Course

# Calculus I

Faculty
Science & Technology
Department
Mathematics
Course Code
MATH 1120
Credits
3.00
Semester Length
15 weeks
Max Class Size
35
Method(s) 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
Learning Activities

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.

## 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 (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 (3)

## Course Offerings

### Summer 2023

CRN
Days
Dates
Start Date
End Date
Instructor
Status
CRN
22100
Tue Thu
Start Date
-
End Date
Start Date
End Date
Instructor Last Name
Marquise
Instructor First Name
Annie
Course Status
Open
Section Notes

MATH 1120 001 - Students must ALSO register in MATH 1120 T01 or T02.

Max
Enrolled
Remaining
Waitlist
Max Seats Count
35
Actual Seats Count
13
22
Actual Wait Count
0
Days
Building
Room
Time
Tue Thu
Building
Coquitlam - Bldg. A
Room
A1230
Start Time
14:30
-
End Time
16:20
CRN
Days
Dates
Start Date
End Date
Instructor
Status
CRN
22247
Mon Wed
Start Date
-
End Date
Start Date
End Date
Instructor Last Name
Funk
Instructor First Name
Daryl
Course Status
Open
Section Notes

MATH 1120 002 - Students must ALSO register in MATH 1120 T03, T04, T05, T06, or T07.

Max
Enrolled
Remaining
Waitlist
Max Seats Count
35
Actual Seats Count
34
1
Actual Wait Count
0
Days
Building
Room
Time
Mon Wed
Building
New Westminster - South Bldg.
Room
S1812
Start Time
12:30
-
End Time
14:20
CRN
Days
Dates
Start Date
End Date
Instructor
Status
CRN
22819
Mon Wed
Start Date
-
End Date
Start Date
End Date
Instructor Last Name
Funk
Instructor First Name
Daryl
Course Status
Open
Section Notes

MATH 1120 003 - Students must ALSO register in MATH 1120 T03, T04, T05, T06, or T07.

Max
Enrolled
Remaining
Waitlist
Max Seats Count
35
Actual Seats Count
34
1
Actual Wait Count
0
Days
Building
Room
Time
Mon Wed
Building
New Westminster - South Bldg.
Room
S1812
Start Time
14:30
-
End Time
16:20
CRN
Days
Dates
Start Date
End Date
Instructor
Status
CRN
23138
Mon Wed
Start Date
-
End Date
Start Date
End Date
Instructor Last Name
Anisef
Instructor First Name
Aubie
Course Status
Open
Section Notes

MATH 1120 004 - Students must ALSO register in MATH 1120 T03, T04, T05, T06, or T07.

Max
Enrolled
Remaining
Waitlist
Max Seats Count
35
Actual Seats Count
32
3
Actual Wait Count
0
Days
Building
Room
Time
Mon Wed
Building
New Westminster - South Bldg.
Room
S3820
Start Time
16:30
-
End Time
18:20