

• define, graph, and solve problems involving hyperbolic functions (optional).

• differentiate and integrate variations of hyperbolic functions (optional).

• find the area between two curves by integration.

• find volumes of solids by the disc, washer, and shell methods. 

• find volumes of solids with known cross sections (optional).

• find arclength of curves and area of surfaces of revolution by integration. 

• calculate physical work (optional).

• find moments and centers of mass (centroids) of discrete systems and of plane regions.

• find pressure exerted by fluids on flat surfaces (optional).

• review integration procedures that the students have learned up to this point.

• perform the following additional methods of integration: integration by parts, trigonometric integrals, trigonometric substitution, partial fractions, and tables.

• recognize indeterminate forms, determine when L’Hopital’s Rule applies and, if it does not, use algebraic methods to change indeterminate forms to other forms where the Rule does apply. 

• evaluate limits which are indeterminate in form by L’Hopital’s Rule.

• evaluate improper integrals.

• solve problems involving sequences and determine whether a sequence converges or diverges.

• identify series and determine whether a series (including geometric and telescoping) converges or diverges.

• use the nth term test to determine convergence.

• use the integral test to determine whether a series converges or diverges.

• identify p-series and determine their convergence.

• use the direct comparison and limit comparison tests to determine whether a series converges or diverges (direct comparison optional).

• determine the absolute or conditional convergence of an alternating series.

• use the ratio and root tests to determine the convergence of series (root test optional).

• approximate functions by Taylor and Maclaurin polynomials and use Taylor’s Theorem to determine the accuracy of the approximation.  

• investigate power series and determine their interval of convergence.

• represent functions by power series (optional).

• find the Taylor and/or Maclaurin series for a function and use the results to integrate a series.

• determine the error involved in approximating expressions by power series (optional).