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Mathematics & Statistics

MAC 2312 — Calculus II — Syllabus

Prerequisites: C (2.0) or better in MAC 2311, or C (2.0) or better in MAC 2281.

Course Description: The course meets for approximately 55 hours during a 15-week semester. Successful completion of the course merits 4 semester hours of credit and provides sufficient background for either MAC 2313 (Calculus III) or MAC 2283 (Engineering Calculus III). The schedule outlined below allows time for four midterm exams plus a cumulative final exam, which are the norms for this course. (Note: A “lecture” is defined as a 50-minute time period.)

Foundations of Knowledge & Learning: This course is part of the University of South Florida’s Foundations of Knowledge and Learning (FKL) Core Curriculum. It is certified for Mathematics and Quantitative Reasoning and will meet the following four dimensions: Critical Thinking, Inquiry-based Learning, Scientific Processes, and Quantitative Literacy. Students enrolled in this course will be expected to participate in the USF General Education assessment effort. This might involve answering questions that measure quantitative reasoning skills (but are not directly related to the course), responding to surveys, or participating in other measurements designed to assess the FKL Core Curriculum learning outcomes.

alt. textbook

Text: Essential Calculus: Early Transcendentals, USF Custom Edition, by Stewart

Alt. Text: Essential Calculus: Early Transcendentals, 2nd Edition, by Stewart

Course Content

5. Integrals (1 week)
5.1 Areas and Distances (omit)
5.2 The Definite Integral (omit)
5.3 Evaluating Definite Integrals (omit)
5.4 The Fundamental Theorem of Calculus (review)
5.5 The Substitution Rule

6. Techniques of Integration (3-4 weeks)
6.1 Integration by Parts
6.2 Trigonometric Integrals and Substitutions
6.3 Partial Fractions
6.4 Integration with Tables and Computer Algebra Systems
6.5 Approximate Integration
6.6 Improper Integrals

7. Applications of Integration (3-4 weeks)
7.1 Areas between Curves
7.2 Volumes
7.3 Volumes by Cylindrical Shells
7.4 Arc Length
7.5 Area of a Surface of Revolution
7.6 Applications to Physics and Engineering (optional)
7.7 Differential Equations (omit)

8. Series (6-7 weeks)
8.1 Sequences
8.2 Series
8.3 The Integral and Comparison Tests
8.4 Other Convergence Tests
8.5 Power Series
8.6 Representing Functions as Power Series
8.7 Taylor and Maclaurin Series
8.8 Applications of Taylor Polynomials

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