Lecture, problem sessions (tutorials) and assignments.
1. Integration
- The definite integral
- The Fundamental Theorem of Calculus
- Applications of integration (area, cumulative change, average value, volume, arc length)
2. Integration techniques
- Substitution
- Integration by parts
- Rational functions and partial fractions
- Improper integrals
- Numerical integration (midpoint and trapezoid rules)
- Taylor polynomials
3. Differential equations
- Solving differential equations
- Equilibria and stability
- Systems of autonomous equations
4. Linear algebra
- Solving systems of linear equations
- Matrices
- (optional) Linear maps, Eigenvectors and Eigenvalues
5. Multi-variable calculus
- Functions of two or more independent variables
- Limits and continuity
- Partial derivatives
- Applications of partial derivatives
(optional) Systems of difference equations
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 biological or life sciences.
By the end of the course, students will be able to:
- compute finite Riemann sums and use to estimate area
- form limits of Riemann sums and write the corresponding definite integral
- recognize and apply the Fundamental Theorem of Calculus
- evaluate integrals involving exponential functions to any base
- evaluate integrals of rational functions
- evaluate integrals involving basic trigonometric functions and integrals whose solutions require inverse trigonometric functions
- choose an appropriate method and apply the following techniques to find antiderivatives and evaluate definite integrals:
- integration by parts
- completing the square for integrals involving quadratic expressions
- partial fractions
- apply integration to problems involving areas, volumes, arc length, velocity and acceleration
- be able to determine the convergence or divergence of improper integrals by the comparison test
- approximate a differentiable function by a Taylor polynomial, determine the remainder term, and compute the error in using the approximation
- solve first-order differential equations by the method of separation of variables; apply to growth and decay problems
- find equilibria of differential equations and determine their stability graphically and analytically
- describe the behavior of solutions of differential equations, starting from different initial conditions
- use systems of differential equations to describe biological systems with multiple interacting components
- solve systems of linear equations
- define matrices and perform algebraic operations on matrices
- define and use functions of two or more independent variables
- find limits of multi-variable functions and describe their continuity
- calculate partial derivatives and apply them to biological science problems
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.
Textbook may vary by semester. Check with College Bookstore for required text.
Sample text:
Neuhauser, Claudia. Calculus for Biology and Medicine. Prentice-Hall.
None.