An introductory differential calculus course with applications chosen for students pursuing biological or medical sciences. Topics include: limits, growth rate and the derivative, elementary functions, optimization and approximation methods and their applications, mathematical models of biological processes.
1. Preliminary material
- Review of algebraic and transcendental functions and their graphs
- Transforming functions using semi-log and log-log graphs
2. Discrete time models, sequences, difference equations
- Exponential growth and decay (discrete time and recursions)
- Sequences and their limiting values
- Population models
3. Limits and continuity
- Limits, limit laws
- Limits at infinity
- Sandwich (squeeze) theorem, trigonometric limits
- Intermediate value theorem
- (optional) Formal definition of a limit
- The derivative (formal definition, geometric interpretation, instantaneous rate of change, as a differential equation)
- Differentiability and continuity
- Differentiation rules (power, product, quotient rules)
- Chain rule, implicit differentiation, related rates, higher order derivatives
- Derivatives of trigonometric and exponential functions
- Derivatives of inverse functions and logarithmic differentiation
- Linear approximation and error propagation
5. Applications of differentiation
- Extrema and the Mean Value Theorem
- Monotonicity and concavity
- Extrema, inflection points and graphing
- L’Hospital’s Rule
- Stability of difference equations
- (optional) Newton’s Method
Methods of Instruction
Lecture, problem sessions (tutorials) 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 criteria:
Assignments and quizzes 0 - 40%
Tutorials 0 - 10%
Term tests - 20 - 70%
Comprehensive final exam - 30 - 40%
Note: All sections of a course with a common final examination will have the same weight given to that examination.
MATH 1123 is a first course in calculus. Together with MATH 1223 it forms a science-based introduction to calculus providing the foundation for continued studies in biological or life sciences.
By the end of this course, students will be able to:
- find limits involving algebraic, exponential, logarithmic, trigonometric, and inverse trigonometric functions by inspection as well as by limit laws
- calculate infinite limits and limits at infinity
- apply L'Hôpital's rule to evaluating limits of the types: 0/0, infinity/infinity, infinity - infinity, 00, infinity0, 1infinity
- determine intervals of continuity for a given function
- calculate a derivative from the definition
- differentiate algebraic, trigonometric and inverse trigonometric functions as well as exponential and logarithmic functions of any base using differentiation formulas and the chain rule
- differentiate functions by logarithmic differentiation
- apply the above differentiation methods to problems involving implicit functions, curve sketching, applied extrema, related rates, and growth and decay problems
- use differentials to estimate the value of a function in the neighbourhood of a given point, and to estimate errors
- apply derivatives to investigate the stability of recursive sequences
- interpret and solve optimisation problems
- sketch graphs of functions including rational, trigonometric, logarithmic and exponential functions, identifying intercepts, asymptotes, extrema, intervals of increase and decrease, and concavity
- compute simple antiderivatives, and apply to first order differential equations
- recognise and apply the Mean Value Theorem and the Intermediate Value Theorem
MATH 1110, or,
BC Pre-calculus 12 with a minium grade of B
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.