BMET 23A00 - Calculus III

Course Description

The goal of the Calculus III course is to prepare students for upper-level quantitative courses in social sciences, especially for econometrics. Basically, it is an advanced course of calculus, with elements of linear algebra.

Enseignants

Riccardo SOMMARIVA,Paolo ZEPPINI

Type

Atelier

Language of tuition

English

Pre-requisite

Basic elements of mathematical calculus, especially use of functions and differentiation.

Semester

Autumn 2024-2025

Course validation

The assessment is ๠๠controle continue", with two sit-in examinations in class 50% weight the first, 40% weight the second, and with participation evaluated at the blackboard during the lecture (10%).

Pedagogical format

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.