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# Calculus 2 for Life Sciences

Course Code: MATH 1223
Faculty: Science & Technology
Department: Mathematics
Credits: 3.0
Semester: 15 weeks
Learning Format: Lecture, Tutorial
course overview

An integral calculus course with applications chosen for students pursuing biological or medical sciences. Topics include: the integral, partial derivatives, differential equations, linear systems and their applications, mathematical models of biological processes.

### Course Content

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

### Methods of Instruction

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 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

course prerequisites

MATH 1123 (or MATH 1120)

### Corequisites

None.

curriculum 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 schedule and availability
course transferability

Below shows how this course and its credits transfer within the BC transfer system.

A course is considered university-transferable (UT) if it transfers to at least one of the five research universities in British Columbia: University of British Columbia; University of British Columbia-Okanagan; Simon Fraser University; University of Victoria; and the University of Northern British Columbia.

For more information on transfer visit the BC Transfer Guide and BCCAT websites.

assessments