Courses

MATH2080 - Elements of Calculus II (Winter)

Outline

Offerings: F, W(3-1)
Prerequisites: 1 of MATH*1000, MATH*1080, MATH*1200, IPS*1110
Corequisites: None
Exclusions: MATH*1010, MATH*1210, IPS*1210

Calendar Description:
The official course outline is presented by the instructor each semester. The material that follows is for general knowledge only - and may change at any time.
Techniques of integration. Introduction to differential equations and the elements of multivariate calculus. Illustrations and emphasis will be on biological applications. An introduction to vectors, multivariable and vector functions, difference equations, partial differentiation and multiple integration.

Intended Students: This course is the continuation of MATH*1080 and is intended for students in the Biological Science, Agricultural, Veterinary Medicine, and Environmental Science (Environmetrics) programs who require or would like one full year of Calculus.

Objectives: This course presents an introduction to multivariable calculus and differential equations in the context of applications in the biological, environmental, and life sciences. The course focuses on the basic concepts and techniques of integral calculus, differential equations, 2nd order difference equations, multivariable and vector functions, partial differentiation, and multiple integration with emphasis on their role in the mathematical modelling of natural phenomena and biological processes. Through the mathematical modelling process, the students are introduced to interdisciplinary reasoning and integration of quantitative and qualitative methods with fundamental concepts in the bio-sciences. Although, due to the emphasis on math modelling, this course contains the topics of differential equations and difference equations, it does not rigorously develop the associated mathematical theory (which is done in MATH*2170).

Content:
* Limits and Differentiation Review.
* L'Hopital's Rule.
* Integration Review. Fundamental Theorem of Calculus.
* Techniques of Integration: substitution, integration by parts, partial fractions.
* First Order Differential Equations. Solution of separable and linear equations, analysis of growth models.
* Equilibria and Their Stability.
* Numerical Solutions of Differential Equations (Euler and the Modified Euler's method).
* Second Order Linear Difference Equations and Applications.
* Vectors, and Functions of more than one variable.
* Parametric curves. Surfaces in Three Dimensions (planes, level curves).
* Differential Calculus of Functions of Several Variables (Partial Derivatives and their interpretations.)
* Tangent Planes, Directional Derivatives, and the Gradient.
* Determining Extrema of Multivariable Functions.
* Extrema with Constraints, Lagrange multipliers.
* Multiple Integration (Double and Iterated Integrals and their applications.)

Representative Texts: Calculus for Biology and Medicine 2nd Edition, by Claudia Neuhauser, Pearson Education Ltd., 2004.

Evaluation: A Typical Evaluation is as follows:

Best 6 of 9 Laboratory Assignments: 20%
Midterm Test 1: 20%
Midterm Test 2: 20%
Final Exam: 40%