Week Topics covered
1

 Differentiable Mappings
 Definition of the Derivative
 Matrix Representation
 Continuity of Differentiable Mappings; Differentiable Paths
2

 Conditions for Differentiability

 The Chain Rule
3

 Product Rule and Gradients
 The Mean Value Theorem

Constrained Extrema and Lagrange Multipliers
4

 Taylor’s Theorem and Higher Derivatives
 Maxima and Minima

5

The Inverse and Implicit Function Theorems and Related Topics
Inverse Function Theorem
6

 Implicit Function Theorem
7

Integration,  Integrable Functions
Volume and Sets of Measure ZeroProperties of the Integral
8

Improper Integrals

Some Convergence Theorems
9

 Double Integrals,

Fubini’s Theorem and the Change of Variables Formula
10

Change of Variables Theorem
Polar Coordinates
11

Triple Integrals, Spherical and Cylindrical Coordinates
 Interchange of Limiting Operations
12

Line Integrals,

Path Independence
13

Green, Gauss and Stoke's Theorems
14

Orthogonal Families of Functions and Fourier Series
Parseval's Identity, Review