Math 210: Calculus III
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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
Course Materials
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.
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 |