MATH 112 Calculus II (4)

Catalog Description:

Further topics in differential and integral calculus, including sequences and series, Taylor polynomials, polar coordinates, methods of integration, and applications of the integral. (Offered each semester.)


Prerequisites:

MATH 110 Calculus I, Part II or MATH 111 Calculus I

  1. Ability to graph functions and identify extrema and asymptotes
  2. Understand the use of Riemann sums in finding areas and volumes.
  3. Understand and use the fundamental theorem of calculus.
  4. Familiarity with the method of substitution for evaluating an integral.


Required Course Materials:

Larson, Hostetler and Edwards, Calculus, 10th edition, Brooks/Cole, 2014 (ISBN: 9781285060286) Web Assign Online Homework Access Card

 

Course Coordinator:

Douglas C. Phillippy, Ph.D., Associate Professor of Mathematics

 

Course Audience:

Students majoring in computer science, engineering, mathematics, physics, or chemistry.


Course Objectives:

  1. To acquire a comparative knowledge of standard coordinate systems and the ability to choose the most efficient system for any specific problem.
  2. To develop a rigorous understanding of sequences and series with ability to determine their convergence or divergence.
  3. To understand applications of the definite integral to problems such as area, volume, arc length, work and centers of mass.
  4. To enhance learning by examining geometric, numerical and algebraic aspects of each topic.
  5. To acquire an understanding of the breadth of mathematics by studying applications in a wide variety of scientific fields.
  6. To use the tools of calculus to formulate and solve multistep problems and to interpret the numerical results.
  7. To enhance the ability to communicate mathematical concepts through a series of written laboratory assignments and classroom discussions.
  8. To select and use technology when appropriate in problem solving.
  9. To develop an ability to recognize calculus concepts in the context of application problems and implement the corresponding processes.
  10. To develop the process of making appropriate conjectures, finding suitable means to test those conjectures and drawing conclusions about their validity.

Topics:

  1. Applications of integration: a) disk method b) shell method c) area between two curves d) arc length and surfaces of revolution e) work f) moments, center of mass and centroids, and g) fluid pressure
  2. Techniques of integration: a) integration by parts b) trig functions and products of trig functions, and c) partial fraction representation of rational functions.
  3. Sequences, arithmetic and geometric, positive terms and limits of sequences.
  4. Infinite series, positive term series, alternating series, conditional convergence, absolute convergence, power series, region of convergence, calculus of power series, and applications of power series.
  5. Polar coordinates and parametric equations: a) study of coordinate systems, b) graphing, and c) areas and arc lengths.
  6. Conic sections: a) representation in both rectangular and polar form and b) graphs with emphasis on applications.

 

 

Reviewed: October 2013 (textbook); August 2011

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