Course

# Calculus 2 for Life Sciences

Faculty
Science & Technology
Department
Mathematics
Course Code
MATH 1223
Credits
3.00
Semester Length
15 weeks
Max Class Size
35
Method Of Instruction
Lecture
Tutorial
Typically Offered
To be determined

## Overview

Course Description
An integral calculus course with applications chosen for students pursuing Life or Health sciences. Topics include: the integral and its applications, partial derivatives, differential equations, numerical and power series, linear systems and their applications, mathematical models of biological processes.
Course Content

1.  Integration

• Riemann Sums
• The Definite and Indefinite Integral
• Fundamental Theorem of Calculus
• Net Change and the Mean Value Theorem

2.  Integration techniques and applications

• Substitution
• Partial Fractions
• Integration by Parts
• Trigonometric Integrals and Trigonometric Substitution
• Improper Integrals
• Areas and Volumes

3.  Differential equations

• Autonomous and Non-Autonomous Equations
• Equilibria and Stability
• Differential Equation Models

4.  Series

• Infinite Sequences and Series
• Tests for Convergence and Divergence of Series
• Power and Taylor Series
• Taylor Polynomials

5.  Multi-variable calculus

• Multivariable functions
• Partial Derivatives
• Optimization

6.  Linear Algebra (optional)

• Matrix Operations
• Markov Chains and Leslie Matrices

Methods Of Instruction

Lecture, problem sessions (tutorials) and assignments.

Means of Assessment

Evaluation will be carried out in accordance with the Douglas College Evaluation Policy.  The instructor will present a written course outline with specific evaluation criteria at the beginning of the semester.  Evaluation will be based on 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 1223 is a second course in calculus.  Together with MATH 1123 it forms a science-based introduction to calculus providing the foundation for continued studies in Life or Health sciences. By the end of the course, students will be able to:

• Apply the endpoint or midpoint rules to calculate finite Riemann sums
• Express definite integrals as limits of Riemann sums and vice-versa
• Apply the Fundamental Theorem of Calculus to definite and indefinite integrals
• Apply integration to calculate areas, volumes, arc length, average values and the net change in a function
• Evaluate integrals using substitution, integration by parts and partial fraction expansions
• Evaluate improper integrals and use the comparison test to establish their convergence or divergence
• Solve separable differential equations and apply differential equations to model populations and other Life Sciences phenomena
• Determine the equilibrium solutions to differential equations and establish their stabiity
• Find partial derivatives of functions of several variables and apply them to solve optimization problems
• Establish the convergence or divergence of numerical sequences and series using the comparison, integral and ratio tests
• Express functions as power series
• Determine Taylor series representations of functions
• Determine Taylor polynomial approximations for functions and establish bounds on errors
• Apply matrix methods to dynamical systems in the Life sciences

Textbook Materials

Textbook may vary by semester.  Check with College Bookstore for required text.

Sample text:

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

## Requisites

### Corequisites

No corequisite courses.

## 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.

## 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 1223
Alexander College (ALEX) ALEX MATH 105 (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 109 (4)
Coast Mountain College (CMTN) CMTN MATH 1XX (3)
College of New Caledonia (CNC) CNC MATH 101 (3)
Columbia College (COLU) COLU MATH 112 (3)
Kwantlen Polytechnic University (KPU) KPU MATH 1230 (3)
Langara College (LANG) LANG MATH 1XXX (3)
North Island College (NIC) NIC MAT 1XX (3)
Northern Lights College (NLC) NLC MATH 106 (3)
Okanagan College (OC) No credit
Simon Fraser University (SFU) SFU MATH 155 (3)
Thompson Rivers University (TRU) TRU MATH 1250 (3)
University Canada West (UCW) UCW MATH 120 (3)
University of British Columbia - Vancouver (UBCV) UBCV MATH 103 (3)
University of Northern BC (UNBC) UNBC MATH 1XX (3)
University of the Fraser Valley (UFV) UFV MATH 112 (4)
University of Victoria (UVIC) UVIC MATH 1XX (1.5)
Vancouver Community College (VCC) VCC MATH 1XXX (3)
Vancouver Community College (VCC) No credit
Vancouver Island University (VIU) VIU MATH 122 (3)