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Mathematics & Statistics

MAC 2242 — Life Sciences Calculus II — Syllabus

Prerequisites: C (2.0) or better in MAC 2241, or C (2.0) or better in MAC 2281, or C (2.0) or better in MAC 2311.

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 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.

textbook

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 Euler’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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