Course

Calculus II

Faculty
Science and Technology
Department
Mathematics
Course code
MATH 1220
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 integral calculus course. Topics include the Riemann integral, techniques of integration, improper integrals, sequences and series, power series and Taylor series. Applications include area and volume, length of a curve, and separable differential equations.
Course content

Definite and Indefinite Integrals

  • Definition of the Riemann integral
  • The Fundamental Theorem of Calculus
  • Antiderivatives and indefinite integrals
  • The Net Change Theorem

Techniques of Integration

  • The substitution rule
  • Integration by parts
  • Trigonometric integrals 
  • Trigonometric substitution
  • Partial fraction decomposition of rational functions 
  • Numerical approximation methods for integrals: Midpoint Rule, Trapezoidal Rule, Simpson's Rule
  • Rationalizing substitutions 
  • Improper integrals

Applications of Integration

  • Area between curves
  • Volumes by cross-sections and cylindrical shells
  • Length of a curve 
  • Separable differential equations work

Parametric Equations and Polar Coordinates

  • Length of curves in parametric form
  • Area of curves in polar coordinates

Sequences and Series

  • Cnvergence/divergence of sequences
    • convergence/divergence of sequences of partial sums
    • sums of infinite geometric series
    • the harmonic series
    • properties of convergent series
  • Integral test
  • Comparison tests
  • Alternating series test
  • Absolute and conditional convergence
  • Ratio and root tests

 Power Series

  • Intervals and radii of convergence
  • Representation of functions as power series
  • Differentiation and integration of power series
  • Taylor and Maclaurin series 
  • Applications of Taylor Polynomials
Learning activities

Classroom time will be used for:

  • Lectures
  • Demonstrations
  • Discussions
  • Problem-solving practice
  • In-class assignments (which may include work in groups).
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%
Class 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’s Course Outline. 

Learning outcomes

Upon successful completion of the course, students will be able to:

  • Compute finite Riemann sums; 
  • Form limits of Riemann sums and write the corresponding definite integral for a given function;
  • Apply the Fundamental Theorem of Calculus to evaluate integrals using basic antiderivatives and techniques of integration;
  • Choose an appropriate integration method to find antiderivatives and evaluate definite integrals; 
  • Approximate the value of a definite integral using numerical approximation methods, including the Midpoint Rule, Trapezoidal Rule and Simpson's Rule;
  • Apply integration techniques to solve problems related to areas, volumes, arc length, position, velocity, acceleration and work;
  • Solve simple separable differential equations; 
  • Determine the convergence or divergence of improper integrals; 
  • Determine convergence/divergence properties of a given sequence or series; 
  • Represent a given function as a power series;
  • Find the Taylor series representation of a given function;
  • Approximate a differentiable function by a Taylor polynomial and compute the error that results from using the approximation; 
  • Determine the radius and interval of convergence of a power series;
  • Find the area of a region bounded by the graph of a polar equation;
  • Find the length of a curve given in Cartesian form or parametric form.
Textbook materials

Consult the Douglas College Bookstore for the current textbook. Examples of textbooks may include:

Stewart. (Current Edition). Calculus: Early Transcendentals. Cengage Learning. 

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. 

Feldman, Joel; Rechnitzer, Andrew and Yeager, Elyse. (2024). CLP-2 Integral Calculus. UBC.

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.

(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 1220
Alexander College (ALEX) ALEX MATH 152 (3)
Athabasca University (AU) DOUG MATH 1120 (3) & DOUG MATH 1220 (3) = AU MATH 265 (3) & AU MATH 266 (3)
Athabasca University (AU) AU MATH 2XX (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 (4)

Course Offerings

Summer 2026

CRN Days Instructor Status
Maximum seats
35
Currently enrolled
0
Remaining seats:
35
On waitlist
0
Building
New Westminster - South Bldg.
Room
S1812
Times:
Start Time
12:30
-
End Time
14:20
Section notes

MATH 1220 001 - Students must ALSO register in MATH 1220 T01, T02, T03, T04 or T05.

CRN Days Instructor Status
Maximum seats
35
Currently enrolled
0
Remaining seats:
35
On waitlist
0
Building
New Westminster - North Bldg.
Room
N1220
Times:
Start Time
12:30
-
End Time
14:20
Section notes

MATH 1220 002 - Students must ALSO enroll in MATH 1220 T01, T02, T03, T04, or T05.

CRN Days Instructor Status
Maximum seats
35
Currently enrolled
0
Remaining seats:
35
On waitlist
0
Building
New Westminster - North Bldg.
Room
N1220
Times:
Start Time
14:30
-
End Time
16:20
Section notes

MATH 1220 003 - Students must ALSO enroll in MATH 1220 T01, T02, T03, T04, or T05.