# BMET 23A00 - Calculus III

Type d'enseignement : Workshop

Semester : Autumn 2018-2019

Number of hours : 24

Language of tuition : English

## Pre-requisite

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 prerequisite 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 ES and S. 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.

## Course Description

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).

## Teachers

MAZARI, Sylvain (Professor)

## 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. Augmented version Students who are enrolled or considering enrolment in UBC's economics courses must also study the following content, as the material covered in this augmented version of the course is a prerequisite for UBC's intermediate level economics courses. Other students may also choose to follow this extra section. Students who are considering following intermediate microeconomics courses during their third year abroad are likely to find the following content useful. The augmented version of the course includes a fourth section: 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.

## Course validation

Students must obtain a final grade of at least 10/20 to pass (2/3 continuous assessment, 1/3 final exam during the last session). The continuous assessment grade consists in three tests (weighted 30% each) and in-class participation (10%). The final exam will cover the entire program: Sections 1, 2 and 3 for the students who choose the basic version of the course. Sections 1, 2, 3 and 4 for the students who choose the augmented version of the course.

## Required reading

James Stewart, (2011). Calculus (Early Transcendentals), International Metric Edition, 7th Edition.