# Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

## MAT 17B: Calculus for Biology and Medicine

**Approved:**2019-09-03, R. Thomas and K. Burke

**Suggested Textbook:**(actual textbook varies by instructor; check your instructor)

"Biocalculus: Calculus, Probability, and Statistics for the Life Sciences," 1st edition, by Stewart/Day (Cengage)

Search by ISBN on Amazon: 9781305114036

Search by ISBN on Amazon: 9781305114036

**Prerequisites:**

MAT 16A, 17A, or 21A with C- or above

**Suggested Schedule:**

Lecture | Section | Comments/Topics |
---|---|---|

1 | 4.6, 5.1 | Antiderivatives, solutions of initial value problems, areas, distances |

2-3 | 5.2 | Definite integrals, midpoint rule |

4 | 5.3 | Fundamental Theorem of Calculus |

5 | 5.4 | Integration by substitution |

6 | 5.5 | Integration by parts |

7 | 5.6 | Partial fractions; mention tables of integrals (5.7) and software packages |

8 | 5.8 | Improper integrals |

9 | 6.1-6.2 | Area between curves, average value |

10 | 6.3 | Further applications to biology |

11 | 6.4 | Volumes |

12 | 7.1 | Modeling with differential equations, solving pure-time differential equations |

13 | 7.2 | Phase plots, equilibria, stability of equilibria |

14 | 7.4 | Separable differential equations |

15 | online notes | Solving first-order linear non-autonomous differential equations using integrating factors |

16 | 7.3 or 7.5 | Direction fields and Euler's method or Systems of autonomous ODEs |

17-18 | 8.1-8.3 | Coordinate systems, vectors, vector operations |

19 | 8.4 | Matrices, matrix multiplication |

20 | 8.5 | Systems of difference equations |

21 | 8.6 | Inverses and determinants of matrices |

22-23 | 8.7 | Eigenvalues and eigenvectors |

24 | 8.8 | Iterated matrix models |

25-27 | Use remaining lectures as buffer for material above and/or to cover optional material from 7.3, 7.5, or 7.6 |

**Additional Notes:**

This course is part of the Inclusive Access program, in which your textbook and other course resources will be made available online. Please consult your instructor on the FIRST DAY of instruction.

This course covers chapters 5-8: integration, differential equations, linear algebra, elements of analytic geometry.

This course covers chapters 5-8: integration, differential equations, linear algebra, elements of analytic geometry.

**Learning Goals:**

Upon completion of this course, students will be able to

- understand the meaning of definite and indefinite integrals,
- understand the relationships between derivatives, antiderivatives, rates of change, indefinite integrals, definite integrals, distances, and areas,
- calculate definite and indefinite integrals using appropriate techniques,
- numerically approximate definite integrals,
- interpret integrals in a biological context, including ecological, physiological, and pharmacological models,
- model biological phenomena using differential equations,
- solve pure-time, separable, and first-order linear differential equations,
- use appropriate graphical techniques to visualize differential equations and their solutions,
- determine and analyze equilibria and their stability,
- visualize vectors and vector operations,
- perform basic operations on vectors and matrices, and
- calculate eigenvectors and eigenvalues.