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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 173174 (Calculus with Analytic Geometry III) 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 VectorValued Functions
11.2 Differentiaton and Intergration of VectorValued 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 
131 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 
133 every other odd 121 odd 1,3,7,11 1,5,11,13,17,19,21 5,7,23,25,31,35,43,49 
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