Lecture, problem sessions (tutorials) and assignments.
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
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
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.
Textbook may vary by semester. Check with College Bookstore for required text.
Sample text:
Neuhauser, Claudia. Calculus for Biology and Medicine. Prentice-Hall.