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 Rⁿ
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