Calculus II for the Social Sciences

Science & Technology
Course Code
MATH 1225
Semester Length
15 weeks
Max Class Size
Method Of Instruction
Typically Offered
New Westminster


Course Description
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.
Course Content
  1. Theory of Integration
  2. Methods and Applications of Integration
  3. Differentiation and Integration of Functions of Two Variables
  4. Differential Equations
  5. Taylor Series
Methods Of Instruction

Lectures and group work

Means of Assessment
Quizzes 0-40%
Term tests 20-70%
Assignments 0-25%
Participation 0-5%
Tutorial 0-10%
Final Exam 30-40%
Learning Outcomes

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.
Textbook Materials

Textbook varies by semester, please see College Bookstore for current version.

Typical texts include:

Hoffmann, Bradley and Miners, Applied Calculus, Canadian edition, McGraw Hill, 2012

Barnett, Ziegler, Byleen, Calculus for Business, Economics, Life Sciences and Social Sciences, 13th edition, Pearson, 2015.




No corequisite courses.


No equivalent courses.

Requisite for

This course is not required for any other course.

Course 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 Transfers

Institution Transfer Details Effective Dates
Alexander College (ALEX) ALEX MATH 105 (3) 2008/09/01 to -
Camosun College (CAMO) CAMO MATH 1XX (3) 2013/01/01 to -
Coquitlam College (COQU) COQU MATH 105 (3) 2017/05/01 to -
Coquitlam College (COQU) COQU MATH 112 (3) 2006/05/01 to 2017/04/30
Kwantlen Polytechnic University (KPU) KPU MATH 1240 (3) 2006/05/01 to 2019/08/31
Langara College (LANG) LANG MATH 1274 (3) 2006/01/01 to -
Simon Fraser University (SFU) SFU MATH 158 (3), Q 2006/05/01 to -
Thompson Rivers University (TRU) TRU MATH 1XX (3) 2006/05/01 to 2010/12/31
Thompson Rivers University (TRU) TRU MATH 1XXX (3) 2011/01/01 to -
University of British Columbia - Okanagan (UBCO) UBCO MATH 142 (3) 2006/05/01 to -
University of British Columbia - Vancouver (UBCV) UBCV MATH 105 (3) 2006/05/01 to -
University of Northern BC (UNBC) UNBC MATH 152 (3) 2006/05/01 to -
University of the Fraser Valley (UFV) UFV MATH 1XX (3) 2006/05/01 to -
University of Victoria (UVIC) UVIC MATH 1XX (1.5) 2006/05/01 to -
Vancouver Island University (VIU) VIU MATH 1st (3) 2014/01/01 to -
Vancouver Island University (VIU) VIU MATH 192 (3) 2006/05/01 to 2013/12/31

Course Offerings

Winter 2021

Start Date
End Date
- 12-Apr-2021
MATH 1225 039 - Guided Study course - contact the Department Chair for information.

This course will include some synchronous on-line activities. Students should plan to be available on-line at scheduled course times. Synchronous on-line activities may include lecture, or they may not. In some courses, synchronous class time may be used instead for active learning components (e.g. discussions, labs).