DSCI 27A01 - Calculus III

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 and Calculus II courses, including functions, limits and derivatives, differentiation rules and equations, integrals, and their applications. 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 when suitable. The course is also open to students who completed a Baccalauréat L spé maths, ES and S.

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 helpful. 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.

It will also cover the following topics: Techniques of Integration (Chapter 7). Integration by Parts. Trigonometric Integrals. Trigonometric Substitutions. Partial Fractions. Numerical Integration. Improper Integrals. Introduction to Differential Equations (Chapter 9).

The exact topics covered will be chosen by the instructor and may vary somewhat from section to section.

The topics covered in chapters 1 to 8 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.

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.