Calculus 2 for Life Sciences
Overview
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
Lecture, problem sessions (tutorials) and assignments.
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.
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 may vary by semester. Check with College Bookstore for required text.
Sample text:
Neuhauser, Claudia. Calculus for Biology and Medicine. Prentice-Hall.
Requisites
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 - Okanagan (UBCO) | UBCO MATH_O 103 (3) |
| University of British Columbia - Vancouver (UBCV) | UBCV MATH_V 101 (3) |
| University of Northern BC (UNBC) | UNBC MATH 1XX (3) |
| University of the Fraser Valley (UFV) | UFV MATH 112 (3) |
| 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) |