Theory and methods of integration of elementary functions. Partial derivatives, optimization and integration of functions of two variables. Elementary first order separable and linear differential equations and Taylor polynomials. Applications from business, life and social sciences develop a meaningful context for the theory throughout the course.
- Theory of Integration
- Methods and Applications of Integration
- Differentiation and Integration of Functions of Two Variables
- Differential Equations
- Taylor Series
Methods of Instruction
Lectures and group work
Means of Assessment
At the end of the course, students will be expected to be able to:
- find an indefinite integral using the antiderivatives of a given function.
- verify the properties of an antiderivative through differentiation.
- solve initial value problems using indefinite integrals.
- find an indefinite integral using substitution.
- evaluate definite integrals using the Fundamental Theorem of Calculus.
- use integrals to solve problems involving area, net change and average value.
- find integrals using integration by parts.
- find integrals using integral tables.
- evaluate improper integrals or describe reasons for divergence.
- estimate definite integrals using numerical techniques.
- use integrals to solve problems from business and science.
- create a symbolic formula to represent a given description of a function of two variables.
- sketch the domain and level curves for a given function of two variables.
- compute all first and second order partial derivatives of a given function of two variables.
- give a qualified interpretation of a partial derivative.
- find critical points of a function of two variables.
- classify the critical points of a function of two variables.
- use the method of Lagrange multipliers to optimize a function of two variables under constraints.
- use the method of least squares to find the regression line relating one variable to another.
- set-up and evaluate double integrals.
- rearrange the order of integration variables to evaluate a double integral.
- use partial derivatives and/or double integrals to solve problems from business and science.
- solve elementary separable and linear differential equations.
- use Euler's Method to approximate solutions to differential equations.
- use differential equations to model and solve problems from business and science.
- use Taylor’s formula to approximate functions and estimate definite integrals.
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.
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.
If your course prerequisites indicate that you need an assessment, please see our Assessment page for more information.