Course Number: MTH 241
Course Title: College Calculus 3
Credit Hours: 4.0
Textbook: Stewart, Calculus: Multivariable (Early Transcendentals, 6th
ed. / UB custom 6th
ed.), Brooks/Cole
Description: Geometry and vectors of n-dimensional space; Green’s
Theorem, Stokes’ Theorem, multidimensional differentiation and integ ration ;
application to two and three-dimensional space.
Prerequisite: MTH 142 with recommended grade of “C” or higher
Syllabus: MTH 241 covers Chapters 12 through Chapter 16 of the text.
| Week |
Section |
Topics |
| 1 |
12.1 – 12.4 |
Three-Dimensional Coordinate Systems , Vectors,
Dot Product , Cross Product |
| 2 |
12.5 – 12.7 |
Equations of Lines and Planes , Cylinders and
Quadratic Surfaces , Cylindrical and Spherical Coordinates |
| 3 |
13.1 – 13.3 |
Vector Functions and Space Curves , Derivatives
and Integrals of Vector Functions, Arc Length and Curvature |
| 4 |
13.4, 14.1 |
Motion in Space: Velocity and Acceleration; Functions of Several
Variables |
| 5 |
14.2 – 14.4 |
Limits and Continuity, Partial Derivatives,
Tangent Planes and Linear Approximation |
| 6 |
14.5 – 14.7 |
Chain Rule, Directional Derivatives and Gradient
Vector, Maximum and Minimum Values |
| 7 |
14,8,
15.1-15.2 |
Lagrange Multiplier, Double Integrals over
Rectangles, Iterated Integrals |
| 8 |
15.3 – 15.5 |
Double Integrals over General Regions, Double
Integrals in Polar Coordinates, Applications of Double Integrals |
| 9 |
15.6 – 15.8 |
Surface Area, Triple Integrals, Triple Integrals
in Cylindrical and Spherical Coordinates
Option: Section 15.9 Change of Variables in Multiple Integrals |
| 10 |
16.1 – 16.4 |
Vector Fields, Line Integrals, Fundamental
Theorem for Line Integrals, Green’s Theorem |
| 11 |
16.5 – 16.7 |
Curl and Divergence, Parametric Surfaces and
their Area, Surface Integrals |
| 12 |
16.8 – 16.9 |
Stokes’ Theorem, Divergence Theorem |
Course Number: MTH 309
Course Title: Introduction to Linear Algebra
Credit Hours: 4.0
Textbook(s): David Lay, Linear Algebra and its Applications, 3rd
ed., Addison Wesley
(UB custom edition is identical to standard editions.)
Description: Linear equations, linear transformations, matrices,
determinants, vector spaces, eigenvalues and eigenvectors, inner products,
orthogonality, quadratic forms.
Prerequisite: MTH 142 (Calculus 2) or MTH 192 (Discrete Math 2)
Syllabus: Chapters 1 through 7 as specified be low .
| Section |
Title |
Topics |
| 1.1 – 1.8 |
Linear Equations in
Linear Algebra |
Systems of linear equations. Row reduction and
echelon forms. Vector equations. Ax-b. Solution sets of linear systems.
Applications of linear systems. Linear independence. Linear
transformations. |
2.1 – 2.3
2.8 – 2.9 |
Matrix Algebra |
Matrix operations . Inverse of a matrix. Characterizations of invertible
matrices. Subspaces of Rn. Dimension and rank. |
| 3.1 – 3.2 |
Determinants |
Introduction to determinants. Properties of
determinants . |
| 4.1 – 4.6 |
Vector Spaces |
Vector spaces and subspaces. Null spaces, column
spaces, and linear transformations. Linearly independent sets, bases.
Coordinate systems. Dimension of a vector space. Rank. |
| 5.1 – 5.5 |
Eigenvalues and
Eigenvectors |
Eigenvectors and eigenvalues. Characteristic
equation. Diagonalization. Eigenvectors and linear transformations.
Complex eigenvalues . |
| 6.1 – 6.5 |
Orthogonality
and Least Squares |
Inner product, length, orthogonality. Orthogonal
sets. Orthogonal projections. Gram-Schmidt process. Least squares
problem . |
| 7.1 – 7.2 |
Symmetric Matrices
and Quadratic Forms |
Diagonalization of symmetric matrices. Quadric
forms. |
