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, predator-prey dynamics, age-structured populations.

the former Applied Mathematics 1412A/B, the former Applied Mathematics 1413.

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.

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.

the former Applied Mathematics 1412A/B, the former Applied Mathematics 1413. If

was completed after September 1, 2016 it is an antirequisite, but not if it was completed before that time.

Elementary techniques of integration; applications of Calculus such as area, volume, and differential equations; functions of several variables, Lagrange multipliers. This course is intended primarily for students in the Social Sciences, but may meet minimum requirements for some Science modules. It may not be used as a prerequisite for any Calculus course numbered 1300 or above.

Introduction to complex numbers, limits, continuity, differentiation of functions of one variable with applications, extreme values, l’Hospital’s rule, antiderivatives, definite integrals, the Fundamental Theorem of Calculus, the method of substitution.

Ontario Secondary School MCV4U or equivalent, or

or the former Applied Mathematics 1412A/B.

APPLMATH 1201A/B

CALCULUS AND PROBABILITY WITH BIOLOGICAL APPLICATIONS

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