Calculus I
Overview
- 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 R²
- 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
Lectures, problem sessions and assignments
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:
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.
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,?)
- James Stewart, Calculus: Early Transcendentals, Current Edition, Brooks/Cole.
- A graphing calculator is also required.
Requisites
Course Guidelines
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.
Course Transfers to Other Institutions
Below are current transfer agreements from Douglas College to other institutions for the current course guidelines only. For a full list of transfer details and archived courses, please see the BC Transfer Guide.
Institution | Transfer details for MATH 1120 |
---|---|
Alexander College (ALEX) | ALEX MATH 151 (3) |
BC Institute of Technology (BCIT) | BCIT MATH 1491 (5) or BCIT MATH 2491 (6.5) |
Camosun College (CAMO) | CAMO MATH 100 (3) |
Capilano University (CAPU) | CAPU MATH 116 (4) |
College of New Caledonia (CNC) | CNC MATH 101 (3) |
College of the Rockies (COTR) | COTR MATH 103 (3) |
Columbia College (COLU) | COLU MATH 113 (3) |
Coquitlam College (COQU) | COQU MATH 101 (3) |
Fraser International College (FIC) | FIC MATH 151 (3) |
Kwantlen Polytechnic University (KPU) | KPU MATH 1120 (3) |
Langara College (LANG) | LANG MATH 1171 (3) |
Okanagan College (OC) | OC MATH 112 (3) |
Simon Fraser University (SFU) | SFU MATH 151 (3) |
Thompson Rivers University (TRU) | TRU MATH 1140 (3) |
Trinity Western University (TWU) | TWU MATH 123 (3) |
University of British Columbia - Okanagan (UBCO) | UBCO MATH_O 100 (3) |
University of British Columbia - Vancouver (UBCV) | UBCV MATH_V 100 (3) |
University of Northern BC (UNBC) | UNBC MATH 100 (3) |
University of the Fraser Valley (UFV) | UFV MATH 111 (3) |
University of Victoria (UVIC) | UVIC MATH 100 (1.5) |
Vancouver Community College (VCC) | VCC MATH 1100 (3) |
Vancouver Island University (VIU) | VIU MATH 121 (4) |
Course Offerings
Winter 2026
CRN | Days | Instructor | Status | More details |
---|---|---|---|---|
CRN
12157
|
Mon Wed | Instructor last name
Marquise
Instructor first name
Annie
|
Course status
Open
|
MATH 1120 001 - Students must ALSO register in a non-conflicting MATH 1120 tutorial at the same campus.
CRN | Days | Instructor | Status | More details |
---|---|---|---|---|
CRN
12158
|
Mon Wed | Instructor last name
Anisef
Instructor first name
Aubie
|
Course status
Open
|
MATH 1120 002 - Students must ALSO register in a non-conflicting MATH 1120 tutorial at the same campus.
CRN | Days | Instructor | Status | More details |
---|---|---|---|---|
CRN
12159
|
Mon Wed | Instructor last name
Anisef
Instructor first name
Aubie
|
Course status
Open
|
MATH 1120 003 - Students must ALSO register in a non-conflicting MATH 1120 tutorial at the same campus.
CRN | Days | Instructor | Status | More details |
---|---|---|---|---|
CRN
12160
|
Mon Wed | Instructor last name
Snider
Instructor first name
Wesley
|
Course status
Open
|
MATH 1120 004 - Students must ALSO register in a non-conflicting MATH 1120 tutorial at the same campus.
CRN | Days | Instructor | Status | More details |
---|---|---|---|---|
CRN
12452
|
Tue Thu | Instructor last name
Funk
Instructor first name
Daryl
|
Course status
Open
|
MATH 1120 005 - Students must ALSO register in a non-conflicting MATH 1120 tutorial at the same campus.
CRN | Days | Instructor | Status | More details |
---|---|---|---|---|
CRN
16430
|
Tue Thu | Instructor last name
Snider
Instructor first name
Wesley
|
Course status
Open
|
MATH 1120 006 - Students must ALSO register in a non-conflicting MATH 1120 tutorial at the same campus.
CRN | Days | Instructor | Status | More details |
---|---|---|---|---|
CRN
17209
|
Tue Thu | Instructor last name
Snider
Instructor first name
Wesley
|
Course status
Open
|
MATH 1120 007 - Students must ALSO register in a non-conflicting MATH 1120 tutorial at the same campus.