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Mathematics & Statistics

**Prerequisites:** C (2.0) or better in MAC 1105, * or* C (2.0) or better in MAC 1140,

**Course Description:** The course has two different formats: daytime sections have two 75-minute auditorium lectures per week and one 50-minute help session; evening sections have two 75-minute lectures per week. Successful completion of the course merits 3 semester hours of credit. The schedule outlined below allows time for four midterm exams plus a cumulative final exam, which are the norms for this course.

**Foundations of Knowledge & Learning:** This course is part of the University of South Floridaâ€™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:** *Brief Calculus: An Applied Approach*, 9th Edition, by Larson

**Course Content**

**Chapter 1: Functions, Graphs, and Limits** (2 weeks)

1.1 The Cartesian Plane and the Distance Formula

1.2 Graphs of Equations

1.3 Lines in the Plane and Slope

1.4 Functions

1.5 Limits

1.6 Continuity

**Chapter 2: Differentiation** (3 weeks)

2.1 The Derivative and the Slope of a Graph

2.2 Some Rules for Differentiation

2.3 Rates of Change: Velocity and Marginals

2.4 The Product and Quotient Rules

2.5 The Chain Rule

2.6 Higher-Order Derivatives

2.7 Implicit Differentiation

2.8 Related Rates

**Chapter 3: Applications of the Derivative** (3 weeks)

3.1 Increasing and Decreasing Functions

3.2 Extrema and the First-Derivative Test

3.3 Concavity and the Second-Derivative Test

3.4 Optimization Problems

3.5 Business and Economics Applications

3.6 Asymptotes

3.7 Curve Sketching: A Summary

3.8 Differentials and Marginal Analysis

**Chapter 4: Exponential and Logarithmic Functions** (2 weeks)

4.1 Exponential Functions

4.2 Natural Exponential Functions

4.3 Derivatives of Exponential Functions

4.4 Logarithmic Functions

4.5 Derivatives of Logarithmic Functions

4.6 Exponential Growth and Decay

**Chapter 5: Integration and Its Applications** (2 weeks)

5.1 Antiderivatives and Indefinite Integrals

5.2 Integration by Substitution and The General Power Rule

5.3 Exponential and Logarithmic Integrals

5.4 Area and the Fundamental Theorem of Calculus

5.5 The Area of a Region Bounded by Two Graphs

5.6 The Definite Integral as the Limit of a Sum (omit)

**Chapter 6: Techniques of Integration** (1 week)

6.1 Integration by Parts and Present Value

6.2 Integration Tables (omit)

6.3 Numerical Integration (omit)

6.4 Improper Integrals (omit)

**Chapter 7: Functions of Several Variables** (omit)

7.1 The Three-Dimensional Coordinate System

7.2 Surfaces in Space

7.3 Functions of Several Variables

7.4 Partial Derivatives

7.5 Extrema of Functions of Two Variables

7.6 Lagrange Multipliers

7.7 Least Squares Regression Analysis

7.8 Double Integrals and Area in the Plane

7.9 Applications of Double Integrals

**Miscellaneous University/College Policies:**

- You are encouraged to take notes and may tape the lectures, but neither your notes nor your tapes are to be sold.
- All unauthorized recordings of class are prohibited. Recordings that accommodate individual student needs must be approved in advance and may be used for personal use during this semester only; redistribution is prohibited.
- Students in need of academic accommodations for a disability may consult with the Office of Students with Disabilities Services (SDS) in SVC 1133 to arrange appropriate accommodations. Students are required to give reasonable notice (typically 5 working days) prior to requesting an accommodation.
- Students who anticipate the necessity of being absent due to the observation of a major religious holiday must provide notice of the date in writing to the instructor by the second class meeting.
**Contingency Course Plan:**In the event of an emergency, it may be necessary for USF to suspend normal operations. During this time, USF may opt to continue delivery of instruction through methods that include but are not limited to: Canvas, Elluminate, Skype, and e-mail messaging and/or alternate scheduling. It is the responsibility of the student to monitor the main USF website, e-mails and MoBull messages for important information about the closure. For information about the continuation of instruction, students are directed to their individual blackboard course sites.**S-U Policy:**Students who want to take this course for a grade of S-U (Satisfactory-Unsatisfactory) must sign the S-U Contract no later than the end of the third week of classes. There will be no exceptions. For further information on S-U grades, please consult the undergraduate catalog.Gordon Rule Math courses cannot be taken for an S-U grade.**Note:****“I” Grade Policy:**A grade of “I” indicates incomplete work and will only be assigned when most of the coursework has already been completed with a passing grade. For further information on “I” grades, please consult the undergraduate catalog.

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