Course
Discontinued
No
Course Code
MATH 1225
Descriptive
Calculus II for the Social 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
Course Designation
None
Industry Designation
None
Contact Hours
Lecture: 4 hrs/week
Tutorial: 1 hr/week
Method(s) Of Instruction
Lecture
Tutorial
Learning Activities
Lectures and group work
Course Description
This course provides an introduction to integral calculus and multivariable calculus for students in business and social sciences. Topics include theory and methods of integration for functions of a single variable, applications of the integral, partial derivatives, optimization and integration of functions of two variables, elementary first order separable and linear differential equations, and Taylor series. Applications from business and social sciences develop a meaningful context for the theory throughout the course.
Course Content
- Theory of Integration
- Methods and Applications of Integration
- Differentiation and Integration of Functions of Two Variables
- Differential Equations
- Taylor Series
Learning Outcomes
Upon completion of the course, successful students will 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 an 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.
- 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.
- apply common convergence tests to determine if a given series converges or diverges.
- compute the Taylor series expansions of functions and determine their interval of convergence.
- find the Taylor series expansion of a function by modifying the series expansion of a related function using substitution, term-wise differentiation, or term-wise integration.
- use Taylor’s formula to approximate functions and estimate definite integrals.
Means of Assessment
Evaluation will be carried out in accordance with the Douglas College 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:
| Quizzes | 0-40% |
| Term tests | 20-70% |
| Assignments | 0-25% |
| Participation | 0-5% |
| Tutorial | 0-10% |
| Final Exam | 30-40% |
Textbook Materials
Consult the Douglas College Bookstore for the latest required textbooks and materials.
Example textbooks include:
Barnett, Ziegler, Byleen, Calculus for Business, Economics, Life Sciences and Social Sciences, current edition, Pearson
Hoffmann and Bradley, Applied Calculus, current edition, McGraw Hill
Prerequisites