Lectures, problem sessions and assignments
- Limits and Continuity
- calculations of limits
- limit theorems
- continuity at a point and on an interval
- essential and removable discontinuities
- Intermediate Value Theorem
- The Derivative
- rates of change and tangent lines
- differentiation from definition
- differentiation formulas and rules
- chain rule
- implicit differentiation
- higher derivatives
- the differential and differential approximations
- linear approximations
- applications to related rates
- Inverse Functions: Exponential, Logarithmic and Inverse Trigonometric Functions
- definitions, properties, and graphs
- differentiation of logarithmic and exponential functions (any base)
- logarithmic differentiation
- differentiation of inverse trigonometric functions
- applications to related rates
- limits involving combinations of exponential, logarithmic, trigonometric, and inverse trigonometric functions
- L'Hôpital's rule
- Graphing and Algebraic Functions
- increasing and decreasing functions
- local extrema
- Rolle's Theorem and Mean Value Theorem
- curve sketching
- concavity; inflection points
- asymptotic behaviour; limits at infinity; infinite limits
- applied maximum and minimum problems
- antidifferentiation
- rectilinear motion
- Parametric Equations and Polar Coordinates
- parametric representation of curves in ¸é²
- derivatives and tangent lines of functions in parametric form
- tangent lines to graphs in polar form
- definitions and relationships between polar and Cartesian coordinates
- graphing of r = f(?)
- Optional Topics (included at the discretion of the instructor).
- a formal limit proof (using epsilonics)
- application of the absolute value and greatest integer functions
- proofs of the rules of differentiation (differentiation formulas) for algebraic functions
- proofs of the differentiation formulas for trigonometric functions from the definition of derivative
- a proof of L'Hôpital's rule for the case of "0/0"
- Newton’s Method
MATH 1120 is a first course in calculus. The four-semester sequence of MATH 1120, 1220, 2321, and 2421 provides the foundation for continued studies in science, engineering, computer science, or a major in mathematics.
At the conclusion of this course, the student should 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, 8/8, 8 - 8, 00, 80, 18
- 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 solve problems in velocity and acceleration, related rates, and functional extrema
- 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 velocity and acceleration
- recognise and apply the Mean Value Theorem and the Intermediate Value Theorem
- be able to convert between parametric and Cartesian forms for simple cases
- use parametric forms to determine first and second derivatives of a function
- sketch graphs of parametric equations and find the slope of a line tangent to the graph at a specified point
- sketch the graph of a polar equation r = f(?), and be able to find intercepts and points of intersection
- find the slope of a line tangent to the graph of a polar equation at a point (r,?)
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:
Weekly quizzes | 0-40% |
Tests | 20-70% |
Assignments | 0-15% |
Attendance | 0-5% |
Class participation | 0-5% |
Tutorials | 0-10% |
Final examination | 30-40% |
Note: All sections of a course with a common final examination will have the same weight given to that examination.
- James Stewart, Calculus: Early Transcendentals, Current Edition, Brooks/Cole.
- A graphing calculator is also required.
MATH 1110; or Principles of Math 12 with a B or better; or Precalculus 12 with a B or better.