Columbia Home
Calculus I Sample Syllabus

Please note that is just a sample syllabus, actual syllabi for the various sections of the course will likely be different each semester. Different instructors may choose somewhat different material. The number of class sessions varies between fall and spring semesters, Monday-Wednesday and Tuesday-Thursday classes.

All section numbers refer to James Stewart, Calculus: Early Transcendentals, 9th Edition.

 Class Material Sections 1 Functions. New functions from old. §1.1, 1.2, 1.3 2 Trigonometric functions. 3 Exponential function, inverse functions, logarithms. §1.4, 1.5 4 Derivative: motivation. Informal definition of limit. §2.1, 2.2 5 Limit laws. Squeeze theorem. §2.3 6 Continuity, asymptotes. §2.5, 2.6 7 Definition of derivative. Derivative as a function. §2.7, 2.8 8 Review. 9 Midterm 1. 10 Derivative of polynomials. Product and quotient rules. §3.1, 3.2 11 Derivatives of trig functions. §3.3 12 Chain rule, implicit differentiation. §3.4, 3.5 13 Derivative of the logarithm. Applications. §3.6, 3.7, 3.8 14 Related rates, linear approximation. §3.9, 3.10 15 Maximization. Mean value theorem. §4.1, 4.2 16 Second derivative, convexity, second derivative test. L’Hospital’s rule. §4.3, 4.4 17 L’Hospital’s rule, more graph sketching. §4.4, 4.5 18 Optimization problems. §4.7 19 Newton’s method. §4.8 20 Antiderivatives. §4.9 21 Review. 22 Midterm 2. 23 Definite integral: definition. §5.1 24 The “area so far” function. §5.2 25 The fundamental theorem of calculus. Evaluating definite integrals via the “net change theorem” §5.3, 5.4 26 Substitution rule. §5.5 27 Areas between curves, average values. §6.1, 6.5 28 Review.