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Math 22 Calculus II [4]
Instructor: J. E. Yukich
Current Course Catalog Description
Applications of integration; techniques of integration; separable differential equations; infinite sequences and series; Taylor’s Theorem and other approximations; curves and vectors in the plane. Textbook
J. Stewart Calculus, Early Transcendentals, 5 ed. References
Course Goals
Students should deploy their mastery of the definite integral to develop. Developing further integration techniques for a wider range of function. Types and to improper integrals, and to solve problems in areas of application such as calculating areas, volumes, arc length, surface area, moments, centers of mass and centroids, solution of separable and linear differential equations, including the equations of exponential growth and decay. Students should master the new notions of parametric and polar curves and their analysis, and of infinite sequences and series, including power series, the associated approximation techniques, representation of functions by Taylor series. Prerequisites by Topic
Concepts and Techniques of single variable calculus as developed in Mathematics 21 (see Course Description for Mathematics 21 and its Annotated Syllabus Outline, appended). Major Topics Covered in the Course
See Catalogue Description, and Course Goals, above; above, also see Annotated Syllabus Outline, appended. Laboratory projects (specify number of weeks on each)
Estimate CSAB Category Content
Data Structures
Every student is required to submit at least _____ written reports (not including exams, tests, quizzes, or commented programs) of typically _____ pages and to make _____ oral presentations of typically _____ minutes duration. Include only material that is graded for grammar, spelling, style, and so forth, as well as for technical content, completeness, and accuracy. Social and Ethical Issues
Improper integrals: convergence and divergence; differential equations and properties of solutions; parametric and polar curves; convergence and divergence of infinite sequences, infinite series, and power series; associated approximation techniques, representation of functions as power series. Approximately 25 – 30% of lecture time is devoted to these topics, mainly in the second half of the course. Problem Analysis
Identification of problem types and matching of techniques mastered to problem types. Solution Design
Devising and carrying out solution strategies to problems from within Mathematics and from a wide range of applications areas. |
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