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 spring semester (12 lectures of 2 hours each).
Dominique TREFOLONI
Atelier
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. Antiderivatives. Areas and Distances. The Definite Integral. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. The Substitution Rule. Areas between Curves.
Autumn 2022-2023
Students must obtain a final grade of at least 10/20 to pass (2/3 continuous assessment, 1/3 final exam).
The continuous assessment grade consists in three tests (weighted 30% each) and in-class participation (10%).
The final exam will cover the entire program.
The course textbook is: James Stewart, (2011). Calculus (Early Transcendentals), International Metric Edition, 7th Edition.
The course covers chapters 12, 13 and 14 of the textbook, and their three main sections:
Vectors and the Geometry of Space (Chapter 12)
Three-Dimensional Coordinate Systems. Vectors. The Dot Product. The Cross Product. Equations of Lines and Planes. Quadric Surfaces. Optional topic: Cylindrical and Spherical Coordinates.
Vector Functions (Chapter 13)
Vector Functions and Space Curves. Derivatives and Integrals of Vector Functions. Motion in Space: Velocity and Acceleration. Optional topic: Arc Length and Curvature.
Partial Derivatives (Chapter 14)
Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes and Differentials. The Chain Rule. Directional Derivatives and the Gradient Vector. Maximum and Minimum Values. Lagrange Multipliers.
Students and instructors may find useful information on the author's website.
Partial Derivatives (Chapter 7)
Integration by Parts. Trigonometric Integrals. Trigonometric Substitutions. Partial Fractions. Numerical Integration. Improper Integrals. Introduction to Differential Equations.
This section on integration will be based both on the textbook and on Khan Academy videos available online. The links for the corresponding videos are available below:
Integration by parts
u-substitution
Trigonometric substitution
Partial Fractions
Improper integrals
Introduction to differential equations
This section will be taught by flipping the classroom: students will first prepare the course content by studying the textbook and the above videos (other videos may be provided during the semester) on their own.
James Stewart, (2011). Calculus (Early Transcendentals), International Metric Edition, 7th Edition.