# Calculus 3

### Videos

Introduction to Calculus 3. Syllabus

**Three Dimensional Coordinate System. Intro to Surfaces**(Th Jan 20, 2022)

Octants and points (Th Jan 20, 2022)

Planes (Th Jan 20, 2022)

Cylinders and spheres (Th Jan 20, 2022)

Surfaces of revolution and cylindrical surfaces (Th Jan 20, 2022)

**Vectors. The Dot and Cross Products**

Vectors (Fri Jan 21, 2022)

Dot product (Fri Jan 21, 2022)

Cross product, part 1 (Fri Jan 21 and Mon Jan 24, 2022)

Cross product, part 2 (Mon Jan 24, 2022)

**Equations of Lines and Planes**

Equations of planes, part 1 (Mon Jan 24, 2022)

Equations of planes, part 2 (Mon Jan 24, 2022)

Equations of lines, part 1 (Mon Jan 24, 2022)

Equations of lines, part 2 (Th Jan 27, 2022)

Equations of lines, part 3 (Th Jan 27, 2022)

**Space Curves. Tangent lines. Arc Length**

Curves: examples, tangent line (Th Jan 27, 2022)

Arc length of a curve (Th Jan 27, 2022)

Practice problems with curves, part 1 (Th Jan 27, 2022)

Practice problems with curves, part 2 (Th, Jan 27, 2022)

**Partial Derivatives**

Partial derivatives, part 1 (Fri, Jan 28, 2022)

Partial derivatives, part 2 (Fri, Jan 28, 2022)

**Tangent plane, implicit functions, the gradient**

Tangent Plane, implicit functions, part 1 (Mon, Jan 31, 2022)

Tangent plane, implicit functions, part 2 (Mon, Jan 31, 2022)

Implicit functions, the gradient (Mon, Jan 31, 2022)

Instructions for Assignment 1 (Th Feb 3, 2022)

**Linear Approximation, Chain Rule**

Linear approximation, Chain rule (Th Feb 3 and Fri Feb 4, 2022)

Review for Exam 1 (Mon Feb 7, 2022)

**Optimization**

Minimum and maximum of functions of two variables (Fri Feb 11, 2022)

Lagrange multipliers, part 1 (Mon Feb 14, 2022)

Lagrange multipliers, part 2 (Th Feb 17, 2022)

**Double integrals**

Double integrals over rectangles, double integrals over general regions (Th Feb 17 and Fri Feb 18, 2022)

Double integrals in polar coordinates (Mon Feb 21, 2022)

Applications, part 1 (surface area) (Th Feb 24, 2022)

Applications, part 2 (average value, mass), assignment 2 questions (Fri Feb 25, 2022)

Review for Exam 2 (Mon Feb 28, 2022)

**Parametric Surfaces**

Parametric surfaces, part 1 (Fri, Mar 4, 2022)

Parametric surfaces, part 2 (Fri Mar 4, 2022)

**Triple integrals**

Introduction to triple integrals (Mon Mar 14, 2022)

Three triple integral practice problems (Mon Mar 14, 2022)

Triple integral applications (Mon Mar 14, 2022)

Average value and center of mass examples (Th Mar 17, 2022)

Tetrahederon problem (Th Mar 17, 2022)

**Substitution in triple integrals. Cylindrical and spherical coordinates**

General substitution. Cylindrical coordinates (Th Mar 17, 2022)

Spherical coordinates (Th Mar 17, 2022)

Two spherical coordinates practice problems (Th Mar 17, 2022)

Ellipsoid (Fri Mar 18, 2022)

Earth coordinates and bumpy sphere

Bounds in spherical coordinates (Fri Mar 18, 2022)

**Line Integrals**

Introduction to line integrals with respect to arc length (Mon Mar 21, 2022)

Line integrals w/r to arc length, examples (Mon Mar 21, 2022)

Introduction to line integrals with respect to coordinates (Th Mar 24, 2022)

Line integrals with respect to coordinates, example 1 (Th Mar 24, 2022)

Line integrals with respect to coordinates, example 2 (Th Mar 24 2022)

Line integrals with respect to coordinates, example 3 (Th Mar 24, 2022)

Instructions for Matlab Project 1 for Spring 2020 class

**Fundamental Theorem**

Conservative field, potential, Fundamental Theorem (Fri Mar 25, 2022)

Fundamental Theorem, example 1

Fundamental Theorem, example 2 (Fri Mar 25, 2022)

Fundamental Theorem, example 3 (Mon Mar 28, 2022)

**Green's Theorem, Divergence and Curl**

Green's Theorem (Mon Mar 28, 2022)

Green's Theorem, two examples (Th Mar 31, 2022)

Divergence (Th Mar 31, 2022)

Curl (Th Mar 31, 2022)

**Sequences**

Sequences, introduction and examples (Fri Apr 1, 2022)

Recursive sequences (Fri Apr 1, 2022)

Fibonacci sequence, golden ratio and power sequence (Fri Apr 1, 2022)

**Series. Divergence Test. Geometric series**

Series introduction, Divergence Test (Fri Apr 8, 2022)

Geometric Series introduction and examples part 1 (Fri Apr 8, 2022)

Geometric Series, examples part 2 (Fri April 8, 2022)

Geometric Series, examples part 3 (Fri April 8, 2022)

Geometric Series, examples part 4 (Mon April 11, 2022)

Fun topics with Geometric Series. 0=1 and Koch snowflake

Pharmacy application of Geometric Series (Mon April 11, 2022)

**Other convergence tests**

Integral Test (Mon April 11, 2022)

Alternating Series Test (Th April 14, 2022)

Ratio Test (Th April 14, 2022)

Root Test (Fri April 15, 2022)

**Power series**

Power series introduction and first two examples (Fri April 15, 2022)

Power series, second two examples (Fri April 15, 2022)

Power series, one more example (Mon April 18, 2022)

Power series, the last example (practice prob. 8) (Mon April 18, 2022)

**Taylor series and polynomials**

Taylor series introduction (Mon April 18, 2022)

Taylor series examples (Th April 21, 2022)

Derivatives and integrals of Taylor series (Th April 21, 2022)

Taylor polynomials (Fri April 22, 2022)

Taylor polynomials - why we use them and some applications (Fri April 22, 2022)

Instructions for Matlab Project 2 for Spring 2020 class

Calc 3 Spring 2020 video

Final exams message

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