## Weekly outline

### January 23 - January 29

## Review

This week we will be reviewing the definition of integral, the fundamental theorem of Calculus, and the basic integration techniques from last semester: change of variables, basic trigonometric integrals, integration by parts, and partial fractions.

### Lecture notes

### Other Links

### Assignments

### January 30 - February 5

### Introduction to series

General series, convergent series, tests for convergenve and divergence, geometric series, and the formula for the sum of a convergent geometric series.

### February 6 - February 12

### Introduction to series (part 2)

Conditional convergence of series, power series, algebra of power series, radius of convergence, power series as functions.

### February 13 - February 19

### Introduction to linear algebra

Linear algebra is an important part of Calculus, hidden under several layers of limits and analysis. The goal of most of Calculus is to reduce problems about continuous functions to problems about linear functions.

### Assignments

### February 20 - February 26

### Introduction to Linear algebra II

This week we will be looking at inner product spaces and orthogonality in arbitrary vector spaces. We will see how to project a vector orthogonally onto a subspace of an inner product space, and how to find bases for vector spaces which consist of prirwise orthogonal vectors. We will also investigate the notion of distance in inner product spaces, and the distance between a vector and a set of vectors.

### February 27 - March 4

### Introduction to Linear Algebra III

We now apply what we saw of linear algebra to the study of vector spaces of functions of one variable. We will see that functions of one variable form an inner-product space under several definitions of inner product, and define what it means for functions to be orthogonal. we will be paying special attention to the spaces of

*n*times continuously differentiable functions and of smooth functions.

### March 5 - March 11

### Applications of the integral

We apply integration to the computation of lengths, volumes and surface areas of special functions. We will be discussing the arc-length formula for parametric functions in the plane, and the computation of volumes and surface areas of solids of revolution.

### Spring Break!!!

### Spring Break!!!

### March 26 - April 1

### Applications of the integral II

We continue the applications of the definits integral to Geometry. We begin by computing the surface area of solids of revolution, and solids of revolution defined by parametric curves. We then apply the definite integral to compute physical quantities, such as the center of mass and the moments of inertia in cases where a single-variable integral is enough.

### April 2 - April 8

### Polar Coordinates

### April 9 - April 15

### April 16 - April 22

### April 23 - April 29

### April 30 - May 6