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Mathematics & Statistics

**Prerequisites:** C (2.0) or better in MAC 1114 * and* C (2.0) or better in MAC 1140,

**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.

**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

Review

**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

Review

**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

Review

**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

Review

**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

Review

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