Calculus II for the Social Sciences

Curriculum guideline

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Course
MATH 1225
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
201430
PLAR
No
Semester length
15 weeks
Max class size
35
Contact hours
Lectures: 4 hrs/week Tutorial: 1 hr/week
Method(s) of instruction
Lecture
Tutorial
Learning activities

Lectures and group work

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
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 differential equations to model and solve problems from business and science.
  • use Taylor’s formula to approximate functions and estimate definite integrals.
Means of assessment
Quizzes 0-40%
Term tests 20-70%
Assignments 0-25%
Participation 0-5%
Tutorial 0-10%
Final Exam 30-40%
Textbook materials

Textbooks and Materials to be Purchased by Students

Hoffmann, Bradley and Rosen, Applied Calculus, 8th edition, McGraw Hill, 2005

Student Solution Guide, McGraw Hill, 2005 (optional)

Prerequisites

MATH 1125