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Mathematics & Statistics

MAC 2281 — Engineering Calculus I — Syllabus

Prerequisites: C (2.0) or better in MAC 1114 and C (2.0) or better in MAC 1140, or C (2.0) or better in MAC 1147, or SAT Math score of 670 or better, or ACT Math score of 29 or better, or College-Level Math CPT score of 90 or better, and knowledge of trigonometry.

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 2282 (Engineering Calculus II) or MAC 2312 (Calculus II). 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

1. Functions and Limits (1 week)
1.1 Functions and Their Representations (review)
1.2 A Catalog of Essential Functions (review)
1.3 The Limit of a Function
1.4 Calculating Limits
1.5 Continuity
1.6 Limits Involving Infinity

2. Derivatives (4 weeks)
2.1 Derivatives and Rates of Change
2.2 The Derivative as a Function
2.3 Basic Differentiation Formulas
2.4 The Product and Quotient Rules
2.5 The Chain Rule
2.6 Implicit Differentiation
2.7 Related Rates
2.8 Linear Approximations and Differentials

3. Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions (1 week)
3.1 Exponential Functions (review)
3.2 Inverse Functions and Logarithms (review)
3.3 Derivatives of Logarithmic and Exponential Functions
3.4 Exponential Growth and Decay (omit)
3.5 Inverse Trigonometric Functions
3.6 Hyperbolic Functions
3.7 Indeterminate Forms and L'Hôpital's Rule

4. Applications of Differentiation (3 weeks)
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 Derivatives and the Shapes of Graphs
4.4 Curve Sketching (omit)
4.5 Optimization Problems
4.6 Newton's Method (omit)
4.7 Antiderivatives

5. Integrals (2-3 weeks)
5.1 Areas and Distances
5.2 The Definite Integral
5.3 Evaluating Definite Integrals
5.4 The Fundamental Theorem of Calculus

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