Math 210: Calculus III

Course Prerequisites

Grade of C or better in Math 181

Course Description

Math 210 is the third and the final part of our standard three-semester calculus sequence. The distinct feature of this part of the course is its focus on the multi-dimensional analysis, as opposed to one-dimensional analysis that students learned in Math 180 (Calculus I) and Math 181 (Calculus II).

Math 210 focuses on important concepts such as that of a vector, a vector field, a function of several variables, partial derivative, a line-integral and multi-variable integrals. The ideas of the vector calculus apply to numerous areas of human knowledge such as engineering, physics, pure mathematics, biology, and many others.

Credit Awarded

3 hours

Textbook

Calculus, Early Transcendentals, by W. Briggs and L. Cochran, 3rd edition, and a MyLabMath access code.

The course will go through Chapters 13-17.

A MyLabMath code can be purchased online, or at the UIC bookstore, with or without the textbook. MyLabMath contains an electronic version of the book.
Unexpired MyLabMath codes can be re-used for for Math 210. To buy the MyLabMath code for the first time, there are two options: an access which is valid for one semester, ISBN 9780135329221, or an access code which is valid for multiple semesters, ISBN 9780135329276.

One should note that only these ISBNs will work with your MyLabMath course. Books with MyMathLab access obtained from Amazon or other sources most likely won’t work.

Sample Exams

Course Schedule

The following is a typical 15-week Fall or Spring semester schedule for MATH 210. During the Summer sessions, the schedule is condensed into 8 weeks.

A topic marked by * may be covered briefly for one or more of the following reasons: it is similar to another one covered previously; it is of less importance for future development of the course material; it is relatively simple and may be given as a reading assignment; it is too advanced at the first reading. Please follow instructions in your class pertaining to these topics.
Sections Topics
Week 1


Sec 13.1-13.3
Discussion of course policies
Vectors on Place, Vectors in Space
Distance, Sphere
Dot Product, Work of Force
Week 2


Sec 13.4-13.5
Cross Product, Torque
Vector and Parametric Equations of a Line
Equations of Planes
Distance from a Point to a Line
Week 3


Sec 13.6, 14.1-14.3
Cylinders, Quadratic Surfaces
Vector-Valued Functions and their Calculus
Physical Concepts of Motion (Velocity, Acceleration, Speed) Using Vetor Calculus
Motion in a Gravitational Field*
Week 4


Sec 14.4, 15.1, 15.2
Arc Length in Cartesian Coordinates
Functions of 2 Variables, Graphs, Level Curves
Functions of 3 Variables, Level Surfaces
Calculus of Multivariable Functions, Limits, Two-Path Test
Week 5

Sec 15.3-15.5
Partial First and Higher Order Derivatives, Clairaut Theorem, Differentiability
Chain Rule, Implicit Differentiation
Gradient, Directional Derivative
Week 6

Sec 15.5, 15.6, Midterm 1
Gradient, Directional Derivative, Applications*
First Midterm Review
Tangent Plane
Week 7

15.6, 15.7
Linear Approximation, Differential
Local Extrema, Critical Points, 2nd Derivative Test
Absolute Optimization
Week 8



Sec 15.8, 16.1, 16.2
The Method of Lagrange Multipliers, Optimization Problems, Extreme Distances
Double Integral as a Volume, Over Rectangles
Double Integrals over More General Regions
Changing Order of Integration, Volumes of Regions Between 2 Surfaces, Area of a Plane Region Using Double Integrals
Week 9

Sec 16.3-16.5
Double Integral in Polar Coordinates
Triple Integrals, Volumens and Masses of Solids
Triple Integrals in Cylindrical Coordinates, Emphasis on Examples
Week 10

Sec 16.5, Midterm 2
Triple Integrals in Cylindrical Coordinates
Review for Midterm
Triple Integrals in Spherical Coordinates
Week 11

Sec 16.6*, 16.7, 17.1
Center of Mass Formulae*
Plane Transformations, Jacobian, Change of Variables
Vector Fields, Radial, Gradient, Potential
Week 12

Sec 17.2, 17.3
Line Integrals of Scalar Functions
Integrals of Fields, Circulation, Flux, Work of Force
Conservative Fields, Finding Potentials, Independence of Path, FTC for those Fields
Week 13

Sec 17.4
Green's Theorem in the circulation and Flux Form
Finding Areas Using GT
Week 14

17.5, 17.6
Div and Curl in 3D
Surface Integrals of Scalar Functions, Surface Area Elements in Spherical, Cylindrical, and Graph Cases
Flux of a Vector Field through a Surface, Physical Examples
Week 15


17.7, 17.8
Stoke's Theorem as a 3D Analogues to 2D Green's Theorems in Circulation Form.
The Divergence Theorem as a 3D Analogue to 2D Green's Theorems in Flux Form
Review for the Final Exam
Week 16
Finals' Week
Cumulative Final Exam