Calculus 3, part 1 of 2

A total of 47.5 hours of lectures

This is an academic level course for university and college engineering. Due to its size, it is divided into two parts. This page describes the first of those two parts.

Level - Intermediate

You need to be familiar with Calculus 1 and Calculus 2 and some Linear Algebra before you can make full use of this course.


Make sure that you check with your professor what parts of the course you will need for your exam. Such things vary from country to country, from university to university, and they can even vary from year to year at the same university.

Calculus 3, part 1 of 2


Get the outline

A detailed list of all the lectures in part 1 of the course, including which theorems will be discussed and which problems will be solved. If you are looking for a particular kind of problem or a particular concept, this is where you should look first.

Get Calculus 3 part 1 on Udemy

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Course Objectives & Outcomes for part 1

Describe position, velocity, speed and acceleration; compute arc length of parametric curves; arc length parametrization.
Several variants of the Chain Rule, involving different kinds functions. You will also learn how to apply these variants of the Chain Rule for problem solving.
Optimization of functions of several variables, both on open domains and on compact domains (Lagrange multipliers on the boundary, etc.).
How to solve problems in multivariable calculus (illustrated with more than 200 solved problems) and why these methods work.
Parameterize some curves (straight lines, circles, ellipses, graphs of functions of one variable, intersections of two surfaces).
Limits, continuity and differentiability for functions of several variables. Theory, geometric intuitions, and lots of problem solving.
Several variants of the Implicit Function Theorem, with various geometrical interpretations; problem solving.