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Math 3, Winter 2013, Schedule (subject to change)

Introduction to Calculus

Dartmouth College, Department of Mathematics

 Lecture Date Sections Topic 1 1/7 1.1 Modeling discrete data: introduction; Method of least squares 2 1/9 1.2-1.4 Lines in the Plane; Functions and their graphs; New functions from old 3 1/11 1.5 Trigonometric functions 4 1/14 1.6 Exponential and logarithmic functions 5 1/16 2.1 Modeling rates of change: introduction 6 1/18 2.2-2.4 The legacy of Galileo, Newton, and Leibniz; Limits of functions; Limits at infinity 7 1/21 (class moved to x-hour) 2.5-2.6 Continuity; Tangent lines and their slopes 8 1/23 2.6-2.7 Tangent lines and their slopes cont.; The derivative 9 1/25 2.8 Differentiation rules 10 1/28 2.9 Derivatives of trigonometric functions 11 1/30 2.10-2.11 The mean value theorem; Intervals of increase/decrease; Implicit differentiation 12 2/1 2.12 Derivatives of exponentials and logarithms 13 2/4 2.13-2.14 Newton’s method; Linear approximations 14 2/6 2.15-2.16 Antiderivatives and initial value problems; Velocity and acceleration 15 2/8 (class moved to x-hour) 2.17 Related rates 16 2/11 3.1 Modeling with differential equations: introduction; Seperable differential equations: first look 17 2/13 3.2-3.3 Exponential growth and decay; Separable differential equations 18 2/15 3.4 Slope fields and Euler’s method 19 2/18 3.5 Issues in curve sketching 20 2/20 3.6 Optimization 21 2/22 4.1 Modeling accumulations: introduction 22 2/25 4.2-4.3 The definite integral; Properties of the definite integral 23 2/27 4.4-4.5 The fundamental theorem of calculus; Techniques of integration (omit integration by parts) 24 3/1 4.6 Trapezoid rule and Simpson’s rule 25 3/4 4.7 Areas between curves 26 3/6 4.9 Arc length 27 3/8 4.10 Inverse trigonometric functions