Course

Calculus I

Faculty
Science & Technology
Department
Mathematics
Course Code
MATH 1120
Credits
3.00
Semester Length
15 weeks
Max Class Size
35
Method Of Instruction
Lecture
Tutorial
Typically Offered
Fall
Summer
Winter

Overview

Course Description
MATH 1120 is an introductory calculus course for science students. The course includes limits, continuity, and the differentiation of algebraic, trigonometric, inverse trigonometric, exponential and logarithmic functions. Differentiation techniques are applied to graphing, extrema, related rates, and rectilinear motion, as well as to parametric and polar equations. This course is taught using a graphing calculator.
Course Content
  1. Limits and Continuity
    • calculations of limits
    • limit theorems
    • continuity at a point and on an interval
    • essential and removable discontinuities
    • Intermediate Value Theorem
  2. 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
  3. 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 
  4. 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
  5. Parametric Equations and Polar Coordinates
    • parametric representation of curves in
    • 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(?)
  6. 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
Methods Of Instruction

Lectures, problem sessions and assignments

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:

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.

Learning Outcomes

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,?)
Textbook Materials
  • James Stewart, Calculus: Early Transcendentals, Current Edition, Brooks/Cole.
  • A graphing calculator is also required.

 

Requisites

Prerequisites

MATH 1110; or Principles of Math 12 with a B or better; or Precalculus 12 with a B or better.

Corequisites

No corequisite courses.

Equivalencies

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

These are for current course guidelines only. For a full list of archived courses please see https://www.bctransferguide.ca

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 (4)
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)
Coquitlam College (COQU) COQU MATH 101 (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 100 (3)
University of British Columbia - Vancouver (UBCV) UBCV MATH 100 (3)
University of Northern BC (UNBC) UNBC MATH 100 (3)
University of the Fraser Valley (UFV) UFV MATH 111 (4)
University of Victoria (UVIC) UVIC MATH 100 (1.5)
Vancouver Community College (VCC) VCC MATH 1100 (3)
Vancouver Island University (VIU) VIU MATH 121 (3)

Course Offerings

Summer 2022

CRN
Days
Dates
Start Date
End Date
Instructor
Status
22100
Tue Thu
09-May-2022
- 10-Aug-2022
09-May-2022
10-Aug-2022
Valadkhani
Arezou
Open
MATH 1120 001 - Students must ALSO register in MATH 1120 T01 or T02.

Max
Enrolled
Remaining
Waitlist
35
25
10
0
Days
Building
Room
Time
Tue Thu
Coquitlam - Bldg. A
A1230
14:30 - 16:20
CRN
Days
Dates
Start Date
End Date
Instructor
Status
22247
Mon Wed
09-May-2022
- 10-Aug-2022
09-May-2022
10-Aug-2022
Snider
Wesley
Waitlist
MATH 1120 002 - Students must ALSO register in MATH 1120 T03, T04, T05, T06, or T07.
Max
Enrolled
Remaining
Waitlist
35
33
2
1
Days
Building
Room
Time
Mon Wed
New Westminster - South Bldg.
S3903
12:30 - 14:20
CRN
Days
Dates
Start Date
End Date
Instructor
Status
22433
Fri
09-May-2022
- 10-Aug-2022
09-May-2022
10-Aug-2022
Valadkhani
Arezou
Open
MATH 1120 T01 - Students must FIRST register in MATH 1120 001.
Max
Enrolled
Remaining
Waitlist
24
11
13
0
Days
Building
Room
Time
Fri
Coquitlam - Bldg. A
A1230
10:30 - 12:20
CRN
Days
Dates
Start Date
End Date
Instructor
Status
22434
Fri
09-May-2022
- 10-Aug-2022
09-May-2022
10-Aug-2022
Valadkhani
Arezou
Open
MATH 1120 T02 - Students must FIRST register in MATH 1120 001.
Max
Enrolled
Remaining
Waitlist
24
14
10
0
Days
Building
Room
Time
Fri
Coquitlam - Bldg. A
A1230
12:30 - 14:20
CRN
Days
Dates
Start Date
End Date
Instructor
Status
22435
Thu
09-May-2022
- 10-Aug-2022
09-May-2022
10-Aug-2022
Snider
Wesley
Waitlist
MATH 1120 T03 - Students must FIRST register in MATH 1120 002, 003, or 004.
Max
Enrolled
Remaining
Waitlist
24
20
4
2
Days
Building
Room
Time
Thu
New Westminster - North Bldg.
N1220
8:30 - 10:20
CRN
Days
Dates
Start Date
End Date
Instructor
Status
22819
Mon Wed
09-May-2022
- 10-Aug-2022
09-May-2022
10-Aug-2022
Snider
Wesley
Open
MATH 1120 003 - Students must ALSO register in MATH 1120 T03, T04, T05, T06, or T07.
Max
Enrolled
Remaining
Waitlist
35
33
2
0
Days
Building
Room
Time
Mon Wed
New Westminster - South Bldg.
S3903
14:30 - 16:20
CRN
Days
Dates
Start Date
End Date
Instructor
Status
22820
Thu
09-May-2022
- 10-Aug-2022
09-May-2022
10-Aug-2022
Snider
Wesley
Open
MATH 1120 T04 - Students must FIRST register in MATH 1120 002, 003, or 004.
Max
Enrolled
Remaining
Waitlist
24
22
2
0
Days
Building
Room
Time
Thu
New Westminster - North Bldg.
N1220
10:30 - 12:20
CRN
Days
Dates
Start Date
End Date
Instructor
Status
22952
Thu
09-May-2022
- 10-Aug-2022
09-May-2022
10-Aug-2022
Snider
Wesley
Open
MATH 1120 T05 - Students must FIRST register in MATH 1120 002, 003, or 004.
Max
Enrolled
Remaining
Waitlist
24
21
3
0
Days
Building
Room
Time
Thu
New Westminster - North Bldg.
N1220
12:30 - 14:20
CRN
Days
Dates
Start Date
End Date
Instructor
Status
23138
Mon Wed
09-May-2022
- 10-Aug-2022
09-May-2022
10-Aug-2022
Jamshid Nejad
Masomeh
Open
MATH 1120 004 - Students must ALSO register in MATH 1120 T03, T04, T05, T06, or T07.


Max
Enrolled
Remaining
Waitlist
35
24
11
0
Days
Building
Room
Time
Mon Wed
New Westminster - South Bldg.
S3825
16:30 - 18:20
CRN
Days
Dates
Start Date
End Date
Instructor
Status
23675
Thu
09-May-2022
- 10-Aug-2022
09-May-2022
10-Aug-2022
Snider
Wesley
Open
MATH 1120 T06 - Students must FIRST register in MATH 1120 002, 003, or 004.
Max
Enrolled
Remaining
Waitlist
24
13
11
0
Days
Building
Room
Time
Thu
New Westminster - North Bldg.
N1220
14:30 - 16:20
CRN
Days
Dates
Start Date
End Date
Instructor
Status
23676
Thu
09-May-2022
- 10-Aug-2022
09-May-2022
10-Aug-2022
Snider
Wesley
Open
MATH 1120 T07 - Students must FIRST register in MATH 1120 002, 003, or 004.
Max
Enrolled
Remaining
Waitlist
24
13
11
0
Days
Building
Room
Time
Thu
New Westminster - North Bldg.
N1220
16:30 - 18:20