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Mathematics 115

Calculus I for the Life Sciences

Length of Course: One Semester (14 weeks)

Classroom Hours per Week: 4 hours 

Number of Credits: 3 credits

Prerequisite: Math 100/110 with a minimum B- OR BC Precalculus 12 with a minimum C

Corequisite: none.


Course Description

This course is designed for students majoring in the Life Sciences. The emphasis is on examples and applications of Differential Calculus in Zoology, Botany, Biochemistry, Microbiology, Genetics, Paleontology, Marine Biology and Ecology.


Course Outline

Length Description

Week 1

Elementary Functions & Mathematical Modeling in Life Sciences

  • Polynomial Functions
  • Elementary Models 
  • Exponential and Logarithmic Functions; Exponential Models 
  • Trigonometric and Inverse Trigonometric Functions

Week 2

Discrete-Time Dynamical Systems

  • Introduction and analysis of discrete-time dynamical systems
  • Modeling with discrete-time dynamical systems
  • A model of gas exchange in the lung
  • Nonlinear dynamics model of selection

Week 3

Limits & Continuity

  • Limits of a functions
  • Infinite limits and limits at infinity
  • Continuity

Week 4

Derivative

  • Derivatives and differentiability
  • Derivatives of polynomial and exponential functions
  • Derivatives of products and quotients
  • The chain rule
  • Derivatives of logarithmic, trigonometric and inverse trigonometric functions
  • Implicit differentiation

Week 5

Derivative

  • Logarithmic differentiation
  • Related rates

Week 6

Applications of Derivatives

  • Extreme values of a function
  • The second derivative and concavity
  • Leading behavior and L’Hopital’s rule

Week 7

Applications of Derivatives

  • Curve sketching

Week 8

Applications of Derivatives

  • Curve sketching

Week 9

Applications of Derivatives

  • Optimization

Week 10

Applications of Derivatives

  • Life Science optima

Week 11

Applications of Derivatives

  • Newton's method
  • Stability of discrete-time dynamical system

Week 12

Applications of Derivatives

  • The logistic dynamical system and more complex dynamics

Week 13

Review

Week 14

Final Exam 

Textbook

Calculus for the Life Sciences: Modelling the Dynamics of Life (Canadian edition) by Adler & Lovric


Course Evaluation

Quizzes and Homework 10-20%
Midterm Exams 20-40%
Final Examination 40-50%

Transferability

Please refer to BC Transfer Guide


Instructors

Arman Ahmadieh B.Sc., M.Sc. (Sharif University of Technology)
Hayri Ardal, B.Sc.(Bogazici), Ph.D. (Simon Fraser)
Kim Peu Chew, B.Sc. (Nanjing), M.A., Ph.D. (British Columbia)
Ana Culibrk, B.Sc., M.Sc. (Belgrade), M.Sc. (British Columbia)
Rika Dong, B.Sc. (Simon Fraser), M.Sc. (Regina)
Sam Ekambaram, B.Sc., M.Sc. (Madras), M.Sc., Ph.D. (Simon Fraser)
Himadri Ganguli, B.Sc., M.Sc. (Chennai), Ph.D. (Simon Fraser)
Peter Hurthig, B.Sc., M.Sc. (British Columbia)
Kamyar Moshksar, B.Sc.(Shiraz), M.Sc. (Waterloo), PhD (Waterloo)