Calculus II is a standard college-level course in Calculus. The course is designed for students working for a degree in science, mathematics, and those planning on certain types of graduate work. In particular, it prepares students for Calculus III and upper-level quantitative courses in social sciences or economics for example microeconomics and macroeconomics. It will cover anti-derivatives, techniques and applications of integration, sequences and series, Taylor polynomials, and differential equations. The course takes place 12 sessions of 2 hours each, consisting of classroom lectures and problem-solving activities.
The prerequisite for Calculus II is material traditionally covered in Calculus I course, including functions, limits and derivatives, differentiation rules, and integrals, and a good knowledge of high school algebra and trigonometry (see below for more details). Calculus II is intended for students who are interested in taking upper-level economics courses.
International students who have obtained a score of 4 or above on the Calculus BC Advanced Placement, or a score of 5 on the Calculus AB Advanced Placement exam, or a score of 6 or above on the International Baccalaureate Calculus exam or a B or above in A Level Further Mathematics may register for this course. The course is also open to students who completed a Baccalauréat L spé maths, ES and S, but who do not master the concepts covered by Calculus I.
Lecture slides will cover all the material required for the final exam and will be shared with students during the semester. Having the course textbook is not mandatory but may be very helpful. The course will cover the following main sections:
1. Integration Techniques and Applications (Chapter 6-8): Review of integration, areas between curves, average value of a function, integration by parts, trigonometric integrals, strategy for integration, arc length, applications to economics and sciences.
2. Sequences and Series (Chapter 11): Sequences, series and the integral test, alternating series, absolute convergence, ratio and root, strategy for series, power series, representations of functions as power series, Taylor series, applications of Taylor polynomials.
3. Introduction to Differential Equations (Chapter 9): Modeling with differential equations, separable equations, linear equations, solving differential equations.
The exact topics covered will be chosen by the instructor and may vary somewhat from section to section.
The exact topics covered will be chosen by the instructor and may vary somewhat from section to section.
Chung Shue CHEN
Séminaire
English
The prerequisites for Calculus II are motivation and a good knowledge of high school algebra and trigonometry. These 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. The Precise Definition of a Limit. Continuity. Limits at Infinity. 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. Anti-derivatives. Areas and Distances. The Definite Integral. The Fundamental Theorem of Calculus.
Spring 2025-2026
The final grade is calculated based on continuous assessment which includes quizzes during the semester and a final exam. The final exam will cover the entire program.
James Stewart, Calculus: Early Transcendentals, 7th edition.