Course

Calculus 1 for Life Sciences

Faculty
Science & Technology
Department
Mathematics
Course Code
MATH 1123
Credits
3.00
Semester Length
15 weeks
Max Class Size
35
Method(s) Of Instruction
Lecture
Tutorial
Typically Offered
To be determined

Overview

Course Description
An introductory differential calculus course with applications chosen for students pursuing biological or medical sciences. Topics include: limits, growth rate and the derivative, elementary functions, optimization and approximation methods and their applications, mathematical models of biological processes.
Course Content

1.  Preliminary material

  • Review of algebraic and transcendental functions and their graphs
  • Transforming functions using semi-log and log-log graphs

2.  Discrete time models, sequences, difference equations

  • Exponential growth and decay (discrete time and recursions)
  • Sequences and their limiting values
  • Population models

3.  Limits and continuity

  • Limits, limit laws
  • Continuity
  • Limits at infinity
  • Sandwich (squeeze) theorem, trigonometric limits
  • Intermediate value theorem
  • (optional) Formal definition of a limit

4.  Differentiation

  • The derivative (formal definition, geometric interpretation, instantaneous rate of change, as a differential equation)
  • Differentiability and continuity
  • Differentiation rules (power, product, quotient rules)
  • Chain rule, implicit differentiation, related rates, higher order derivatives
  • Derivatives of trigonometric and exponential functions
  • Derivatives of inverse functions and logarithmic differentiation
  • Linear approximation and error propagation

5.  Applications of differentiation

  • Extrema and the Mean Value Theorem
  • Monotonicity and concavity
  • Extrema, inflection points and graphing
  • Optimization
  • L’Hospital’s Rule
  • Stability of difference equations
  • (optional) Newton’s Method
  • Antiderivatives
Learning Activities

Lecture, problem sessions (tutorials) and assignments.

Means of Assessment

Evaluation will be carried out in accordance with Douglas College policy.  The instructor will present a written course outline with specific evaluation criteria at the beginning of the semester.  Evaluation will be based on some of the following criteria:

Assignments and quizzes  0 - 40%

Tutorials 0 - 10%

Term tests - 20 - 70%

Comprehensive final exam - 30 - 40%

Note: All sections of a course with a common final examination will have the same weight given to that examination.

Learning Outcomes

MATH 1123 is a first course in calculus.  Together with MATH 1223 it forms a science-based introduction to calculus providing the foundation for continued studies in biological or life sciences.

By the end of this course, students will be able to:

  • find limits involving algebraic, exponential, logarithmic, trigonometric, and inverse trigonometric functions by inspection as well as by limit laws
  • calculate infinite limits and limits at infinity
  • apply L'Hôpital's rule to evaluating limits of the types: 0/0, infinity/infinity, infinity - infinity, 00,  infinity0, 1infinity
  • determine intervals of continuity for a given function
  • calculate a derivative from the definition
  • differentiate algebraic, trigonometric and inverse trigonometric functions as well as exponential  and logarithmic functions of any base using differentiation formulas and the chain rule
  • differentiate functions by logarithmic differentiation
  • apply the above differentiation methods to problems involving implicit functions, curve sketching, applied extrema, related rates, and growth and decay problems
  • use differentials to estimate the value of a function in the neighbourhood of a given point, and to estimate errors
  • apply derivatives to investigate the stability of recursive sequences
  • interpret and solve optimisation problems
  • sketch graphs of functions including rational, trigonometric, logarithmic and exponential functions, identifying intercepts, asymptotes, extrema, intervals of increase and decrease, and concavity
  • compute simple antiderivatives, and apply to first order differential equations
  • recognise and apply the Mean Value Theorem  and  the Intermediate Value Theorem
Textbook Materials

Textbook will vary by semester, see College Bookstore for current textbook.

Sample text:

Neuhauser, Claudia. Calculus for Biology and Medicine.  Prentice-Hall. 2011.

A graphing calculator may be required.

Requisites

Prerequisites

MATH 1110, or,

BC Pre-calculus 12 with a minium grade of B

Corequisites

None

Equivalencies

MATH 1120

Course Guidelines

Course Guidelines for previous years are viewable by selecting the version desired. If you took this course and do not see a listing for the starting semester / year of the course, consider the previous version as the applicable version.

(Current)

Course Transfers

These are for current course guidelines only. For a full list of archived courses please see https://www.bctransferguide.ca

Institution Transfer Details for MATH 1123
Alexander College (ALEX) ALEX MATH 104 (3)
Athabasca University (AU) AU MATH 2XX (3)
Athabasca University (AU) DOUG MATH 1123 (3) & DOUG MATH 1223 (3) = AU MATH 265 (3) & AU MATH 2XX (3)
Capilano University (CAPU) CAPU MATH 108 (3)
Coast Mountain College (CMTN) CMTN MATH 1XX (3)
College of the Rockies (COTR) COTR MATH 113 (3)
Columbia College (COLU) COLU MATH 111 (3)
Kwantlen Polytechnic University (KPU) KPU MATH 1130 (3)
Langara College (LANG) LANG MATH 1XXX (3)
North Island College (NIC) NIC MAT 181 (3)
Northern Lights College (NLC) NLC MATH 105 (3)
Okanagan College (OC) No credit
Simon Fraser University (SFU) SFU MATH 154 (3)
Thompson Rivers University (TRU) TRU MATH 1150 (3)
Trinity Western University (TWU) TWU MATH 1XX (3)
University Canada West (UCW) UCW MATH 110 (3)
University of British Columbia - Okanagan (UBCO) UBCO MATH 100 (3)
University of British Columbia - Vancouver (UBCV) UBCV MATH 102 (3)
University of Northern BC (UNBC) UNBC MATH 1XX (3)
University of the Fraser Valley (UFV) UFV MATH 111 (4)
University of Victoria (UVIC) UVIC MATH 100 (1.5)
Vancouver Community College (VCC) VCC MATH 1XXX (3)
Vancouver Community College (VCC) No credit
Vancouver Island University (VIU) VIU MATH 121 (3)

Course Offerings

Winter 2023