# 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 17A: Calculus for Biology and Medicine

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

This course requires the Math Placement Exam. Read More.

**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:**

Two years of high school algebra, plane geometry, plane trigonometry, and analytical geometry, and satisfying the Mathematics Placement Requirement.

**Suggested Schedule:**

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

1-3 | 1.1-1.5 | Preliminaries: Elementary functions and graphing. Include one full lecture on transformation of functions, log transforms, and log-log/semi-log plot |

4-5 | 1.6, 2.1 | Sequences, discrete-time models, and limits of sequences |

6-8 | 2.2-2.5 | Limits of functions: limit laws, limits at infinity, algebraic methods, continuity |

9 | 3.1 | Derivatives as rates of change, tangent lines |

10-12 | 3.2, 3.3 | Derivatives as functions, differentiability, higher derivatives, power rule, basic differentiation rules, derivatives of exponential functions, derivatives of sine and cosine |

13 | 3.4 | Product and quotient rules |

14-15 | 3.5 | Chain rule, implicit differentiation, related rates |

16 | 3.6 | Exponential growth and decay |

17 | 3.7 | Derivatives of inverse and logarithmic functions |

18 | 3.8 | Linear approximation (Optional: Newton's method, Taylor polynomials) |

19 | 4.1 | Extrema |

20 | 4.2 | Monotonicity and concavity (Optional: Mean Value Theorem) |

21 | 4.2 | Graphing – Examples including sigmoidal curves |

22 | 4.3 | L'Hospital's rule |

23-24 | 4.4 | Optimization |

25 | 4.5 | Stability of fixed points in recursions |

26-27 | Use remaining lectures as buffer for material above and/or to cover optional material in 3.8 |

**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 1-4: limits and derivatives; applications of differentiation in biology; recursions.

This course covers chapters 1-4: limits and derivatives; applications of differentiation in biology; recursions.

**Learning Goals:**

Upon completion of this course, students will be able to

- use appropriate transformations to find power law and exponential relationships,
- create discrete-time models of biological phenomena and analyze their behavior,
- understand the meaning of limits and derivatives of functions,
- calculate limits and derivatives of functions using appropriate techniques,
- interpret derivatives in a biological context, including ecological, physiological, and pharmacological models,
- approximate functions and bound error using derivatives,
- apply problem-solving skills and knowledge of calculus to solve related rates and optimization problems, and
- use derivatives to predict the behavior of and graph functions.