1

Sequences Series and Power Series:

·                    Sequences and convergence

·                     Infinite series

·                    Telescoping ,Geometric and Harmonic series

Pages 519--535

2

Convergence tests for positive series:

·        n-th  term test,

·        integral test,

·        comparison test,

·        limit comparison test

·         root test ratio test

Pages 535--542

3

·                    Absolute and conditional convergence

·                    Alternating series test

·                    Power series

Algebraic Operations on Power Series – Differentiation and Integration of Power Series

Pages 546--564

4

·                    Taylor Polynomial

·                    Taylor and Maclaurin series

Maclaurin Series for Some Elementary Functions

·                     Binomial theorem and Binomial series

Pages 565--576

Pages 581--584

 5

Vectors and Coordinate geometry in 3-space:

·                    Cartesian coordinates in 3 dimension

Describing Sets in the Plane - In 3-Space

·                    A little matrix algebra

Arithmetic of Matrices – Determinants – Linear Equations  

·                    Vectors and dot product 

The Cross Product as a Determinant - Vectors in 3-Space

·                    The cross product in 3 space

Pages 593--619

Pages 631--636

 6

·                    Planes and lines

Vector valued functions:

·                    Vector functions of one variable in 2 and 3 dimensions

Differentiating Combinations of Vectors

Functions of several variables :

·                    Functions of several variables

Graphical Representations

Pages 619--624

Pages 651—658

Pages 705--713

 7

·                    Quadric Surfaces

·                     Limits and continuity

·                    Partial derivatives

·                    Tangent planes and normal lines

·                    Higher order derivatives

·                    The Chain Rule

Pages 628--631

Pages 713--718

8

·                    Divergence

·                    Linear approximations, differentiability

A Mean-Value Theorem

Pages 718--732

Pages 743--746

9

·                    Chain Rule

·                    Gradient

Geometric properties of the gradient vector

·                    Directional derivatives

Using the gradient to find directional derivatives

·                    Implicit differentiation

Implicit Functions – Systems of Equations  - Jacobian Determinant

Pages 732--743

Pages 751--774

10

Applications of  Differentiation:

·                    Local extreme values

Necessary and Sufficient conditions for extreme values – Classifying Critical Points

·                    Absolute extreme on restricted domains (Lagrange Multipliers)

Pages 783--803

11

Multiple integration:

·                    Riemann sums

·                    Double integrals

The double integral over a rectangle  - Double integrals over more general domains – Properties of the Double integral

·                    Iteration of double integrals in Cartesian coordinates

·                    Mean Value Theorem

A Mean Value Theorem for Double Integrals

Pages 836--856

12

·                    Polar coordinates and polar curves

·                    Double integrals in Polar coordinates

Area of a polar region

·                    General change of variables in double integrals

Pages 505--510

Pages 856--867

13

 Line integrals of real valued functions:

·                    Curves and parametrizations

·                    Arclength

Piecewise Smooth Curves

·                    Evaluating line integrals of real valued functions

·                    Conservative fields

Necessary conditions for a conservative plane vector field

Pages 666--671

Pages 910—916

Pages 900--903

14

·                    Line integral of vector fields

Independence of Path

·                    Green’s theorem in the plane

Pages 916--924

Pages 963--966