18.02 - Calculus II - Notes, Exercises, & Solutions

Table of Contents


Part I


D. Determinants (4 pages)

M. Matrices and Linear Algebra (10 pages)

K. Kepler's Second Law (2 pages)

TA. The Tangent Plane Approximation (6 pages)

LS. The Method of Least Squares (3 pages)

SD. The Second Derivative Test (4 pages)

N. Non-independent Variables (8 pages)

P. Partial Differential Equations (3 pages)

I. Limits in Iterated Integrals (4 pages)

CV. Changing Variables in Multiple Integrals (7 pages)

G. Gravitational Attraction (2 pages)


Part II

V. Vector Calculus (Sections V1-V15)


V1. Plane Vector Fields (5 pages)

V2. Gradient Fields and Exact Differentials (5 pages)

V3. Two-dimensional Flux (3 pages)

V4. Green's Theorm in Normal Form (4 pages)

V5. Simply Connected Regions (5 pages)

V6. Multiply-connected Regions; Topology (4 pages)

V7. Laplace's Equation and Harmonic Functions (7 pages)

V8. Vector Fields in Space (2 pages)

V9. Surface Integrals (6 pages)

V10. The Divergence Theorem (4 pages)

V11. Line Integrals in Space (4 pages)

V12. Gradient Fields in Space (4 pages)

V13. Stokes' Theorem (6 pages)

V14. Some Topological Questions (4 pages)

V15. Relation to Physics (6 pages)


Part III

E. 18.02 Exercises


Exercises for Vectors and Matrices (sections 1A to 1K, 12 pages) - Solutions (13 pages)

Exercises for Partial Differentiation (sections 2A to 2K, 9 pages) - Solutions (16 pages)

Exercises for Double Integrals (sections 3A to 3D, 4 pages) - Solutions (7 pages)

Exercises for Line Integrals in the Plane (sections 4A to 4I, 7 pages) - Solutions (7 pages)

Exercises for Triple Integrals (sections 5A to 5C, 3 pages) - Solutions (5 pages)

Exercises for Vector Integral Calculus in Space (6A to 6H, 8 pages) - Solutions (9 pages)

(exercises with * are not solved)

Notes and Exercises originally authored by Arthur Mattuck (with assistance of T. Shifrin, S. Leduc)
© M.I.T. 2010