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Mathematics & Statistics

**Prerequisites:** C (2.0) or better in MAC 2241, * or* C (2.0) or better in MAC 2281,

**Course Description:** Successful completion of the course merits 3 semester hours of credit. The schedule outlined below allows time for three midterm exams plus a cumulative final exam, which are the norms for this course. Students in this course are encouraged to submit projects that explore mathematical topics in the sciences.

**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:** *Biocalculus: Calculus, Probability, and Statistics for the Life Sciences*, by Stewart and Day

**Course Content**

**Chapter 3. Derivatives** (0.5 week)

3.8 Linear Approximations and Taylor Polynomials

**Chapter 5. Integrals** (2 weeks)

5.4 The Substitution Rule

5.5 Integration by Parts

5.6 Partial Fractions

5.7 Integration Using Tables and Computer Algebra Systems

5.8 Improper Integrals

**Chapter 6. Applications of Integrals** (2 weeks)

6.1 Areas Between Curves

6.2 Average Values

6.3 Further Applications to Biology

6.4 Volumes

**Chapter 7. Differential Equations** (2 weeks)

7.1 Modeling with Differential Equations

7.2 Phase Plots, Equilibria, and Stability

7.3 Direction Fields and Eulerâ€™s Method

7.4 Separable Equations

7.5 Systems of Differential Equations

7.6 Phase Plane Analysis

**Chapter 8. Vectors and Matrix Models** (2.5 weeks)

8.1 Coordinate Systems

8.2 Vectors

8.3 The Dot Product

8.4 Matrix Algebra

8.5 Matrices and the Dynamics of Vectors

8.6 The Inverse and Determinant of a Matrix

8.7 Eigenvalues and Eigenvectors

8.8 Iterated Matrix Models

**Chapter 9. Multivariable Calculus** (2 weeks)

9.1 Functions of Several Variables

9.2 Partial Derivatives

9.3 Tangent Planes and Linear Approximations

9.4 The Chain Rule

9.5 Directional Derivatives and the Gradient Vector

9.6 Maximum and Minimum Values

**Chapter 10. Systems of Linear Differential Equations** (omit)

10.1 Qualitative Analysis of Linear Systems

10.2 Solving Linear Systems of Differential Equations

10.3 Applications

10.4 Systems of Nonlinear Differential Equations

**Chapter 11. Descriptive Statistics** (omit)

11.1 Numerical Descriptions of Data

11.2 Graphical Descriptions of Data

11.3 Relationships Between Variables

11.4 Populations, Samples, and Inference

**Chapter 12. Probability** (2 weeks)

12.1 Principles of Counting

12.2 What is Probability?

12.3 Conditional Probability

12.4 Discrete Random Variables

12.5 Continuous Random Variables

**Chapter 13. Inferential Statistics** (omit)

13.1 The Sampling Distribution

13.2 Confidence Intervals

13.3 Hypothesis Testing

13.4 Contingency Table Analysis

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