Week  Topics  Study Materials  Materials 
1 
Vectorvalued functions and their graphs,
a gentle introduction to paths, and surfaces


J. Marsden, A. Tromba
Vector Calculus, 5th Edition.

2 
Basic topology of R^2 and R^3
Limits and continuity of several valued functions


J. Marsden, A. Tromba
Vector Calculus

3 
Differentiation: Partial Derivatives
Differentiabilty, Fundamental lemma
Properties of derivative: Sums, Products, Quotients, Chain Rule


J. Marsden, A. Tromba
Vector Calculus

4 
Directional Derivative,
Parametrization of paths, Arclength, Gradient: Tangent Planes to level surfaces, normal vectors


J. Marsden, A. Tromba
Vector Calculus

5 
Higherorder partial derivatives,
Extrema of Realvalued functions


J. Marsden, A. Tromba
Vector Calculus

6 
Vector Fields, Divergence and Curl, Curl of a vector field,
Basic identities of vector analysis
Geometrical interpretation of divergence


J. Marsden, A. Tromba
Vector Calculus

7 
Multiple integrals: Double integral
over a rectangle, Fubini's Theorem,
Properties of Integration:Linearity, Homogeneity, Monotonicity, Additivity


J. Marsden, A. Tromba
Vector Calculus.

8 
Double Integral over general regions, Changing the order of integration


J. Marsden, A. Tromba
Vector Calculus.

9 
Triple Integral,
The change of variables in integration,
applications of integration


J. Marsden, A. Tromba
Vector Calculus.

10 
Line Integrals


J. Marsden, A. Tromba
Vector Calculus.

11 
Green's Theorem


J. Marsden, A. Tromba
Vector Calculus.

12 
Parametrized surfaces, orientation, area of a surface,
Surface Integrals of realvalued functions


J. Marsden, A. Tromba
Vector Calculus.

13 
Surface integrals of vector valued functions, Divergence and Stokes Theorems


J. Marsden, A. Tromba
Vector Calculus.

14 
Divergence Theorem, Stokes Theorem continue, Conservative vector fields


J. Marsden, A. Tromba
Vector Calculus.
