## Class lecture notes

Lecture Notes for sections 9.1-9.5

Lecture Notes for section 9.6

Lecture Notes for sections 9.7

Lecture Notes for sections 10.1

Lecture Notes for section 10.2

Lecture Notes for section 10.4

Lecture Notes for section 11.1

Lecture Notes for sections 11.2 and 11.3

Lecture Notes for section 11.4

Lecture Notes for sections 11.5 and 11.6

Lecture Notes for sections 11.6 and 11.7

Lecture Notes for section 11.7

Lecture Notes for section 11.8

Lecture Notes for section 12.1

Lecture Notes for of section 12.2

Lecture Notes for of section 12.3

Lecture Notes for of section 12.4

Lecture Notes for of section 12.5

Lecture Notes for of section 12.7

Lecture Notes for of section 12.8

Lecture Notes for of section 13.1

Lecture Notes for of section 13.2

Lecture Notes for of section 13.3

Lecture Notes for of section 13.4

Lecture Notes for of section 13.5

Lecture Notes for of section 13.6

Lecture Notes for of section 13.7

Lecture Notes for Final Exam Review 1

Lecture Notes for Final Exam Review 2

## by Eugenio Aulisa

Vectors in 2D and 3D, Cylindrical Surfaces and Sphere, 9.1-9.2

Dot Product and Cross Products, 9.3-9.4

Parametric Equations, the Eq. of the Line in 3D, the Eq. of the Plane, 9.5-9.6

Vector Value Functions, Limit, Continuity and Derivative, 10.1-10.2

Integral of a Vector Function, T, N, s , k, 10.2 and 10.4

Functions of Several Variables, 11.1

Limit, Continuity and Partial Derivatives, 11.2-11.3

Tangent Plane, Incremental Approximation, Differentiabiliy, Chain Rule, 11.4-11.5

Directional Derivative, Gradient, and Relative Extrema, 11.6-11.7

Absolute Extrema, 11.7

Lagrange Multipliers and Double Integrals on R, 11.8-12.1

Double Integrals on Non-Rectangular Region and Polar Coordinates, 12.2-12.3

Double Integrals in Polar Coordinates, 12.3

Surface Area and Triple Integrals in Rectangular Coordinates, 12.4-12.5

Triple Integrals in Rectangular and Cylindrical Coordinates, 12.5 and 12.7

Triple Integrals in Cylindrical and Spherical Coordinates, 12.7

Jiacobian and Vector Fields, 12.7-13.1

Line Integrals, 13.2

Conservative Vector Fields, 13.3

Green's Theorem, 13.4

Surface Integrals and Stokes' Theorem, 13.5 and 13.6

Stokes' and Divergence Theorems, 13.6 and 13.7

## by Eugenio Aulisa

Vectors in 2D and 3D reference system, Sec 9.1-9.2

Vectors in 3D, dot product and cross product, Sec 9.2-9.4

The equation of the line in 3D and parametric equations, Sec 9.5

The equation of the plane and quadric surfaces, Sec 9.6-9.7

Quadric surfaces and vector value functions, Sec 9.7-10.1

Vector value functions, limit, continuity, derivative, and integration, Sec 10.1-10.2

Unit tangent vector, principal unit normal vector, arch length, curvature, Sec 10.4

Function of several variables, limit and continuity, Sec 11.1 and 11.2

Partial Derivatives, Sec 11.3

Tangent plane, incremental approximation, total differential and differentiability, Sec 11.4

Multivariable Chain Rule, Sec 11.5 (missing lecture! To be added)

Directional derivative, gradient and relative extrema, Sec 11.6-11.7

Absolute extrema, theorem of Lagrange multiplier, Sec 11.7-11.8

Double integral on rectangular region, Sec 12.1

Double integral on non-rectangular region and in polar coordinates, Sec 12.2-12.3

Double integral in polar coordinates and surface area, Sec 12.3 - 12.4

Surface area and triple integrals, Sec 12.4-12.5

Triple integrals in cylindrical coordinates, Sec 12.7

Integration in spherical coordinates and Jacobian, Sec 12.7 - 12.8

Vector fields, Sec 13.1

Line integrals, Sec 13.2

Conservative vector fields and Green's theorem, Sec 13.3-13.4

Surface and flux integrals, Sec 13.5

Stokes's and divergence theorem, Secs 13.6-13.7

## by Magdalena Toda

TTU Math2450 Calculus3 Sec 9.5-9 6

TTU Math2450 Calculus3 Sec 9.7

TTU Math2450 Calculus3 Sec 10.1

TTU Math2450 Calculus3 Sec 10.2 and 10.4 part 1

TTU Math2450 Calculus3 Sec 10.2 and 10.4 part 2

TTU Math2450 Calculus3 Sec 10.2 and 10.4 part 3

TTU Math2450 Calculus3 Sec 11.1 and 11.2

TTU Math2450 Calculus3 Sec 11.2 and 11.3

TTU Math2450 Calculus3 Sec 11.4 part 1

TTU Math2450 Calculus3 Sec 11.4 and 11.5

TTU Math2450 Calculus3 Sec 11.5 and 11.6

TTU Math2450 Calculus3 Sec 11.6 and 11.7

TTU Math2450 Calculus3 Sec 11.7 and 11.8

TTU Math2450 Calculus3 Sec 12.1 and 12.2

TTU Math2450 Calculus3 Sec 12.3 (large board)

TTU Math2450 Calculus3 Sec 12.3 (Substitute)

TTU Math2450 Calculus3 Sec 12.4

TTU Math2450 Calculus3 Sec 12.5

TTU Math2450 Calculus3 Sec 12.6 - 12.7

TTU Math2450 Calculus3 Sec 12.7 - 12.8

TTU Math2450 Calculus3 chap. 10-11-12 review

TTU Math2450 Calculus3 Sec 13.1 - 13.2

TTU Math2450 Calculus3 Sec 13.2 - 13.3

TTU Math2450 Calculus3 Secs 13.3

TTU Math2450 Calculus3 Secs 13.4 -13.5

TTU Math2450 Calculus3 Secs 13.6 - 13.7