vcc.ca
MATH 1100: Calculus 1
Effective date
September 2015
Department
UT Math
School
Arts and Sciences
Description
This course is designed to provide students with a fundamental knowledge of differential calculus. Topics include the concepts of limit and continuity; rates of change; basic differentiation rules; derivatives of algebraic and transcendental functions; applied optimization problems; implicit differentiation and related rates; the mean value theorem; linear approximations; curve sketching; simple differential equations and models; antiderivatives; simple parametric equations and polar coordinates.
Credits
3.0
Year of study
1st Year Post-secondary
Prerequisites
Both MATH 0983 and MATH 0993 with a minimum grade of ‘B’, or MATH 1020 with a minimum grade of ‘C’, or Precalculus 12 with a minimum grade of ‘B’, or Math Precalculus Test with a minimum score of 22 out of 30, or equivalent.
Corequisites
None
Course Learning Outcomes
Upon successful completion of this course, students will be able to:
- Evaluate limits of functions analytically, graphically and numerically
- Determine continuity of polynomial and transcendental functions
- Apply the Intermediate Value Theorem in solving applied problems
- Compute derivatives and antiderivatives of functions
- Solve applied optimization (max/min) problems
- Apply L'Hopital's Rule to study the behaviour of functions
- Estimate function values utilizing linear approximations
- Solve initial value problems
- Derive general solutions of simple differential equations and find particular solutions satisfying initial conditions
- Derive differential equations which explain mathematical models in the applied sciences
Prior Learning Assessment & Recognition (PLAR)
Recognition - Math 1100 Challenge Exam with a C (not accepted for the UT Engineering Certificate or the UT Computer Science and Software Systems Certificate).
Hours
Lecture, Online, Seminar, Tutorial: 60
Total Hours: 60
Total Hours: 60
Instructional Strategies
Lectures coupled with computer lab exercises
Grading System
Letter Grade (A-F)
Passing grade
D
Evaluation Plan
|
Type |
Percentage |
Assessment activity |
|
Assignments |
30 |
|
|
Midterm Exam |
35 |
Written, MC, SA, problems |
|
Final Exam |
35 |
Written, MC, SA, problems |
Course topics
- Prelude to Calculus: tangent lines and slope predictors; limit concept; more limits; concept of continuity The Derivative: the derivative and rates of change; basic differentiation rules; chain rule; derivatives of algebraic functions; maxima and minima of functions; applied optimization problems; derivatives of trigonometric functions and their inverses; exponential and logarithmic functions; implicit differentiation and related rates; successive approximations and Newton’s method.
- Applications of the Derivative: differentials and linear approximations; increasing and decreasing functions; mean value theorem; first derivative test and applications; curve sketching; higher derivatives and concavity; simple curve sketching and asymptotes; indeterminate forms and L'Hopital's rule; more indeterminate forms
- Antiderivatives: antiderivatives and initial value problems
- Differential Equations: simple equations and models
Notes:
- Course contents and descriptions, offerings and schedules are subject to change without notice.
- Students are required to follow all College policies including ones that govern their educational experience at VCC. Policies are available on the VCC website at:
https://www.vcc.ca/about/governance--policies/policies/. - To find out if there are existing transfer agreements for this course, visit the BC Transfer Guide at https://www.bctransferguide.ca.