**What are you going to learn?**

**Content**

Perform differential calculus operations on functions of several variables including continuity, partial derivatives and directional derivatives. Estimate multiple integrals in different coordinate systems including Cartesian, polar, cylindrical and spherical coordinates. Perform calculus operations on vector-valued functions.

**Chapter 1. Introduction**

Parametric Equations

Calculus of Parametric Curves

Polar Coordinates

Area and Arc Length in Polar Coordinates

Conic Sections

Elements of Quality System

Vectors in 2D

Vectors in 3D

Vectors Operations

Equations of Lines and Planes in Space

Quadratic Surfaces

Cylindrical and Spherical Coordinates

**Chapter 2. 3D Vectors**

**Chapter 3. Vector Valued Function of Several Variables**

Introduction

Level Curves

Limits and Continuity

Differentiation: Partial and Directional Derivatives

Arc Length and Curvature

Motion in 3D

**Chapter 4. Derivative of Functions of Several Variables**

Functions of Several Variables

Limits and Continuity

Tangent Planes and LinearApproximations

Composition and the Chain Rule

Directional Derivatives and the Gradient

Critical Points

Lagrange Multipliers

**Chapter 5. Integration**

Introduction

Double Integrals over Rectangular Regions

Double Integrals over General Regions

Double Integrals in Polar Coordinates

Triple Integrals

Triple Integrals in cylindrical and Spherical Coordinates

Applications

Change of Variables in Multiple Integrals

**Chapter 6. Vector Calculus**

Introduction

Vector Fields

Line Integrals

Conservative Vector Fields

Green's Theorem

Divergence and Curl

Surface Integrals

Stoke's Theorem

The Divergence Theorem

### Bibliography

Edwards, Henry C., and David E. Penney.

. 6th ed. Lebanon, IN: Prentice Hall, 2002.*Multivariable Calculus*Apostol, T.M.

. 2d Ed. Wiley, 1969.*Calculus*,Vol 2

### Webgraphy

https://openstax.org/books/calculus-volume-3/pages/4-1-functions-of-several-variables.

https://www.geeksforgeeks.org/how-to-do-calculus=with-python/.

https://docs.sumpy.org/latest/tutorials/intro-tutorial/calculus.html