Lectures Notes: Topics in Vector Calculus
MA 510, Vector Calculus, Spring 2025.
Midterm 1: Thursday February 20, 2025. Time: 8:00-9:30 p.m. Location: LWSN B155
Midterm 2: Thursday April 10, 2025. Time: 8:00-9:30 p.m. Location: LWSN B155
Office hours: Wednesday 1:30-2:30 p.m. or by appointment
Book: Jerrold E. Marsden and Anthony J. Tromba, Vector Calculus, Sixth Edition, W.H. Freeman and Company, New York.
Section 1.3: Matrices, Determinants, and Cross Product
Section 1.4: Cylindrical and Spherical Coordinates
Section 2.1: Real-Valued Functions
Section 2.2: Limits and Continuity
Section 2.3: Differentiation, continuation
Section 2.5: Properties of Derivatives
Section 2.6: Gradients and Directional Derivatives
Section 3.1: Iterated Partial Derivatives
Section 3.3: Extrema of Real-Valued Functions
Section 3.4: Constrained Extrema and Lagrange Multipliers
Section 4.1: Acceleration and Newton's Second Law
Section 4.4: Divergence and Curl
Sections 5.1 and 5.2: Double Integral over a Rectangle
Sections 5.3 and 5.4: Doble Integral Over More General Regions, Changing the Order of Integration
Section 6.2: The Change of Variables Theorem
Sections 6.2: The Change of Variable Theorem, continuacion
Sections 7.1 and 7.2: Path Integral, Line integral
Section 7.2: Line integral, continuation
Section 7.3: Parametrized Surfaces
Section 7.4: Area of a Surface
Section 7.5: Integrals of Scalar Functions over Surfaces
Section 7.6: Surface Integrals of Vector Fields
Section 8.3: Conservative Fields
Remarks on the Divergence Theorem
Applications of the Divergence Theorem and Stokes' Theorem
Homework
HW 1: Due on Friday January 24
1.1: 13, 17, 21, 25
1.2: 11, 13, 15, 17, 21
1.3: 6, 7, 16a, 17, 29, 30, 35
1.4: 1, 8
1.5: 3, 7
HW 2: Due on Friday January 31
2.1: 3, 6, 8, 9, 13, 21, 25, 33, 42
2.2: 1, 2, 6, 9(a), 25, 33.
2.3: 2, 5, 9, 12, 13
HW 3: Due on Friday February 7
2.3: 16, 17, 22, 25, 27
2.4: 1, 3, 5, 7, 13, 16, 17, 19, 23
2.5: 2(f), 3(b), 8, 10, 13, 15, 17, 19, 20, 22, 26
HW 4: Due on Friday February 14
2.6: 3, 4, 5, 7, 8(a), 15, 22(a), 31
3.1: 4, 11, 12, 22, 25, 31, 32
3.2: 2, 3, 8
HW 5: Due on Monday February 24
3.3: 13, 23, 31, 41
3.4: 2, 3, 13
HW 6: Due on Saturday March 1
4.1: 1, 4, 6, 9, 10
4.2: 3, 9, 13, 17
4.3: 9, 10, 18, 22
4.4: 1, 4, 14, 15, 22, 25, 27, 28
HW 7: Due on Friday March 7
5.1: 1(b), 14
5.2: 1(a), 1(b), 4
HW 8: Due on Sunday March 23
5.3: 1, 2, 4(a)(c)(e), 6, 15
5.4: 1, 2, 3
5.5: 1, 6, 8, 9, 13, 17, 18, 24
6.1: 3, 5, 6, 7
6.2: 3, 4, 7, 25, 26, 30, 33
HW 9: Due on Friday March 28
7.1: 10, 18(a), 20
7.2: 1, 3, 5, 11, 18, 19
HW 10: Due Friday Monday April 7
7.3: 3, 7, 9, 14, 15, 18, 22(a)
7.4: 1, 5, 7, 13
7.5: 3, 5, 7, 16
7.6: 5, 7, 8, 13
HW 11: Due Friday April 18
8.2: 3, 13, 14, 23
8.1: 1, 2, 3, 10
HW 12: Due Friday April 25
8.3: 1, 3, 5, 7, 13
8.4: 1, 2, 3, 5, 7, 9, 16