M.I.T. 18.02 Notes, Exercises and Solutions

Part I
D. Determinants
M. Matrices and Linear Algebra
K. Kepler's Second Law
TA. The Tangent Plane Approximation
LS. The Method of Least Squares
SD. The Second Derivative Test
N. Non-independent Variables
P. Partial Differential Equations
I. Limits in Iterated Integrals
CV. Changing Variables in Multiple Integrals
G. Gravitational Attraction

Part II:   V. Vector Calculus (Sections V1-V15)
V1. Plane Vector Fields
V2. Gradient Fields and Exact Differentials
V3. Two Dimensional Flux
V4. Green's Theorem in Normal Form
V5. Simply Connected Regions
V6. Multiply-connected Regions; Topology
V7. Laplace's Equation and Harmonic Functions
V8. Vector Fields in Space
V9. Surface Integrals
V10. The Divergence Theorem
V11. Line Integrals in Space
V12. Gradient Fields in Space
V13. Stokes' Theorem
V14. Some Topological Questions
V15. Relation to Physics

Exercises and Solutions (exercises with * are not solved)
1.  Vectors and Matrices Solutions
2. Partial Differentiation Solutions
3. Double Integrals Solutions
4. Line Integrals in the Plane Solutions
5. Triple Integrals Solutions
6. Vector Calculus in Space Solutions
SP.   Supplementary Problems with Selected Solutions and Hints

Notes and Exercises by A. Mattuck, with the assistance of T.Shifrin and S. LeDuc, and including a section on non-independent variables by Bjorn Poonen.

© M.I.T. 2010-2014     Entire set of notes in one pdf file