This course is a supplement to MATH 1120-Calculus I with an emphasis on proving theorems from MATH 1120. Topics include the limit, continuity, differentiability, proof of differentiation rules, proof of the Mean Value Theorem and L’Hôpital’s rule. MATH 1120 must be taken at the same time as MATH 1121.
- Applications of differentiability
Methods of Instruction
Lectures, assignments, group work
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:
- Tests: 25-70%
- Assignments: 0-20%
- Group work: 0-10%
- Attendance: 0-5%
- Final examination: 0-40%
Upon completion of MATH 1121 the student should be able to:
- State the precise (epsilon-delta) definition of a limit
- Apply the (epsilon-delta) definition of a limit to evaluate limits of linear and quadratic functions
- State the precise (epsilon-delta) definition of continuity at a point
- Prove a function is continuous at a point using the precise definition of continuity at a point
- Prove that algebraic combinations of functions are continuous at a point
- Prove that functions are continuous on an interval
- Solve existence problems using the Intermediate Value Theorem
- State the definition of the derivative
- Apply the concepts of the limit, continuity and differentiability to the absolute value function, the greatest integer function, the Dirichlet function and the modified Dirichlet function
- Prove the linearity rules for differentiation using the definition of the derivative
- Prove the product rule for differentiation using the definition of the derivative
- Prove the quotient rule for differentiation using the definition of the derivative
- Prove the chain rule for differentiation using the definition of the derivative
- Prove the power rule for non-negative exponents, integer exponents, rational exponents and real number exponents
- Prove the differentiation formulas for trigonometric functions using the definition of the derivative
- Prove the differentiation rule for the inverse of a differentiable function
- Prove L’Hôpital’s rule for the case of “0/0”
- Prove Fermat’s Theorem, Rolle’s Theorem and the Mean Value Theorem
- Use the Mean Value Theorem to prove properties of differentiable functions such as, but not limited to, the test for monotonicity and the test for concavity
- Derive Newton’s Method and use it to solve problems
MATH 1110 with a grade of A or better OR Precalculus 12 with a grade of A or better and Calculus 12.
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.