Course

Calculus I

Faculty
Science and Technology
Department
Mathematics
Course code
MATH 1120
Credits
3.00
Semester length
15 weeks
Max class size
35
Method(s) of instruction
Lecture
Tutorial
Course designation
None
Industry designation
None
Typically offered
Fall
Summer
Winter

Overview

Course description
This course is an introductory differential calculus course for science students. Topics include limits, continuity, differentiation rules for elementary functions, applications of the derivative, optimization problems, properties of elementary functions and their graphs, and differentiation of curves defined by parametric equations and curves given in polar coordinates. Students with credit for MATH 1123 may not take MATH 1120 for further credit.
Course content
  • 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
Learning activities

Lectures, demonstrations, discussions, problem solving, in-class individual or group assignments.

Means of assessment

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.

Learning outcomes

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.
Textbook materials

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. 

Requisites

Prerequisites

One of MATH 1110

or

Precalculus 12 with a B or better

or

Successful completion of the Douglas College Math Assessment (DCOM)

Corequisites

No corequisite courses.

Equivalencies

MATH 1123

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.

(Current)

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)
Athabasca University (AU) AU MATH 2XX (3)
Athabasca University (AU) DOUG MATH 1120 (3) & DOUG MATH 1220 (3) = AU MATH 265 (3) & AU MATH 266 (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

Summer 2026

CRN Days Instructor Status
Maximum seats
35
Currently enrolled
0
Remaining seats:
35
On waitlist
0
Building
New Westminster - North Bldg.
Room
N4217
Times:
Start Time
12:30
-
End Time
14:20
Section notes

MATH 1120-002 Students must ALSO register in a non-conflicting MATH 1120 tutorial at the same campus.

CRN Days Instructor Status
Maximum seats
35
Currently enrolled
0
Remaining seats:
35
On waitlist
0
Building
New Westminster - North Bldg.
Room
N4217
Times:
Start Time
14:30
-
End Time
16:20
Section notes

MATH 1120-003 Students must ALSO register in a non-conflicting MATH 1120 tutorial at the same campus.

CRN Days Instructor Status
Maximum seats
35
Currently enrolled
0
Remaining seats:
35
On waitlist
0
Building
New Westminster - North Bldg.
Room
N4217
Times:
Start Time
16:30
-
End Time
18:20
Section notes

MATH 1120-004 Students must ALSO register in a non-conflicting MATH 1120 tutorial at the same campus.