Calculus (S)

Calculus courses are offered jointly by the Departments of Applied Mathematics and Mathematics. For course descriptions of other mathematics courses at the Year 1 and senior levels, please refer to the course listing in APPLIED MATHEMATICS (S) and MATHEMATICS (S).

 Calculus 1000A/B - Calculus I
Review of limits and derivatives of exponential, logarithmic and rational functions. Trigonometric functions and their inverses. The derivatives of the trig functions and their inverses. L'Hospital's rules. The definite integral. Fundamental theorem of Calculus. Simple substitution. Applications including areas of regions and volumes of solids of revolution.
Antirequisite(s): The former Calculus 1100A/B, Calculus 1500A/B, Applied Mathematics 1413
Prerequisite(s): Ontario Secondary School MCV4U or Mathematics 0110A/B
Corequisite(s):
Pre-or Corequisite(s):
Extra Information: 4 lecture hours, 0.5 course.
 Calculus 1301A/B - Calculus II
For students requiring the equivalent of a full course in calculus at a less rigorous level than Calculus 1501A/B.  Integration by parts, partial fractions, integral tables, geometric series, harmonic series, Taylor series with applications, arc length of parametric and polar curves, first order linear and separable differential equations with applications.
Antirequisite(s):
Prerequisite(s): A minimum mark of 55% in one of Calculus 1000A/B, 1500A/B, or the former 1100A/B .
Corequisite(s):
Pre-or Corequisite(s):
Extra Information: 4 lecture hours, 0.5 course.
 Calculus 1500A/B - Calculus I for the Mathematical Sciences
An enriched version of Calculus 1000A/B. Basic set theory and an introduction to mathematical rigour. The precise definition of limit. Derivatives of exponential, logarithmic, rational trigonometric functions. L'Hospital's rule. The definite integral. Fundamental theorem of Calculus. Integration by substitution. Applications.
Antirequisite(s): Calculus 1000A/B, the former 1100A/B, Applied Mathematics 1413.
Prerequisite(s): Ontario Secondary School MCV4U or Mathematics 0110A/B.
Corequisite(s):
Pre-or Corequisite(s):
Extra Information: 4 lecture hours, 0.5 course.
 Calculus 1501A/B - Calculus II for Mathematical and Physical Sciences
Students who intend to pursue a degree in Actuarial Science, Applied Mathematics, Astronomy, Mathematics, Physics, or Statistics should take this course. Techniques of integration; The Mean Value Theorem and its consequences; series, Taylor series with applications; parametric and polar curves with applications; first order linear and separable differential equations with applications.
Antirequisite(s):
Prerequisite(s): A minimum mark of 60% in one of Calculus 1000A/B, the former 1100A/B or 1500A/B.
Corequisite(s):
Pre-or Corequisite(s):
Extra Information: 4 lecture hours, 0.5 course.
 Calculus 2302A/B - Intermediate Calculus I
Three dimensional analytic geometry: dot and cross product; equations for lines and planes; quadric surfaces; vector functions and space curves; arc length; curvature; velocity; acceleration. Differential calculus of functions of several variables: level curves and surfaces; limits; continuity; partial derivatives; tangent planes; differentials; chain rule; implicit functions; extrema; Lagrange multipliers.
Antirequisite(s):
Prerequisite(s): A minimum mark of 55% in Calculus 1501A/B or Calculus 1301A/B, or Applied Mathematics 1413.
Corequisite(s):
Pre-or Corequisite(s):
Extra Information: 3 lecture hours, 0.5 course.
 Calculus 2303A/B - Intermediate Calculus II
Integral calculus of functions of several variables: double, triple and iterated integrals; applications; surface area. Vector integral calculus: vector fields; line integrals in the plane; Green's theorem; independence of path; simply connected and multiply connected domains; parametric surfaces and their areas; divergence and Stokes' theorem.
Antirequisite(s):
Prerequisite(s):
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Extra Information: 3 lecture hours, 0.5 course.
 Calculus 2402A/B - Calculus with Analysis for Statistics
Functions of multiple variables and their differential calculus. The gradient and the Hessian. Constrained and unconstrained optimization of scalar-valued functions of many variables: Lagrange multipliers. Multidimensional Taylor series. Integrating scalar-valued functions of several variables: Jacobian transformations. Pointwise and uniform convergence. Power series.
Antirequisite(s):
Prerequisite(s): Calculus 1301A/B or 1501A/B or Applied Mathematics 1413, in each case with a minimum mark of 55%.
Corequisite(s):
Pre-or Corequisite(s):
Extra Information: 3 lecture hours, 0.5 course.
 Calculus 2502A/B - Advanced Calculus I
Differential calculus of functions of several variables: level curves and surfaces; limits; continuity; partial derivatives; total differentials; Jacobian matrix; chain rule; implicit functions; inverse functions; curvilinear coordinates; derivatives; the Laplacian; Taylor Series; extrema; Lagrange multipliers; vector and scalar fields; divergence and curl.
Antirequisite(s):
Prerequisite(s): A minimum mark of 60% in Calculus 1501A/B or Applied Mathematics 1413, or Calculus 1301A/B with a mark of at least 85%.
Corequisite(s):
Pre-or Corequisite(s):
Extra Information: 3 lecture hours, 0.5 course.