Course

Calculus II

Faculty
Science & Technology
Department
Mathematics
Course Code
MATH 1220
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 1220 is an introduction to integral calculus. It develops the concept of the integral and its applications. Other topics include techniques of integration, improper integrals, sequences and series of numbers, Taylor series, polar coordinates, parametric equations, and separable differential equations.
Course Content

Introduction to the Integral

  • sigma notation
  • Riemann sums
  • the definite integral
  • the Fundamental Theorem of Calculus
  • antiderivatives; elementary substitutions
  • applications to area under and between curves, volume and work

Techniques of Integration

  • parts
  • trigonometric substitution
  • trigonometric integrals (products and powers)
  • partial fractions (linear factors and distinct quadratic factors)
  • rationalizing substitutions
  • improper integrals

Applications of Integration

  • areas between curves
  • volumes by cross sections and cylindrical shells
  • work
  • separable differential equations
  • arc length

Infinite Series

  • sequences
  • sum of a geometric series
  • absolute and conditional convergence
  • comparison tests
  • alternating series
  • ratio and root test
  • integral test
  • power series
  • differentiation and integration of power series
  • Taylor and Maclaurin series
  • polynomial approximations; Taylor polynomials

Parametric Equations and Polar Coordinates

  • areas and arc lengths of curves in polar coordinates
  • areas and arc lengths of functions in parametric form

Optional Topics (included at the discretion of the instructor)

  • tables of integrals
  • approximation of integrals by numerical techniques
  • Newton's law of cooling, Newton's law when force is proportional to velocity, and logistics curves
  • a heuristic "proof" of the Fundamental Theorem of Calculus
  • the notion of the logarithm defined as an integral
  • further applications of Riemann sums and integration
  • binomial series
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 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

At the conclusion of this course, the student should be able to:

  • compute finite Riemann sums and use to estimate area
  • form limits of Riemann sums and write the corresponding definite integral
  • recognize and apply the Fundamental Theorem of Calculus
  • evaluate integrals involving exponential functions to any base
  • evaluate integrals involving basic trigonometric functions and integrals whose solutions require inverse trigonometric functions
  • choose an appropriate method and apply the following techniques to find antiderivatives and evaluate definite integrals:
    • integration by parts
    • trigonometric and rationalizing substitution
    • completing the square for integrals involving quadratic expressions
    • partial fractions
    • integrals of products of trigonometric functions
  • apply integration to problems involving areas, volumes, arc length, work, velocity and acceleration
  • be able to determine the convergence or divergence of improper integrals either directly, or by using the comparison test
  • determine if a given sequence converges or diverges
  • determine if a sequence is bounded and/or monotonic
  • determine the sum of a geometric series
  • be able to choose an appropriate test and determine series convergence/divergence using:
    • integral test
    • simple comparison test
    • limit comparison test
    • ratio test
    • root test (optional)
    • alternating series test
  • distinguish and apply concepts of absolute and conditional convergence of a series
  • determine the radius and interval of convergence of a power series
  • approximate a differentiable function by a Taylor polynomial, determine the remainder term, and compute the error in using the approximation
  • find a Taylor or Maclaurin series representing specified functions by:
    • "direct" computation
    • means of substitution, differentiation or integration of related power series
  • find the area of a region bounded by the graph of a polar equation or parametric equations
  • find the lengths of curves in polar coordinates or in parametric form
  • solve first order differential equations by the method of separation of variables; apply to growth and decay problems
Textbook Materials

Consult the Douglas College bookstore for the current textbook. Examples of textbooks under consideration include:
Stewart, Calculus: Early Transcendentals, Cengage Learning, current edition
Anton, Bivens, and Davis, Calculus: Early Transcendentals, Wiley, current edition
Briggs, Cochran, and Gillet, Calculus: Early Transcendentals, Pearson, current edition
Edwards and Penney, Calculus: Early Transcendentals, Pearson, current edition

A graphing calculator may also be required.

Requisites

Prerequisites

MATH 1120 or MATH 1123

Corequisites

No corequisite courses.

Equivalencies

No equivalent 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.

(Current)

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 1220
Alexander College (ALEX) ALEX MATH 152 (3)
Camosun College (CAMO) CAMO MATH 101 (3)
Capilano University (CAPU) CAPU MATH 126 (3)
College of New Caledonia (CNC) CNC MATH 102 (3)
College of the Rockies (COTR) COTR MATH 104 (3)
Columbia College (COLU) COLU MATH 114 (3)
Coquitlam College (COQU) COQU MATH 102 (3)
Fraser International College (FIC) FIC MATH 152 (3)
Kwantlen Polytechnic University (KPU) KPU MATH 1220 (3)
Langara College (LANG) LANG MATH 1271 (3)
Okanagan College (OC) OC MATH 122 (3)
Simon Fraser University (SFU) SFU MATH 152 (3)
Thompson Rivers University (TRU) TRU MATH 1240 (3)
Trinity Western University (TWU) TWU MATH 124 (3)
University of British Columbia - Okanagan (UBCO) UBCO MATH_O 101 (3)
University of British Columbia - Vancouver (UBCV) UBCV MATH_V 101 (3)
University of Northern BC (UNBC) UNBC MATH 101 (3)
University of the Fraser Valley (UFV) UFV MATH 112 (3)
University of Victoria (UVIC) UVIC MATH 101 (1.5)
Vancouver Community College (VCC) VCC MATH 1200 (3)
Vancouver Island University (VIU) VIU MATH 122 (3)

Course Offerings

Winter 2025

CRN Days Instructor Status
Maximum Seats
35
Currently Enrolled
9
Remaining Seats:
26
On Waitlist
0
Building
Coquitlam - Bldg. C
Room
C1006
Times:
Start Time
10:30
-
End Time
12:20
Section Notes

MATH 1220 001 - Must also register in one of MATH 1220 T01 or T02.

CRN Days Instructor Status
Maximum Seats
35
Currently Enrolled
28
Remaining Seats:
7
On Waitlist
0
Building
New Westminster - South Bldg.
Room
S1814
Times:
Start Time
12:30
-
End Time
14:20
Section Notes

MATH 1220 002 - Must also register in one of MATH 1220 T03, T04, T05, T06, T07 or T08.

CRN Days Instructor Status
Maximum Seats
35
Currently Enrolled
35
Remaining Seats:
0
On Waitlist
0
Building
New Westminster - South Bldg.
Room
S1814
Times:
Start Time
14:30
-
End Time
16:20
Section Notes

MATH 1220 003 - Must also register in one of MATH 1220 T03, T04, T05, T06, T07 or T08.

CRN Days Instructor Status
Maximum Seats
35
Currently Enrolled
23
Remaining Seats:
12
On Waitlist
0
Building
New Westminster - South Bldg.
Room
S3820
Times:
Start Time
16:30
-
End Time
18:20
Section Notes

MATH 1220 004 - Must also register in one of MATH 1220 T03, T04, T05, T06, T07, or T08.

CRN Days Instructor Status
Maximum Seats
35
Currently Enrolled
35
Remaining Seats:
0
On Waitlist
6
Building
New Westminster - South Bldg.
Room
S3820
Times:
Start Time
12:30
-
End Time
14:20
Section Notes

MATH 1220 005 - Must also register in one of MATH 1220 T03, T04, T05, T06, T07 or T08.