Mathematics · Columbia University
Excellent introductory course to calculus.
All of the general principles of Calculus; at times did feel like we were going a little more advance but overall good experience.
In calculus 1 I learned about the fundamentals of advanced math thinking, which has broadened my view of mathematics in general. Furthermore, calculus 1 has led me to my developing of a “ thinking outside of the box” approach to solving problems, which I have yet to encounter in any high school mathematics course. Overall, calculus 1, with the assistance of our passionate teacher, professor Vincentelli, has developed me into a much better mathematician and problem solver.
I was able to refresh my understanding of calculus as well learn more about errors when evaluating functions.
partial derivatives, differential equations, the fundamental theorem of calculus, the net change theorem, limits, little O notation.
Basic Calculus: Limits, Derivatives, Integrals, and other theorems related to these operations.
If you want an excellent introduction to calculus, this is the course to take.
I'd recommend this course to students who will need take subsequently higher level math courses, as I feel this course will prepare you for those. 1 Columbia University: Arts & Sciences Fall 2024 Course: MATHUN1101_007_2024_3-CALCULUSI : MATHUN1101_007_2024_3 - CALCULUS I Instructor: Marco Antonio Sangiovanni Vincentelli
Squeeze theorem, intermediate value theorem, monotone theorem, constancy theorem, derivatives and their rules, principle of induction, strong intermediate value theorem, differential equations, implicit differentiation in curves, Little O-notation, approximations of functions by polynomials, newton's method, implicit function theorem, Taylor series, limits, net change theorem, inequalities, areas between two graphs, inequality preserving theorem, average value theorem, mean value theorem, shift substitution, scale substitution, shift and scale theorem, general substitution theorem, 2 out of 3 theroem, and integration patterns.
Derivatives and integrals, many theorems in calc one