BC's Indigenous Public Post-Secondary Institute

MATH-065 - Calculus -

MATH-065 - Calculus -

Course Details
The ABE Provincial Level Calculus course is designed to (1) provide students with the mathematical knowledge and skills needed for post-secondary academic and career programs and (2) ease the transition from Provincial level Mathematics to first year calculus at college and university. Some of the topics include limits, derivatives and their applications, and the anti-derivative.
Part of the:
  • Available/Required in the following Programs:
  • College Readiness - Qualifying Courses
  • Prerequisites : MATH 063, Pre-Cal Math 12 or instructor permission.
    Course Outline
    Instructors Qualifications: Relevant Bachelor's Degree or Equivalent.
    Office Hours: 1.5 Per week
    Contact Hours: 90
    Student Evaluation
    Assignments/Chapter tests/Midterm Exam 50-70%, Final Exam 30-50%, Total 100%. Grading procedures follow NVIT policy.
    Learning Outcomes: Prelude to Calculus
    It is expected that learners should be able to:
  • demonstrate an understanding of the concept of the limit and notation used in expressing the limit of a function;
  • evaluate the limit of a function analytically, graphically and numerically;
  • distinguish between the limit of a function as x approaches a and the value of the function at x = a;
  • demonstrate an understanding of the concept of one and two-sided limits;
  • evaluate limits at infinity;
  • determine vertical and horizontal asymptotes using limits;
  • determine continuity of functions at a point x = a;
  • determine discontinuities and removable discontinuities; and
  • determine continuity of polynomial, rational, and composite functions.

  • Optional Outcomes:
  • determine continuity of trigonometric functions; and
  • determine limits of trigonometric functions.

  • The Derivative
    It is expected that learners should be able to:
  • define and evaluate the derivative;
  • distinguish between continuity and differentiability of a function;
  • determine the slope of a tangent line to a curve at a given point;
  • calculate derivatives of elementary, rational and algebraic functions;
  • distinguish between rate of change and instantaneous rate of change;
  • apply differentiation rules to applied problems;
  • use Chain Rule to compute derivatives of composite functions;
  • solve rate of change application problems;
  • determine local and global extreme values of a function; and
  • solve applied optimization (max/min) problems.

  • Optional Outcomes:
  • calculate derivatives of trigonometric functions and their inverses;
  • calculate derivatives of exponential and logarithmic functions;
  • use logarithmic differentiation;
  • calculate derivatives of functions defined implicitly;
  • solve related rates problems; and
  • use Newton‘s Method.

  • Applications of the Derivative
    It is expected that learners should be able to:
  • determine critical numbers and inflection points of a function;
  • compute differentials;
  • use the First and Second Derivative Tests to sketch graphs of functions; and
  • use concavity and asymptotes to sketch graphs of functions.

  • Optional Outcomes:
  • differentiate implicitly;
  • understand and use the Mean Value Theorem; and
  • apply L‘Hopital‘s Rule to study the behaviour of functions.

  • Antiderivatives
    It is expected that learners should be able to:
  • compute antiderivatives of linear combinations of functions;
  • use antidifferentiation to solve rectilinear motion problems;
  • use antidifferentiation to find the area under a curve; and
  • evaluate integrals using integral tables and substitutions.

  • Optional Outcomes:
  • use antidifferentiation to find the area between two curves;
  • compute Riemann sums;
  • apply the Trapezoidal Rule; and
  • solve initial value problems.

  • Optional Outcomes:
    Differential Equations
    It is expected that learners should be able to:
  • derive a general solution of differential equations and find a particular solution satisfying initial conditions; and
  • derive differential equations that explain mathematical models in the applied sciences.
  • Text and Materials: William L. Briggs and Lyle Cochran. Single Variable Calculus. Current Edition. New York. Pearson
    Other Resources:
    Transfer Credits: For more information visit: www.bctransferguide.ca
    Other Information: Education Council approved February 2013.