The goal of Calculus III is to prepare students for upper-level quantitative courses in the social sciences, especially for econometrics. The course takes place during the semester (12 lectures of 2 hours each).
This course is a standard college-level course in calculus. The prerequisite for Calculus III is material traditionally covered in Calculus I courses, including functions, limits and derivatives, differentiation rules, and integrals. Calculus III is intended for students who are interested in taking upper-level economics courses. For example, this course is a prerequisite for Columbia University's Intermediate Microeconomics and Econometrics courses. The augmented version of this course (see below) is a perquisite for the University of British Columbia's intermediate economics courses. International students who have obtained a score of 5 on the Calculus BC Advanced Placement, or a score of 7 on the International Baccalaureate Calculus exam or an A in A-Level Further Mathematics may register for this course. Students who obtained a score of 4 on the Calculus BC Advanced Placement exam, or a score of 5 on the Calculus AB Advanced Placement exam, or a 6 on the IB HL Calculus exam or a B on the A-Level Further Maths exam may also register for Calculus III. The course is also open to students who completed a Baccalauréat L spé maths, ES and S.
Chung Shue CHEN
Séminaire
English
The topics covered in chapters 1 to 6 of the course textbook are a prerequisite for Calculus III. These topics include limits, derivatives and integrals. Students who register for this course need to have already studied the following concepts: Essential Functions. Exponential Functions. Inverse Functions and Logarithms. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Derivatives and Rates of Change. The Derivative as a Function. Derivatives of Polynomials and Exponential Functions. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Implicit Differentiation. Derivatives of Logarithmic Functions. Exponential Growth and Decay. Related Rates. Linear Approximations and Differentials. Maximum and Minimum Values. The Mean Value Theorem. Anti-derivatives. Areas and Distances. The Definite Integral. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. The Substitution Rule. Areas between Curves
Spring 2024-2025
Grading: 1/2 on continuous assessment and 1/2 on final exam. The continuous assessment grade consists in quizzes for each chapter. The final exam will cover the entire program.
James Stewart, Calculus: Early Transcendentals, 7th edition