Contents of this page:
Documents Available:
Core Curriculum
FirstYear Sciences Calculus
A first year (twosemester) Sciences Calculus course must include all the topics from
the Core Topics list. It is expected that coverage of this material would
constitute threequarters of the course(s) with the remaining onequarter chosen from the Additional
Topics list. For breadth, at least four Additional Topics should be included.
Reference Text: Edwards & Penney, Calculus, Early Transcendentals, Fifth Edition,
Prentice Hall,1998.
Core Topics (75%)
 Limits, continuity, intermediate value theorem
 Differentiation
First and second derivatives with geometric and physical interpretations
Mean value theorem
Derivatives of exp and log functions, exponential growth and decay
Derivatives of trigonometric functions and their inverses
Differentiation rules (including chain rule, implicit differentiation)
Linear approximations and Newton’s Method
Optimization  local and absolute extrema with applications
 Taylor polynomials and special Taylor series (sin, cos, exp, 1/(1x))
 Curve sketching
 Integration
Definition of the definite integral
Areas of plane regions
Average value of a function
Fundamental Theorem of Calculus
Integration techniques: substitution (including trig substitution), parts, tables, partial
fractions
Applications of integration
 Numerical Integration (including The Trapezoidal Rule)
 Improper integrals: evaluation and convergence estimates
 Differential equations (firstorder linear) with applications
Additional Topics (25%)
 Sequences and series
 Arc length, volumes, centroids, surface areas
 Additional differential equations topics
 Complex numbers
 Continuous probability density functions
 Polar coordinates and parametric equations (with calculus applications)
 Additional numerical methods (eg. Simpson’s Rule)
 Related rates
 L’Hôpital’s Rule
Jump to top of page
Core Curriculum
FirstYear Social
Sciences/Business Calculus
A first year (twosemester) Social Sciences/Business Calculus course must include all
the topics from the Core Topics list. It is expected that coverage of this material
would constitute approximately twothirds of the course(s) with the remaining onethird
chosen from the Additional Topics list. For breadth, at least four Additional
Topics should be included.
Reference Text: Haeussler and Paul, Introductory Mathematical Analysis for Business,
Economics, and the Life and Social Sciences, Ninth Edition, Prentice Hall,
1998.
Core Topics (67%)
 Limits, continuity, intermediate value theorem
 Differentiation
First and second derivatives with geometrical and physical interpretations
Applications to economics, business and social sciences
Derivatives of exp and log functions, exponential growth and decay with applications
Derivatives of trigonometric functions
Differentiation rules (including chain rule, implicit differentiation)
Linear approximations and Newton’s Method
Optimization  local and absolute extrema with applications
 Curve sketching
 Integration
Definition of the definite integral
Areas
Average value of a function
Fundamental Theorem of Calculus
Integration techniques: substitution, parts, tables
Applications of integration
 Numerical integration (including The Trapezoidal Rule)
 Differential equations (firstorder linear) with applications
Additional Topics (33%)
 Introduction to probability and statistics
 Partial derivatives and Lagrange multipliers
 Matrix analysis and Gaussian Elimination
 Sequences and series
 Arc length, volumes, centroids, surface areas
 Taylor polynomials and special Taylor series (sin, cos, exp, 1/(1x))
 Improper integrals: evaluation and convergence estimates
 Continuous probability density functions
 Related rates
 Derivatives of inverse trigonometric functions
 Further techniques of integration
 Additional numerical integration methods
Jump to top of page
Transfer Proposal for
FirstYear Calculus
The BCcupm affirms the autonomy of BC's postsecondary institutions in their freedom to
design calculus courses to meet the needs of their unique constituencies. However, the
diversity of calculus courses in first year offerings in these institutions has created
difficulties for transferring students and their institutions. For example, while current
firstyear "business" calculus courses at SFU, UBC and UVic share many common
topics, the additional material covered by these institutions is irreconcilable within a
single twoterm calculus sequence.
This proposal addresses the significant challenges encountered by students transferring
firstyear calculus courses and by their sending institutions. To lessen the impact of
these challenges, we propose that all postsecondary institutions in BC recognize a common
curriculum for firstyear calculus courses. Such recognition will have the following
benefits for students and their institutions:
 Provide transferring students with a solid background for subsequent math courses
requiring firstyear calculus.
 Allow primarily sending institutions to design calculus courses that will meet the needs
of their students posttransfer.
 Guide primarily receiving institutions in assessing the adequacy of courses proposed for
transfer.
Recommendations:
 That the BCcupm accept the Report of the FirstYear Calculus Subcommittee and endorse
the Core Sciences Calculus and Core Social Sciences/Business Calculus curricula as
described in this report.
 That receiving institutions grant full transfer credit to firstyear calculus courses
from other BC postsecondary institutions whose courses are consistent with the curricula
as described in this report.
 That, when designing or modifying firstyear calculus courses, all BC postsecondary
mathematics departments strive to include within their courses the calculus topics as
described in this report.
 That any postsecondary institution sensing that the Core Calculus curricula as
described in this report require a full or partial review raise its concerns at the next
regularly scheduled meeting of the BCcupm.
 That, in the absence of an earlier full review, the Core Calculus curricula be subject
to a mandatory, full review after five years.
Jump to top of page
Core Calculus Subcommittee
Bruce Kadonoff, Chair; Rustum Choksi; David Leeming; Philip Loewen; Casey McConill; Leo
Neufeld
