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Advanced Calculus II
by Kiryl Tsishchanka

SYLLABUS
GRADE CALCULATOR
WolframAlpha
Advanced Calculus II Tests
Online Tests, Midterm Exams, Quizzes

Weeks Dates Sections Handouts
1
Aug 24 Section 1.1 Vectors in two- and three-dimensional space
Aug 26
Section 1.2 The inner product, length, and distance
2
Aug 29
Section 1.3 Matrices, determinants, and the cross product
Aug 31
Section 1.4
Cylindrical and spherical coordinates
Sep 2
Section 1.5 n-dimensional Euclidean space
3
Sep 7 Section 2.1
The geometry of real-valued functions
Sep 9 Section 2.2
Limits and continuity + Examples

4

Sep 12 Section 2.3
Differentiation
Sep 14 Section 2.4
Introduction to paths
Sep 16 Section 2.5
Properties of the derivative
5
Sep 19 Section 2.6
Gradients and directional derivatives
Sep 21 Section 3.1
Iterated partial derivatives
Sep 23 Sections 1.1-1.5, 2.1-2.6
MIDTERM 1
6
Sep 26 Section 3.2
Taylor's theorem + Introduction
Sep 28 Section 3.3
Extrema of real-valued functions
Sep 30

7

Oct 3 Section 3.4
Constrained extrema and Lagrange multipliers
Oct 5 Section 3.5
The implicit function theorem
Oct 7 Section 4.1
Acceleration and Newton's Second Law

8

Oct 10 Section 4.2
Arc length
Oct 12 Section 4.3
Vector fields
Oct 14 Section 4.4
Divergence and curl 1, 2

9

Oct 17 Section 5.1
Introduction
Oct 19 Section 5.2
The double integral over a rectangle
Oct 21 Section 5.3
The double integral over more general regions

10

Oct 24 Section 5.4
Changing the order of integration
Oct 26 Section 5.5
The triple integral
Oct 28 Section 6.1
The geometry of maps
11
Oct 31 Section 6.2
The change of variables theorem
Nov 2 Section 6.3
Applications of double, triple integrals
Nov 4 Sections 3.1-3.5, 4.1-4.4, 5.1-5.5
MIDTERM 2
12
Nov 7, 9, 11
Section 7.1
The path integral 1, 2
Section 7.2
Line integrals

13

Nov 14 Section 7.3
Parametrized surfaces
Nov 16 Section 7.4
Area of a surface
Nov 18 Section 7.5
Integrals of scalar functions over surfaces
14
Nov 21 Section 7.6
Surface integrals of vector functions
Nov 23-26 Thanksgiving holidays

15

Nov 28 Section 8.1
Green's theorem 1, 2
Nov 30 Section 8.2
Stokes’ theorem 1, 2
Dec 2 Section 8.3
Conservative fields
16
Dec 5 Section 8.4
Gauss’ theorem 1, 2
17
Dec 13 (Tue) 9:00-12:00
Cumulative FINAL EXAM