MCCCD Official Course Competencies:

MAT236  19966-20064

Technical Calculus III

1.

Evaluate the convergence or divergence of an infinite series of constants. (I)

2.

Compute a power series representation of a function and calculate its interval of convergence. (II)

3.

Analyze the existence and character of the solution(s) of a system of linear equations using a row-echelon form of the augmented matrix or coefficient matrix determinant. (III, IV)

4.

Display knowledge of matrix and determinant operations and properties. (III, IV)

5.

Determine a basis for a vector space. (V)

6.

Determine whether a set of vectors is a vector space and whether a subset of vectors is a subspace. (VI)

MCCCD Official Course Outline:

MAT236  19966-20064

Technical Calculus III

I. Infinite Series

A. Definition

1. Geometric series

2. Divergence test

B. Integral test

C. Comparison tests

1. Standard

2. Limit form

D. Absolute convergence

1. Definition

2. Alternate series test

II. Power Series

A. Interval of convergence

B. Taylor series

C. Differentiation and integration of power series

III. Linear Equations and Matrices

A. Linear systems

1. Methods of elimination

2. Dependent and inconsistent systems

B. Matrices

1. Operations on matrices

2. Properties of matrix operations

3. Inverse of a matrix

4. Solutions of equations using matrices

IV. Determinants

A. Definitions and properties

B. Cofactor expansion

V. Vectors and Vector Spaces

A. Vectors in R2 and R3

1. Vector operations

2. Orthogonal and unit vectors

B. Vector spaces and subspaces

1. Properties of vector spaces

2. Definition of a subspace

3. Span of a set of vectors

C. Linear independence

D. Basis and dimension

1. Definition of a basis

2. Finite and infinite-dimensional vector spaces

E. Rank of a matrix

1. Row rank and column rank

2. Consistency of non homogeneous linear systems