Michael Newman

MAT 1320 Lecture 1: Introduction, The most important function, and more functions

MAT 1320 Lecture 2: Modifying, Composition and Exponential Functions

MAT 1320 Lecture 3: Tangents, Limits and Limit Laws

MAT 1320 Lecture 4: Continuity, Intermediate Value Theorem, Limits to Infinity

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Intuitive definition of limits; continuity, statement of intermediate value theorem. Quick review of basic derivative formulas: products, chain rule, exponentials, and trigonometric functions. Derivatives of quotients, logarithms, inverse trigonometric functions. Finite difference approximations of derivatives. Analysis of functions via the first and the second derivatives; 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.

Calculus I

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