Lecture: 4 hours/week
and
Tutorial: 2 hours/week
Lectures, demonstrations, discussions, problem solving, in-class individual or group assignments.
- Limits
- Intuitive notion of the limit of a function
- The limit laws
- The Squeeze Theorem
- Limits at infinity horizontal asymptotes
- Infinite limits and vertical asymptotes
- Continuity
- Definition of continuity at a point
- Jump, removable, and infinite discontinuities
- Continuity on an interval
- The Intermediate Value Theorem
- The Derivative
- Definition of the derivative of a function
- Rates of change and tangent lines
- Differentiation rules:
- the product and quotient rules
- derivatives of polynomial, root, rational, exponential, trigonometric, inverse trigonometric and logarithmic functions
- the chain rule
- implicit differentiation
- logarithmic differentiation
- Higher derivatives
- Applications of the Derivative
- The Mean Value Theorem
- Behaviours of functions:
- intervals of increase/decrease
- concavity and inflection points
- local and global extreme values
- curve sketching
- L'Hôpital's Rule
- Newton’s Method
- Optimization problems
- Differentials and linear approximation
- Related rates problems
- Applications to physical sciences
- Differentiation of parametrically defined curves in the plane
- Differentiation of curves in polar coordinates
- The notion of an antiderivative and basic antidifferentiation formulas
Upon successful completion of the course, students will be able to:
- Evaluate limits involving elementary functions using the limit laws;
- Analyze infinite limits and calculate limits at infinity;
- Use L'Hôpital's Rule to evaluate indeterminate limits;
- Determine intervals of continuity for a given function;
- Find the derivative of a function and the value of the derivative at a point using the definition of the derivative;
- Use various rules and techniques for differentiation to compute derivatives of elementary functions;
- Apply the concept of the derivative to describe behaviour and properties of elementary functions, including by sketching graphs, identifying intervals on which the function is increasing/decreasing and concave up/down, and identifying extrema and asymptotes;
- Apply differentiation methods to solve problems involving related rates and optimization;
- Find linear approximations and differentials of elementary functions and apply them to solve problems;
- Apply differentiation methods to solve problems involving implicitly defined functions;
- Apply Newton's Method to approximate the solution of an equation to a specified level of accuracy;
- Apply the concept of the derivative and the antiderivative to solve problems involving velocity and acceleration, as well as to other problems in the physical and social sciences;
- State and apply the Mean Value Theorem and the Intermediate Value Theorem;
- Find the (rectilinear) equation of a line tangent to a parametrically defined curve at a given point;
- Sketch graphs and find derivatives of functions given in polar coordinates;
- Find the (rectilinear) equation of a line tangent to a curve given by an equation using polar coordinates.
Assessment will be in accordance with the Douglas College Evaluation Policy. The instructor will present a written course outline with specific evaluation criteria at the beginning of the semester. Evaluation will be based on the following:
| Quizzes | 0-20% |
| Test(s) | 20-70% |
| Assignments | 0-15% |
| Attendance | 0-5% |
| Participation | 0-5% |
| Tutorials | 0-10% |
| Final Examination | 30-40% |
| Total | 100% |
Instructors may use a student’s record of attendance and/or level of active participation in the course as part of the student’s graded performance. Where this occurs, expectations and grade calculations regarding class attendance and participation will be clearly defined in the Instructor Course Outline.
Consult the Douglas College Bookstore for the latest required textbooks and materials. Example textbooks and materials may include:
Stewart, James. (current edition). Calculus: Early Transcendentals. Brooks/Cole.
Feldman, Joel; Rechnitzer, Andrew; and Yeager, Elyse. (2024). CLP-1 Differential Calculus. UBC.
Anton, Bivens, and Davis. (current edition). Calculus: Early Transcendentals. Wiley.
Briggs, Cochran, and Gillet. (current edition). Calculus: Early Transcendentals. Pearson.
Edwards and Penney. (current edition). Calculus: Early Transcendentals. Pearson.
One of MATH 1110
or
Precalculus 12 with a B or better
or
Successful completion of the Douglas College Math Assessment (DCOM)