
Calculus
Calculus 050a/b, 051a/b, 081a/b, 250a/b, 251a/b, 280a/b, and 281a/b are offered jointly by the Departments of Applied Mathematics and Mathematics. Calculus 091a/b is offered by the Department of Applied 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), DIFFERENTIAL EQUATIONS (S), LINEAR ALGEBRA (S) and MATHEMATICS (S) 
Calculus 050a/b, Calculus I  
 Description: 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): Mathematics 030, Applied Mathematics 026.  Prerequisite(s): Grade 12U Advanced Functions and Introductory Calculus (MCB4U) or Mathematics 012a/b.  4 lecture hours, 0.5 course.  back to top 
Calculus 051a/b, Calculus II for Mathematical and Physical Sciences  
 Description: 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): Calculus 081a/b, Applied Mathematics 026.  Prerequisite(s): A minimum mark of 60% in Calculus 050a/b.  4 lecture hours, 0.5 course.  back to top 
Calculus 081a/b, Calculus II  
 Description: For students requiring the equivalent of a full course in calculus at a less rigorous level than Calculus 051a/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): Calculus 051a/b, Applied Mathematics 026.  Prerequisite(s): A minimum mark of 55% in Calculus 050a/b.  4 lecture hours, 0.5 course.  back to top 
Calculus 091a/b, Mathematical Applications for Biological Sciences  
 Description: Applications of integration, integration using mathematical software packages. Scaling and allometry. Basic probability theory. Fundamentals of linear algebra: vectors, matrices, matrix algebra. Difference and differential equations. Each topic will be illustrated by examples and applications from the biological sciences, such as population growth, predatorprey dynamics, agestructured populations.  Antirequisite(s): Mathematics 030.  Prerequisite(s): Calculus 050a/b.  3 lecture hours, 1 tutorial hour, 0.5 course.  back to top 
Calculus 250a/b, Advanced Calculus I  
 Description: 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): Calculus 280a/b, Applied Mathematics 290a.  Prerequisite(s): A minimum mark of 60% in Calculus 051a/b or Applied Mathematics 026, or Calculus 081a/b with a mark of at least 85%.  Pre or Corequisite(s): Linear Algebra 040a/b or the former Mathematics 202a.  3 lecture hours, 0.5 course.  back to top 
Calculus 251a/b, Advanced Calculus II  
 Description: Integral calculus of functions of several variables: multiple integrals; Leibnitz' rule; arc length; surface area; Green's theorem; independence of path; simply connected and multiply connected domains; three dimensional theory and applications; divergence theorem; Stokes' theorem.  Antirequisite(s): Calculus 281a/b, Applied Mathematics 291b.  Prerequisite(s): A minimum mark of 60% in Calculus 250a/b.  3 lecture hours, 0.5 course.  back to top 
Calculus 280a/b, Intermediate Calculus I  
 Description: 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): Calculus 250a/b, Applied Mathematics 290a.  Prerequisite(s): A minimum mark of 55% in Calculus 051a/b or Calculus 081a/b, or Applied Mathematics 026.  3 lecture hours, 0.5 course.  back to top 
Calculus 281a/b, Intermediate Calculus II  
 Description: 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): Calculus 251a/b, Applied Mathematics 291b.  Prerequisite(s): Calculus 250a/b or Calculus 280a/b.  3 lecture hours, 0.5 course.  back to top 

