MAT 1321 Foundations of Calculus I
3 units
Mathematics
Faculty of Science
Instantaneous rate of change and definition of limits; continuity, statement of intermediate value theorem. Derivatives of polynomials using limits, derivatives of sums, products, the chain rule, derivatives of rational, trigonometric, exponential, and radical functions. Derivatives of quotients, logarithms, inverse trigonometric functions. Finite difference approximations of derivatives. Analysis of functions via the first and the second derivatives. Applications to finding maxima and minima. Concavity and points of inflection, and graph sketching; statements of extreme and mean value theorems. L'Hospital's rule. Implicit differentiation, related rates, optimization, linear approximation, Newton’s method. The definite integral and the fundamental theorem of calculus. Antiderivatives of elementary functions, techniques of integration (integration by parts, substitutions, partial fractions). Numerical integration: mid-point, trapezoidal rule and Simpson's rule; error analysis.
Components:
Discussion Group
Lecture
Requirements:
Previously Offered Terms:
Fall
Winter
French Equivalent: