# Multivariable Calculus

Course Description:

An introduction to functions of several variables , partial differentiation,
multiple

integrals, vector analysis, matrix algebra, determinants, solutions of linear
systems

of equations , and vector spaces (optional).

Prerequisites:

Math 173-174 (Calculus with Analytic Geometry I-II) or equivalent .

Course Objectives:

The first part of this course is designed to introduce the student to the
concepts of

functions of several variables, partial derivatives and multiple integrals , and
vector

analysis. The remainder of this course is an introduction to linear algebra .

Instructional Materials:

Textbook: Calculus, seventh edition, by Larson, Hostetler, and Edwards:

Houghton Mifflin Co. Boston.

Elementary Linear Algebra, fifth edition, by Larson, Edwards, and

Falvo: Houghton Mifflin Co. Boston.

Scientific Calculator : Required

Graphing Calculator : Preferred

Disability Services Policy:

Reasonable accommodations will be made for students with disabilities

provided those students have registered with the Office of Disability

Services. Present your teacher with the documentation.

Course Content:

Chapter 11 : Vector- Valued Functions

11.1 Vector-Valued Functions

11.2 Differentiaton and Intergration of Vector-Valued Functions

11.3 Velocity and Acceleration

11.4 Tangent Vectors and Normal Vectors

11.5 Arc Length and Curvature

Chapter 12 : Functions of Several Variables

12.5 Chain Rules for Functions of Several Variables

12.6 Directional Derivatives and Gradients

12.7 Tangent Planes and Normal Lines

12.8 Extrema of Functions of Two Variables

12.9 Applications of Extrema of Functions of Two Variables

12.10 Lagrange Multipliers

Chapter 13 : Multiple Integration

13.1 Iterated Integrals and Area in the Plane

13.2 Double Integrals and Volume

13.3 Change of Variables : Polar Coordinates

13.5 Surface Area

13.6 Triple Integrals and Applications

13.7 Triple Integrals in Cylindrical and Spherical Coordinates

Chapter 14 : Vector Analysis

14.1 Vector Fields

14.2 Line Integrals

14.3 Conservative Vector Fields and Independence of Path

14.4 Green’s Theorem

14.6 Surface Integrals

14.7 Divergence Theorem

14.8 Stokes’ Theorem

Course Content : Linear Algebra

Chapter 1 : Systems of Linear Equations

1.2 Gaussian Elimination and Gauss -Jordan Elimination

1.3 Applications of Systems of Linear Equations

Chapter 2: Matrices

2.1 Operations with Matrices

2.2 Properties of Matrix Operations

2.3 The Inverse of a Matrix

2.5 Applications of Matrix Operations

Chapter 3: Determinants

3.1 The Determinant of a Matrix

3.2 Evaluation of a Determinant Using Elementary Operations

3.3 Properties of Determinants

3.4 Introduction to Eigenvalues

3.5 Applications of Determinants

Chapter 4: Vector Spaces

4.1 Vectors in R^{n}

4.2 Vector Spaces

4.3 Subspaces of Vector Spaces

4.4 Spanning Sets and Linear Independence

4.5 Basis and Dimension

Assignments and Test Schedule

For Calculus by Larson, Hostetler, & Edwards

SECTION | PAGE | ASSIGNMENT |

11.1 11.2 11.3 11.4 11.5 |
791 800 808 817 829 |
3,11,13,15,17,19,27,35,41,47,51,59,65,71,77 3,9,15,17,19,25,33,39,45,49,51,55 3,15,21,41,45 3,7,15,25,27,41 1,9,17,23,29,35,39,45 |

12.5 12.6 12.7 12.8 12.9 12.10 Test 1 |
882 893 902 911 917 927 |
1,9,17,21,29,31,37,43 5,9,13,17,31,35,41,45,57 1,3,513,15,21,27,29,47,55 1,5,7,9,21,25,49,53,59 1,7,9 5,19,25 |

13.1 13.2 13.3 13.5 13.6 13.7 Test 2 |
942 951 960 976 986 993 |
7,15,21,25,29,33,55,61,67 1,9,15,25,37,43 9,13,19,21,25,31,39 3,11,21 1,5,9,17,21,25 1,3,11,15 |

14.1 14.2 14.3 14.4 14.6 14.7 14.8 Test 3 |
1017 1029 1039 1048 1071 1079 1086 |
3,9,23,37,43,51,55,59,61 1,9,13,23,29,41,53,57 1,3,9,11,15,17,21,29,35 3,9,15,21,27 1,7,19,25 3,9,17 9,11,17 |

For Linear Algebra by Larson , Hostetler, & Falvo | ||

1.2 1.3 |
25 39 |
1-31 odd 25, 27 |

2.1 2.2 2.3 2.5 |
55 69 83 111 |
3, 9, 13, 15, 17 23, 31 1, 5, 9, 11, 25, 27 15,27,31 |

3.1 3.2 3.3 3.4 3.5 |
127 137 146 152 164 |
3, 7, 11, 19, 21, 41, 43, 45 17, 21, 25 23,25 31, 33 1,3,5,9,11 1,5,17,27 |

4.1 4.2 4.3 4.4 4.5 Test 4 |
183 191 200 213 224 |
1-33 every other odd 1-21 odd 1,3,7,11 1,5,11,13,17,19,21 5,7,23,25,31,35,43,49 |

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