# MA 222 Calculus 3

### Videos

Introduction to Calculus 3. Syllabus

Three Dimensional Coordinate System. Intro to Surfaces (Mon. Jan 25, 2021)
Octants and points (Mon. Jan 25, 2021)
Planes (Mon. Jan 25 and Th Jan 28, 2021)
Cylinders and spheres (Th, Jan 28, 2021)
Surfaces of revolution and cylindrical surfaces (Th, Jan 28, 2021)

Vectors. The Dot and Cross Products
Vectors (Th, Jan 28, 2021)
Dot product (Th, Jan 28, 2021)
Cross product, part 1 (Th, Jan 28 and Fri Jan 29, 2021)
Cross product, part 2 (Fri. Jan 29, 2021)

Equations of Lines and Planes
Equations of planes, part 1 (Fri. Jan 29, 2021)
Equations of planes, part 2 (Fri. Jan 29, 2021)
Equations of lines, part 1 (Mon. Feb 1, 2021)
Equations of lines, part 2 (Mon. Feb 1, 2021)
Equations of lines, part 3 (Mon. Feb 1, 2021)

Space Curves. Tangent lines. Arc Length
Curves: examples, tangent line (Th, Feb 4, 2021)
Arc length of a curve (Th, Feb 4, 2021)
Practice problems with curves, part 1 (Th, Feb 4, 2021)
Practice problems with curves, part 2 (Th, Feb 4, 2021)

Partial Derivatives
Partial derivatives, part 1 (Fri, Feb 5, 2021)
Partial derivatives, part 2 (Fri, Feb 5, 2021)

Instructions for Assignment 1 for Spring 2019 class

Implicit functions, Tangent plane, Linear Approximation, Chain Rule
Implicit functions, Tangent plane, Linear approximation part 1 (Mon, Feb 8, 2021) video to be added in 2022
Linear approximation, part 2, Chain rule (Th, Feb 11, 2021)
Review for Exam 1 (Mon, Feb 15, 2021)

Optimization
Minimum and maximum of functions of two variables (Fri, Feb 12, 2021)
Lagrange multipliers, part 1 (Fri, Feb 19, 2021)
Lagrange multipliers, part 2 (Mon, Feb 22, 2021)

Double integrals
Double integrals over rectangles, double integrals over general regions (Th, Feb 25, 2021)
Double integrals in polar coordinates (Fri, Feb 26, 2021)
Applications, part 1 (surface area) (Mon, Mar 1, 2021)
Applications, part 2 (average value, mass), assignment 2 questions (Th, Mar 4, 2021)
Review for Exam 2 (Mon, Mar 8, 2021)

Parametric Surfaces
Parametric surfaces, part 1 (Fri, Mar 5, 2021)
Parametric surfaces, part 2 (Fri, Mar 12, 2021)

Triple integrals
Introduction to triple integrals (Mon Mar 15, 2021)
Three triple integral practice problems (Mon Mar 15 and Th Mar 18, 2021)
Triple integral applications (Mon Mar 15 and Th Mar 18, 2021)
Average value and center of mass examples (Th Mar 18, 2021)
Tetrahederon problem (Th Mar 18, 2021)

Substitition in triple integrals. Cylindrical and spherical coordinates
General substitition. Cylindrical coordinates (Th Mar 18, 2021)
Spherical coordinates (Th Mar 18, 2021)
Two spherical coordinates practice problems (Fri Mar 19, 2021)
Ellipsoid (Fri Mar 19, 2021)
Earth coordinates and bumpy sphere
Bounds in spherical coordinates (Fri Mar 19, 2021)

Line Integrals
Introduction to line integrals with respect to arc length (Mon Mar 22, 2021)
Line integrals w/r to arc length, examples (Mon Mar 22, 2021)
Introduction to line integrals with respect to coordinates (Th Mar 25, 2021)
Line integrals with respect to coordinates, example 1 (Th Mar 25, 2021)
Line integrals with respect to coordinates, example 2 (Th Mar 25 and Fri Mar 26, 2021)
Line integrals with respect to coordinates, example 3 (Fri Mar 26, 2021)

Instructions for Matlab Project 1 for Spring 2020 class

Fundamental Theorem
Conservative field, potential, Fundamental Theorem (Fri Mar 26, 2021)
Fundamental Theorem, example 1
Fundamental Theorem, example 2 (Mon Mar 29, 2021)
Fundamental Theorem, example 3 (Mon Mar 29, 2021)

Green's Theorem, Divergence and Curl
Green's Theorem (Th April 1, 2021)
Green's Theorem, two examples (Th April 1, 2021)
Divergence (Fri Apr 2, 2021)
Curl (Fri Apr 2, 2021)

Sequences
Sequences, introduction and examples (Fri Apr 2, 2021)
Recursive sequences (Fri Apr 9, 2021)
Fibonacci sequence, golden ratio and power sequence (Fri Apr 9, 2021)

Series. Divergence Test. Geometric series
Series introduction, Divergence Test (Fri Apr 9, 2021)
Geometric Series introduction and examples part 1 (Mon Apr 12, 2021)
Geometric Series, examples part 2 (Mon April 12, 2021)
Geometric Series, examples part 3 (Mon April 12 or Th April 15, 2021)
Geometric Series, examples part 4 (Th April 15, 2021)
Fun topics with Geometric Series. 0=1 and Koch snowflake
Pharmacy application of Geometric Series (Th April 15, 2021)

Other convergence tests
Integral Test (Th April 15, 2021)
Alternating Series Test (Th April 15, 2021)
Ratio Test (Fri April 16, 2021)
Root Test (Fri April 16, 2021)

Power series
Power series introduction and first two examples (Mon April 19, 2021)
Power series, second two examples (Mon April 19, 2021)
Power series, one more example (Th April 22, 2021)
Power series, the last example (practice prob. 8) (Th April 22, 2021)

Taylor series and polynomials
Taylor series introduction (Th April 22, 2021)
Taylor series examples (Th April 22, 2021)
Derivatives and integrals of Taylor series (Fri April 23, 2021)
Taylor polynomials (Fri April 23, 2021)
Taylor polynomials - why we use them and some applications (Fri April 23, 2021)

Instructions for Matlab Project 2 for Spring 2020 class

Calc 3 Spring 2020 video

Final exams message