Calculus 2 for Life Sciences

Curriculum Guideline

Effective Date:
Course
Discontinued
No
Course Code
MATH 1223
Descriptive
Calculus 2 for Life Sciences
Department
Mathematics
Faculty
Science & Technology
Credits
3.00
Start Date
End Term
Not Specified
PLAR
No
Semester Length
15 weeks
Max Class Size
35
Contact Hours
Lecture - 4 hours per week Tutorial - 2 hours per week
Method(s) Of Instruction
Lecture
Tutorial
Learning Activities

Lecture, problem sessions (tutorials) and assignments.

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

 

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

 

 

Means of Assessment

Evaluation will be carried out in accordance with the ÁñÁ«ÊÓƵ 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 Materials

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

Sample text:

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

Prerequisites
Equivalencies
Which Prerequisite