This course is an introduction to differential calculus for students in business, social sciences and biological sciences. Topics include limits, differentiation techniques for algebraic, logarithmic, exponential and trigonometric functions, mathematical modeling, applications to graphing and optimization, implicit differentiation and differentials.
- Limits and Limit Laws
- Tangent Lines and the Derivative
- Differentiation Rules and Implicit Differentiation
- Related Rates
- Marginal Analysis and Differentials
- Applications to Graphing Functions
- Determining the Extrema of Functions
- Additonal techniques of Business Analysis
Methods of Instruction
Lectures, tutorials, problem sessions and assignments
Means of Assessment
Evaluation will be carried out in accordance with Douglas College policy. The instructor will present a written course outline with specific evaluation criteria at the beginning of the semester. Evaluation will be based on some of the following:
Upon completion of MATH 1125 the student should be able to:
- evaluate elementary limits involving algebraic, exponential, logarithmic and trigonometric functions
- describe the concept of continuity and determine intervals upon which a function is continuous
- apply the intermediate value theorem
- find average and instantaneous rates of change
- find derivatives and relate them to tangent lines and instantaneous rates of change
- use differentiation rules to compute the derivatives of algebraic, exponential, logarithmic, trigonometric and implicit functions
- formulate and solve problems involving marginal analysis, elasticity, points of diminishing returns, and other forms of economic modeling
- apply the concepts of differentials and linear approximations
- sketch graphs of functions by applying first and second derivative techniques as well as analysis of vertical, horizontal and slant asymptotes
- use differentiation to determine the local and absolute extrema of functions
- use calculus methods to solve problems of time value of money: interest, annuities, loans, investments and the value of a continuous money flow
Additional topics that may be included in the course:
- compute the definite and indefinite integral of a function
- use integration techniques (substitution, integration by parts and others) to compute integrals
- apply the integral to problems in Business and the Social Sciences
- use Newton’s method to determine points of intersection
- solving problems involving Markov Chains, Linear Programming and Game Theory
MATH 1105; or MATH 1110; or Principles of Math 12 with a B or better or an approved equivalent; or Precalculus 12 with a B or better.
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.