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June 18th

June 18th

# College Calculus 3

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.
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