Instructors: Brian Mintz, Alice Schwarze, Jack Petok.

Course on canvas.dartmouth.edu.

## Syllabus

 Lectures Sections in Text Brief Description NO LECTURES WEEK 1 WEEK 2 1/9-1/13 1 1.1, 1.2 Introduction; review of functions 2 1.2, 1.3, 1.4, 1.5 More review of functions: inverse functions, trig functions, exponential and logarithmic functions 3 2.1-2.2 A preview of calculus; the limit of a function 4 2.2-2.3 More on limits basic limit laws Week 3 1/17-1/20 5 2.4 Continuity 6 2.5 The precise definition of a limit 7 3.1 The derivative of a function Week 4 1/23-1/27 8 3.2 The derivative as a function 9 3.3 Differentiation rules 10 3.4-3.5 Derivatives as rates of change 11 3.6-3.7 The chain rule; derivative of an inverse Week 5 1/30-2/3 EXAM 1: 1/30 12 3.8 Implicit differentiation 13 3.9 Derivatives of exponential and logarithmic functions 14 4.1 Related rates Week 6 2/6-2/10 15 4.2 Linear approximations and differentials 16 4.3 Maxima and minima 17 4.4 The mean value theorem Week 7 2/13-2/17 18 4.5 Derivatives and the shape of a graph (including the second derivative test) 19 4.6 Limits at infinity and asymptotes; sketching a graph using calculus 20 4.7 More optimization problems Week 8 2/20-2/24 Exam 2: 2/20 21 4.8, 4.10 L'hÃ´pital's rule; antiderivatives 22 5.1-5.2 Approximating area under a curve: Riemann sums; the definite integral 23 5.2 More on the definite integral Week 9 2/27-3/3 24 5.3-5.4 The fundamental theorem of calculus 25 5.4 Net change theorem; integrating even and odd functions 26 5.5 (+5.6, 5.7) Substitution Week 10 27 V2 3.1 Integration by parts