Lecture, problem sessions (tutorials) and assignments.
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
- Continuity
- Limits at infinity
- Sandwich (squeeze) theorem, trigonometric limits
- Intermediate value theorem
- (optional) Formal definition of a limit
4. Differentiation
- 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
- Optimization
- L’Hospital’s Rule
- Stability of difference equations
- (optional) Newton’s Method
- Antiderivatives
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
Evaluation will be carried out in accordance with ÁñÁ«ÊÓƵ 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.
Textbook will vary by semester, see College Bookstore for current textbook.
Sample text:
Neuhauser, Claudia. Calculus for Biology and Medicine. Prentice-Hall. 2011.
A graphing calculator may be required.
MATH 1110, or,
BC Pre-calculus 12 with a minium grade of B
None